Transcript
Landmark experiments ... in physics
PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Fri, 01 Jun 2012 23:39:58 UTC
Contents Articles Astronomy
1
BOOMERanG experiment
1
Cosmic Background Explorer
3
Wilkinson Microwave Anisotropy Probe
Electromagnetism & Special Relativity
10 23
Fizeau experiment
23
Fizeau–Foucault apparatus
27
Hafele–Keating experiment
28
Hammar experiment
32
Ives–Stilwell experiment
33
Lunar Laser Ranging experiment
36
Kennedy–Thorndike experiment
40
Michelson–Gale–Pearson experiment
41
Michelson–Morley experiment
42
Oil drop experiment
56
Oxford Electric Bell
61
Rømer's determination of the speed of light
62
Sagnac effect
71
Terrella
77
Trouton–Noble experiment
79
Trouton–Rankine experiment
86
Gravity & General Relativity
88
Cavendish experiment
88
De Sitter double star experiment
94
Gravity Probe A
95
Gravity Probe B
96
Pound–Rebka experiment
102
Schiehallion experiment
104
Mechanics
112
Atwood machine
112
Barton's Pendulums
115
Bedford Level experiment
116
Beverly Clock
118
Galileo's Leaning Tower of Pisa experiment
120
Heron's fountain
121
Magdeburg hemispheres
123
Rubens' tube
125
Pitch drop experiment
128
Spouting can
130
Particle & Nuclear Physics
131
Bevatron
131
Chicago Pile-1
134
Cowan–Reines neutrino experiment
137
Geiger–Marsden experiment
139
Homestake experiment
142
Large Hadron Collider
143
Molten-Salt Reactor Experiment
157
PS210 experiment
164
Trinity
165
Quantum mechanics
179
Afshar experiment
179
Davisson–Germer experiment
184
Delayed choice quantum eraser
186
Double-slit experiment
193
Elitzur–Vaidman bomb tester
202
Eötvös experiment
205
Franck–Hertz experiment
207
Quantum eraser experiment
209
Stern–Gerlach experiment
212
References Article Sources and Contributors
217
Image Sources, Licenses and Contributors
222
Article Licenses License
226
1
Astronomy BOOMERanG experiment The BOOMERanG experiment (Balloon Observations Of Millimetric Extragalactic Radiation and Geophysics) measured the cosmic microwave background radiation of a part of the sky during three sub-orbital (high altitude) balloon flights. It was the first experiment to make large, high fidelity images of the CMB temperature anisotropies. By using a telescope which flew at over 42,000 meters high, it was possible to reduce the atmospheric absorption of microwaves to a minimum. This allowed massive cost reduction compared to a satellite probe, though only a small part of the sky could be scanned.
The Telescope being readied for launch
The first was a test flight over North America in 1997. In the two subsequent flights in 1998 and 2003 the balloon was launched from McMurdo Station in the Antarctic. It was carried by the Polar vortex winds in a circle around the South Pole, returning after two weeks. From this phenomenon the telescope took its name. The BOOMERanG team was led by Andrew E. Lange of Caltech and Paolo de Bernardis of the University of Rome La Sapienza.[1]
Instrumentation The experiment uses bolometers[2] for radiation detection. These bolometers are kept at a temperature of 0.27 kelvin. At this temperature the material has a very low heat capacity according to the Debye law, thus incoming microwave light will cause a strong temperature change, proportional to the intensity of the incoming waves, which is measured with sensitive thermometers. A 1.2 mirror[3] focuses the microwaves onto the focal plane which consist of 16 horns. These horns, operating at 145 GHz, 245 GHz and 345 GHz, are arranged into 8 pixel. So only a tiny fraction of the sky can be seen concurrently so the telescope has to rotate to scan the whole field of view.
BOOMERanG experiment
2
Results Together with experiments like Saskatoon, TOCO, MAXIMA, and others, the BOOMERanG data from 1997 and 1998 determined the angular diameter distance to the surface of last scattering with high precision. When combined with complementary data regarding the value of Hubble's constant, the Boomerang data determined the geometry of the Universe to be flat (see [4] and [5]), supporting the supernova evidence for the existence of dark energy. The 2003 flight of Boomerang resulted in extremely high signal-to-noise ratio maps of the CMB temperature anisotropy, and a measurement of the polarization of the CMB. CMB Anisotropy measured by BOOMERanG
References [1] Glanz, James (27 April 2000). "Clearest Picture of Infant Universe Sees It All and Questions It, Too" (http:/ / www. nytimes. com/ 2000/ 04/ 27/ us/ clearest-picture-of-infant-universe-sees-it-all-and-questions-it-too. html?pagewanted=1). The New York Times. . Retrieved 2010-02-23. [2] "Instrumentation of the BOOMERranG experiment" (http:/ / cmb. phys. cwru. edu/ kisner/ b2kweblog/ hardware. html). Ted's Weblog. 2002-01-29. . Retrieved 2007-04-06. [3] "Boomerang Instrument" (http:/ / www. astro. caltech. edu/ ~lgg/ boomerang_instr. htm). Caltech Observational Cosmology Group. 2003-06-01. . Retrieved 2007-04-06. [4] http:/ / xxx. arxiv. org/ abs/ astro-ph/ 9911445 [5] http:/ / xxx. arxiv. org/ abs/ astro-ph/ 0004404
External links • • • • •
Main (Caltech) Site (http://boom.caltech.edu) Data site (http://cmb.phys.cwru.edu/boomerang/) report on the 1998 flight (http://stratocat.com.ar/fichas-e/1998/MCM-19981229.htm) report on the 2003 flight (http://stratocat.com.ar/fichas-e/2003/MCM-20030106.htm) Polarization Sensitive Bolometric Detector (http://it.arxiv.org/abs/astro-ph/0209132v1)
Cosmic Background Explorer
3
Cosmic Background Explorer Cosmic Background Explorer (COBE)
General information NSSDC ID
1989-089A
Organization
NASA
[1]
Major contractors Goddard Space Flight Center Launch date
November 18, 1989
Launched from
Vandenberg Air Force Base
Launch vehicle
Delta rocket
Mission length
≈4 years
Mass
2,270 kg
Orbit height
900.2 km
Orbit period
103 minutes
Location
Earth orbit Instruments
DIRBE
Diffuse Infrared Background Experiment
FIRAS
Far-InfraRed Absolute Spectrophotometer
DMR
Differential Microwave Radiometer
Website
LAMBDA - Cosmic Background Explorer
[2]
The COsmic Background Explorer (COBE), also referred to as Explorer 66, was a satellite dedicated to cosmology. Its goals were to investigate the cosmic microwave background radiation (CMB) of the universe and provide measurements that would help shape our understanding of the cosmos. This work provided evidence that supported the Big Bang theory of the universe: that the CMB was a near-perfect black-body spectrum and that it had very faint anisotropies. Two of COBE's principal investigators, George Smoot and John Mather, received the Nobel Prize in Physics in 2006 for their work on the project. According to the Nobel Prize committee, "the COBE-project can also be regarded as the starting point for cosmology as a precision science".[3]
Cosmic Background Explorer
4
History In 1974, NASA issued an Announcement of Opportunity for astronomical missions that would use a small- or medium-sized Explorer spacecraft. Out of the 121 proposals received, three dealt with studying the cosmological background radiation. Though these proposals lost out to the Infrared Astronomical Satellite (IRAS), their strength made NASA further explore the idea. In 1976, NASA formed a committee of members from each of 1974's three proposal teams to put together their ideas for such a satellite. A year later, this committee suggested a polar-orbiting satellite called COBE to be launched by either a Delta rocket or the Space Shuttle. It would contain the following instruments:[4]
Instruments Instrument
Acronym
Description
Principal Investigator
Differential Microwave Radiometer
DMR
a microwave instrument that would map variations (or anisotropies) in the CMB
George Smoot
Far-InfraRed Absolute Spectrophotometer
FIRAS
a spectrophotometer used to measure the spectrum of the CMB
John Mather
Diffuse InfraRed Background Experiment
DIRBE
a multiwavelength infrared detector used to map dust emission
Mike Hauser
NASA accepted the proposal provided that the costs be kept under $30 million, excluding launcher and data analysis. Due to cost overruns in the Explorer program due to IRAS, work on constructing the satellite at Goddard Space Flight Center (GSFC) did not begin until 1981. To save costs, the infrared detectors and liquid helium dewar on COBE would be similar to those used on IRAS. COBE was originally planned to be launched on a Space Shuttle mission STS-82-B in 1988 from Vandenberg Air Force Base, but the Challenger explosion delayed this plan when the Shuttles were grounded. NASA kept COBE's engineers from going to other space agencies to launch COBE, but eventually, a redesigned COBE was placed into sun-synchronous orbit on November 18, 1989 aboard a Delta rocket. A team of American scientists announced, on Launch of the COBE spacecraft November 18, 1989. April 23, 1992, that they had found the primordial "seeds" (CMBE anisotropy) in data from COBE. The announcement was reported worldwide as a fundamental scientific discovery and ran on the front page of the New York Times. The Nobel Prize in Physics for 2006 was jointly awarded to John C. Mather, NASA Goddard Space Flight Center, and George F. Smoot, University of California, Berkeley, "for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation."
Cosmic Background Explorer
5
Spacecraft COBE was an Explorer class satellite, with technology borrowed heavily from IRAS, but with some unique characteristics. The need to control and measure all the sources of systematic errors required a rigorous and integrated design. COBE would have to operate for a minimum of 6 months, and constrain the amount of radio interference from the ground, COBE and other satellites as well as radiative interference from the Earth, Sun and Moon.[5] The instruments required temperature stability and to maintain gain, and a high level of cleanliness to reduce entry of stray light and thermal emission from particulates. The need to control systematic error in the measurement of the CMB anisotropy and measuring the zodiacal cloud at different elongation angles for subsequent modeling required that the satellite rotate at a 0.8 rpm spin rate.[5] The spin axis is also tilted back from the orbital velocity vector as a precaution against possible deposits of residual atmospheric gas on the optics as well against the infrared glow that would result from fast neutral particles hitting its surfaces at extremely high speed. In order to meet the twin demands of slow rotation and three-axis attitude control, a sophisticated pair of yaw angular momentum wheels were employed with their axis oriented along the spin axis .[5] These wheels were used to carry an angular momentum opposite that of the entire spacecraft in order to create a zero net angular momentum system. The orbit would prove to be determined based on the specifics of the spacecraft’s mission. The overriding considerations were the need for full sky coverage, the need to eliminate stray radiation from the instruments and the need to maintain thermal stability of the dewar and the instruments.[5] A circular Sun-synchronous orbit satisfied all these requirements. A 900 km altitude orbit with a 99° inclination was chosen as it fit within the capabilities of either a Shuttle (with an auxiliary propulsion on COBE) or a Delta rocket. This altitude was a good compromise between Earth's radiation and the charged particle in Earth's radiation belts at higher altitudes. An ascending node at 6 p.m. was chosen to allow COBE to follow the boundary between sunlight and darkness on Earth throughout the year. The orbit combined with the spin axis made it possible to keep the Earth and the Sun continually below the plane of the shield, allowing a full sky scan every six months. The last two important parts pertaining to the COBE mission were the dewar and Sun-Earth shield. The dewar was a 650 liter superfluid helium cryostat designed to keep the FIRAS and DIRBE instruments cooled during the duration of the mission. It was based on the same design as one used on IRAS and was able to vent helium along the spin axis near the communication arrays. The conical Sun-Earth shield protected the instruments from direct solar and Earth based radiation as well as radio interference from Earth and the COBE's transmitting antenna. Its multilayer insulating blankets provided thermal isolation for the dewar.[5]
Cosmic Background Explorer
6
Scientific findings The science mission was conducted by the three instruments detailed previously: DIRBE, FIRAS and the DMR. The instruments overlapped in wavelength coverage, providing consistency check on measurements in the regions of spectral overlap and assistance in discriminating signals from our galaxy, solar system and CMB.[5] COBE's instruments would fulfill each of their objectives as well as making observations that would have implications outside of COBE’s initial scope.
The famous map of the CMB anisotropy formed from data taken by the COBE spacecraft.
Black-body curve of CMB
Data from COBE showed a perfect fit between the black body curve predicted by big bang theory and that observed in the microwave background.
During the long gestation period of COBE, there were two significant astronomical developments. First, in 1981, two teams of astronomers, one led by David Wilkinson of Princeton and the other by Francesco Melchiorri of the University of Florence, simultaneously announced that they detected a quadrupole distribution of CMB using balloon-borne instruments. This finding would have been the detection of the black-body distribution of CMB that FIRAS on COBE was to measure. In particular, the Florence group claimed a detection of intermediate angular scale anisotropies at the level 100 microkelvins [6] in agreement with later measurements made by the BOOMERanG experiment. However, a number of other experiments attempted to duplicate their results and were unable to do so.[4]
Second, in 1987 a Japanese-American team led by Andrew Lange and Paul Richards of UC Berkeley and Toshio Matsumoto of Nagoya University made an announcement that CMB was not that of a true black body.[7] In a sounding rocket experiment, they detected an excess brightness at 0.5 and 0.7 mm wavelengths. With these developments serving as a backdrop to COBE’s mission, scientists eagerly awaited results from FIRAS. The results of FIRAS were startling in that they showed a perfect fit of the CMB and the theoretical curve for a black body at a temperature of 2.7 K, thus proving the Berkeley-Nagoya results erroneous. FIRAS measurements were made by measuring the spectral difference between a 7° patch of the sky against an internal black body. The interferometer in FIRAS covered between 2 and 95 cm−1 in two bands separated at 20 cm−1. There are two scan lengths (short and long) and two scan speeds (fast and slow) for a total of four different scan modes. The data were collected over a ten month period.[8]
Cosmic Background Explorer
7
Intrinsic anisotropy of CMB The DMR was able to spend four years mapping the detectable anisotropy of cosmic background radiation as it was the only instrument not dependent on the dewar’s supply of helium to keep it cooled. This operation was able to create full sky maps of the CMB by subtracting out galactic emissions and dipole at various frequencies. The cosmic microwave background fluctuations are extremely faint, only one part in 100,000 compared to the 2.73 kelvin average temperature of the radiation field. The cosmic microwave background radiation is a remnant of the Big Bang and the fluctuations are the imprint of density contrast in the early universe. The density ripples are believed to have produced structure formation as observed in the universe today: clusters of galaxies and vast regions devoid of galaxies (NASA).
Detecting early galaxies DIRBE also detected 10 new far-IR emitting galaxies in the region not surveyed by IRAS as well as nine other candidates in the weak far-IR that may be spiral galaxies.
Data obtained at each of the three DMR frequencies—31.5, 53, and 90 GHz—following dipole subtraction.
Galaxies that were detected at the 140 and 240 μm were also able to provide information on very cold dust (VCD). At these wavelengths, the mass and temperature of VCD can be derived. When these data were joined with 60 and 100 μm data taken from IRAS, it was found that the far-infrared luminosity arises from cold (≈17–22 K) dust associated with diffuse HI cirrus clouds, 15-30% from cold (≈19 K) dust associated with molecular gas, and less than 10% from warm (≈29 K) dust in the extended low-density HII regions.[9]
DIRBE On top of the findings DIRBE had on galaxies, it also made two other significant contributions to science.[9] The DIRBE instrument was able to conduct studies on interplanetary dust (IPD) and determine if its origin was from asteroid or cometary particles. The DIRBE data collected at 12, 25, 50 and 100 μm were able to conclude that grains of asteroidal origin populate the IPD bands and the smooth IPD cloud.[10] The second contribution DIRBE made was a model of the Galactic disk as seen edge-on from our position. According to the model, if our Sun is 8.6 kpc from the Galactic center, then the sun is 15.6 pc above the midplane of the disk, which has a radial and vertical scale lengths of 2.64 and 0.333 kpc, respectively, and is warped in a way consistent with the HI layer. There is also no indication of a thick disk.[11]
Model of the Galactic disk as seen edge-on from our position
To create this model, the IPD had to be subtracted out of the DIRBE data. It was found that this cloud, which as seen from Earth is Zodiacal light, was not centered on the Sun, as previously thought, but on a place in space a few million kilometers away. This is due to the gravitation influence of Saturn and Jupiter.[4]
Cosmic Background Explorer
Cosmological implications In addition to the science results detailed in the last section, there are numerous cosmological questions left unanswered by COBE’s results. A direct measurement of the extragalactic background light (EBL) can also provide important constraints on the integrated cosmological history of star formation, metal and dust production, and the conversion of starlight into infrared emissions by dust.[12] By looking at the results from DIRBE and FIRAS in the 140 to 5000 μm we can detect that the integrated EBL intensity is ≈16 nW/(m2·sr). This is consistent with the energy released during nucleosynthesis and constitutes about 20–50% of the total energy released in the formation of helium and metals throughout the history of the universe. Attributed only to nuclear sources, this intensity implies that more than 5–15% of the baryonic mass density implied by big bang nucleosynthesis analysis has been processed in stars to helium and heavier elements.[12] There were also significant implications into star formation. COBE observations provide important constraints on the cosmic star formation rate, and help us calculate the EBL spectrum for various star formation histories. Observation made by COBE require that star formation rate at redshifts of z ≈ 1.5 to be larger than that inferred from UV-optical observations by a factor of 2. This excess stellar energy must be mainly generated by massive stars in yet-undetected dust enshrouded galaxies or extremely dusty star forming regions in observed galaxies.[12] The exact star formation history cannot unambiguously be resolved by COBE and further observations must be made in the future. On June 30, 2001, NASA launched a follow-up mission to COBE led by DMR Deputy Principal Investigator Charles L. Bennett. The Wilkinson Microwave Anisotropy Probe has clarified and expanded upon COBE's accomplishments.
Notes [1] http:/ / nssdc. gsfc. nasa. gov/ nmc/ masterCatalog. do?sc=1989-089A [2] http:/ / lambda. gsfc. nasa. gov/ product/ cobe/ [3] "The Nobel Prize in Physics 2006" (http:/ / nobelprize. org/ nobel_prizes/ physics/ laureates/ 2006/ info. html) (PDF). The Royal Swedish Academy of Sciences. 2006-10-03. . Retrieved 2011-08-23. [4] Leverington, David (2000). New Cosmic Horizons: Space Astronomy from the V2 to the Hubble Space Telescope. Cambridge: Cambridge University Press. ISBN 0-521-65833-0. [5] Boggess, N.W., J.C. Mather, R. Weiss, C.L. Bennett, E.S. Cheng, E. Dwek, S. Gulkis, M.G. Hauser, M.A. Janssen, T. Kelsall, S.S. Meyer, S.H. Moseley, T.L. Murdock, R.A. Shafer, R.F. Silverberg, G.F. Smoot, D.T. Wilkinson, and E.L. Wright (1992). "The COBE Mission: Its Design and Performance Two Years after the launch". Astrophysical Journal 397 (2): 420. Bibcode 1992ApJ...397..420B. doi:10.1086/171797. [6] Melchiorri, Francesco; Melchiorri, Bianca O.; Pietranera, Luca; Melchiorri, B. O. (November 1981). "Fluctuations in the microwave background at intermediate angular scales" (http:/ / articles. adsabs. harvard. edu/ cgi-bin/ nph-iarticle_query?1981ApJ. . . 250L. . . 1M& amp;data_type=PDF_HIGH& amp;whole_paper=YES& amp;type=PRINTER& amp;filetype=. pdf). The Astrophysical Journal 250: L1. Bibcode 1981ApJ...250L...1M. doi:10.1086/183662. . Retrieved 2011-08-23. [7] Hayakawa, S., Matsumoto, T., Matsuo, H., Murakami, H., Sato, S., Lange A. E. & Richards, P. (1987). "Cosmological implication of a new measurement of the submillimeter background radiation" (http:/ / articles. adsabs. harvard. edu/ / full/ 1987PASJ. . . 39. . 941H/ 0000941. 000. html). Astronomical Society of Japan, Publications 39 (6): 941-948. Bibcode 1987PASJ...39..941H. ISSN 0004-6264. . Retrieved 17 May 2012. [8] Fixsen, D. J.; Cheng, E. S.; Cottingham, D. A.; Eplee, R. E., Jr.; Isaacman, R. B.; Mather, J. C.; Meyer, S. S.; Noerdlinger, P. D.; Shafer, R. A.; Weiss, R.; Wright, E. L.; Bennett, C. L.; Boggess, N. W.; Kelsall, T.; Moseley, S. H.; Silverberg, R. F.; Smoot, G. F.; Wilkinson, D. T. (1994). "Cosmic microwave background dipole spectrum measured by the COBE FIRAS instrument". Astrophysical Journal 420 (2): 445–449. Bibcode 1994ApJ...420..445F. doi:10.1086/173575. [9] T. J. Sodroski et al. (1994). "Large-Scale Characteristics of Interstellar Dust from COBE DIRBE Observations". The Astrophysical Journal 428 (2): 638–646. Bibcode 1994ApJ...428..638S. doi:10.1086/174274. [10] Spiesman, W.J., M.G. Hauser, T. Kelsall, C.M. Lisse, S.H. Moseley, Jr., W.T. Reach, R.F. Silverberg, S.W. Stemwedel, and J.L. Weiland (1995). "Near and far infrared observations of interplanetary dust bands from the COBE Diffuse Infrared Background Experiment". Astrophysical Journal 442 (2): 662. Bibcode 1995ApJ...442..662S. doi:10.1086/175470. [11] Freudenreich, H.T. (1996). "The shape and color of the galactic disk". Astrophysical Journal 468: 663–678. Bibcode 1996ApJ...468..663F. doi:10.1086/177724. See also Freudenreich, H.T. (1997). "The shape and color of the galactic disk: Erratum". Astrophysical Journal 485 (2): 920. Bibcode 1997ApJ...485..920F. doi:10.1086/304478. [12] Dwek, E., R. G. Arendt, M. G. Hauser, D. Fixsen, T. Kelsall, D. Leisawitz, Y. C. Pei, E. L. Wright, J. C. Mather, S. H. Moseley, N. Odegard, R. Shafer, R. F. Silverberg, and J. L. Weiland (1998). "The COBE Diffuse Infrared Background Experiment search for the cosmic
8
Cosmic Background Explorer infrared background: IV. Cosmological Implications". Astrophysical Journal 508 (1): 106–122. arXiv:astro-ph/9806129. Bibcode 1998ApJ...508..106D. doi:10.1086/306382.
References • Arny, Thomas T. (2002). Explorations: An Introduction to Astronomy (3rd ed.). Dubuque, Iowa: McGraw-Hill. ISBN 978-0-07-241593-3. • Liddle, A. R.; Lyth, D. H. (1993). "The Cold Dark Matter Density Perturbation". Physics Report—Review Section of Physics Letters 231 (1–2): 1–105. arXiv:astro-ph/9303019. Bibcode 1993PhR...231....1L. doi:10.1016/0370-1573(93)90114-S. • Odenwald, S., J. Newmark, and G. Smoot (1998). "A study of external galaxies detected by the COBE Diffuse Infrared Background Experiment". Astrophysical Journal 500 (2): 554–568. arXiv:astro-ph/9610238. Bibcode 1998ApJ...500..554O. doi:10.1086/305737.
Further reading • Mather, John C.; Boslough, John (1996). The Very First Light: The True Inside Story of the Scientific Journey Back to the Dawn of the Universe. New York: BasicBooks. ISBN 0-465-01575-1. • Smoot, George; Smoot, George; Davidson, Keay (1993). Wrinkles in Time. New York: W. Morrow. ISBN 0-688-12330-9.
External links • NASA's website on COBE (http://lambda.gsfc.nasa.gov/product/cobe/) • NASA informational video prior to COBE launch (http://anon.nasa-global.edgesuite.net/anon.nasa-global/ ccvideos/GSFC_20091117_COBE20th.asx) • COBE Mission Profile (http://solarsystem.nasa.gov/missions/profile.cfm?MCode=COBE) by NASA's Solar System Exploration (http://solarsystem.nasa.gov) • APOD picture of the COBE dipole (http://antwrp.gsfc.nasa.gov/apod/ap030209.html), showing the 600 kps motion of the Earth relative to the cosmic background radiation • Cosmic Background Explorer (http://www.scholarpedia.org/article/Cosmic_background_explorer_(COBE)) article from Scholarpedia
9
Wilkinson Microwave Anisotropy Probe
10
Wilkinson Microwave Anisotropy Probe Wilkinson Microwave Anisotropy Probe
General information [1]
NSSDC ID
2001-027A
Organization
NASA
Launch date
June 30, 2001, 19:46 UTC
Launched from
Cape Canaveral Air Force Station
Launch vehicle
Delta II 7425-10
Mission length
10 years, 11 months and 2 days elapsed
Mass
840 kg
Type of orbit
Lissajous orbit
Location
L2 Instruments
K-band 23 GHz
52.8 MOA beam
Ka-band 33 GHz 39.6 MOA beam Q-band 41 GHz
30.6 MOA beam
V-band 61 GHz
21 MOA beam
W-band 94 GHz
13.2 MOA beam
Website
http:/ / map. gsfc. nasa. gov References:
[2][3][4]
The Wilkinson Microwave Anisotropy Probe (WMAP) – also known as the Microwave Anisotropy Probe (MAP), and Explorer 80 – is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat – the Cosmic Microwave Background Radiation – across the full sky.[5][6] Headed by Professor Charles L. Bennett, Johns Hopkins University, the mission was developed in a joint partnership between the NASA Goddard Space Flight Center and Princeton University.[7] The WMAP spacecraft was launched on June 30, 2001, at 19:46:46 GDT, from Florida. The WMAP mission succeeds the COBE space mission and was the second medium-class (MIDEX) spacecraft of the Explorer program. In 2003, MAP was renamed WMAP in honor of cosmologist David Todd Wilkinson (1935–2002),[7] who had been a member of the mission's science team. WMAP's measurements played the key role in establishing the current Standard Model of Cosmology: the Lambda-CDM model. WMAP data are very well fit by a universe that is dominated by dark energy in the form of a cosmological constant. Other cosmological data are also consistent, and together tightly constrain the Model. In the Lambda-CDM model of the universe, the age of the universe is 13.75 ± 0.11 billion years. The WMAP mission's determination of the age of the universe to better than 1% precision was recognized by the Guinness Book of World Records. The current expansion rate of the universe is (see Hubble constant) of 70.5 ± 1.3 km·s−1·Mpc−1. The
Wilkinson Microwave Anisotropy Probe content of the universe presently consists of 4.56% ± 0.15% ordinary baryonic matter; 22.8% ± 1.3% Cold dark matter (CDM) that neither emits nor absorbs light; and 72.6% ± 1.5% of dark energy in the form of a cosmological constant that accelerates the expansion of the universe. Less than 1% of the current contents of the universe is in neutrinos, but WMAP's measurements have found, for the first time in 2008, that the data prefers the existence of a cosmic neutrino background[8] with an effective number of neutrino flavors of 4.4 ± 1.5, consistent with the expectation of 3.06. The contents point to a "flat" Euclidean flat geometry, with the ratio of the energy density in curvature to the critical density 0.0179 < Ωk <0.0081 (95%CL). The WMAP measurements also support the cosmic inflation paradigm in several ways, including the flatness measurement. According to Science magazine, the WMAP was the Breakthrough of the Year for 2003.[9] This mission's results papers were first and second in the "Super Hot Papers in Science Since 2003" list.[10] Of the all-time most referenced papers in physics and astronomy in the SPIRES database, only three have been published since 2000, and all three are WMAP publications. On May 27, 2010, it was announced that Bennett, Lyman A. Page, Jr., and David N. Spergel, the latter both of Princeton University, would share the 2010 Shaw Prize in astronomy for their work on WMAP.[11] As of October 2010, the WMAP spacecraft is in a graveyard orbit after 9 years of operations.[12] The Astronomy and Physics Senior Review panel at NASA Headquarters has endorsed a total of 9 years of WMAP operations, through September 2010.[4] All WMAP data are released to the public and have been subject to careful scrutiny. Recent examinations of WMAP data has uncovered systematic errors. A predictable, scan-induced quadrupole pattern of the WMAP mission is in perfect agreement with the published WMAP quadrupole. Scan-induced anisotropy is a common problem for all sweep missions and like the foreground emissions, should be removed from final maps.[13] Some of the correction techniques and analyses by critics have been duplicated by third parties and appear correct.[14] After corrections all that remains is a nearly featureless surface and hence much less information than originally published. Some aspects of the data are statistically unusual for the Standard Model of Cosmology. For example, the greatest angular-scale measurements, the quadrupole moment, is somewhat smaller than the Model would predict, but this discrepancy is not highly significant. A large cold spot and other features of the data are more statistically significant, and research continues into these.
Objectives The WMAP objective is to measure the temperature differences in the Cosmic Microwave Background (CMB) radiation. The anisotropies then are used to measure the universe's geometry, content, and evolution; and to test the Big Bang model, and the cosmic inflation theory.[2] For that, the mission is creating a full-sky map of the CMB, with a 13 arcminute resolution via multi-frequency observation. The map requires the fewest systematic errors, no correlated pixel noise, and accurate calibration, to ensure angular-scale accuracy greater than The universe's timeline, from inflation to the its resolution.[2] The map contains 3,145,728 pixels, and uses the WMAP. HEALPix scheme to pixelize the sphere.[15] The telescope also measures the CMB's E-mode polarization,[2] and foreground polarization;[8] its life is 27 months; 3 to reach the L2 position, 2 years of observation.[2]
11
Wilkinson Microwave Anisotropy Probe
12
Development The MAP mission was proposed to NASA in 1995, selected for definition study in 1996, and approved for development in 1997.[4][16] The WMAP was preceded by two missions to observe the CMB; (i) the Soviet RELIKT-1 that reported the upper-limit measurements of CMB anisotropies, and (ii) the U.S. COBE satellite that reported large-scale CMB fluctuations, and the ground-based and balloon experiments measuring the small-scale fluctuations in patches of sky: the Boomerang, the Cosmic Background Imager, and the Very Small Array. The WMAP is 45 times more sensitive, with 33 times the angular resolution of its COBE satellite predecessor.[3]
A comparison of the sensitivity of WMAP with COBE and Penzias and Wilson's telescope. Simulated data.
Spacecraft The telescope's primary reflecting mirrors are a pair of Gregorian 1.4m x 1.6m dishes (facing opposite directions), that focus the signal onto a pair of 0.9m x 1.0m secondary reflecting mirrors. They are shaped for optimal performance: a carbon fibre shell upon a Korex core, thinly-coated with aluminium and silicon oxide. The secondary reflectors transmit the signals to the corrugated feedhorns that sit on a focal plane array box beneath the primary reflectors.[2]
WMAP spacecraft diagram
The receivers are polarization-sensitive differential radiometers measuring the difference between two telescope beams. The signal is amplified with HEMT low-noise amplifiers. There are 20 feeds, 10 in each direction, from which a radiometer collects a signal; the measure is the difference in the sky signal from opposite directions. The directional separation azimuth is 180 degrees; the total angle is 141 degrees.[2] To avoid collecting Milky Way galaxy foreground signals, the WMAP uses five discrete radio frequency bands, from 23 GHz to 94 GHz.[2]
Illustration of WMAP's receivers
Wilkinson Microwave Anisotropy Probe
13
Property
K-band Ka-band Q-band V-band W-band
Central wavelength (mm) 13
9.1
7.3
4.9
3.2
Central frequency (GHz) 23
33
41
61
94
Bandwidth (GHz)
5.5
7.0
8.3
14.0
20.5
Beam size (arcminutes)
52.8
39.6
30.6
21
13.2
Number of radiometers
2
2
4
4
8
System temperature (K)
29
39
59
92
145
Sensitivity (mK s
0.8
0.8
1.0
1.2
1.6
)
|+ Properties of WMAP at different frequencies[2] The WMAP's base is a 5.0m-diameter solar panel array that keeps the instruments in shadow during CMB observations, (by keeping the craft constantly angled at 22 degrees, relative to the sun). Upon the array sit a bottom deck (supporting the warm components) and a top deck. The telescope's cold components: the focal-plane array and the mirrors, are separated from the warm components with a cylindrical, 33 cm-long thermal isolation shell atop the deck.[2] Passive thermal radiators cool the WMAP to ca. 90 degrees K; they are connected to the low-noise amplifiers. The telescope consumes 419 W of power. The available telescope heaters are emergency-survival heaters, and there is a transmitter heater, used to warm them when off. The WMAP spacecraft's temperature is monitored with platinum resistance thermometers.[2] The WMAP's calibration is effected with the CMB dipole and measurements of Jupiter; the beam patterns are measured against Jupiter. The telescope's data are relayed daily via a 2 GHz transponder providing a 667kbit/s downlink to a 70m Deep Space Network telescope. The spacecraft has two transponders, one a redundant back-up; they are minimally active – ca. 40 minutes daily – to minimize radio frequency interference. The telescope's position is maintained, in its three axes, with three reaction wheels, gyroscopes, two star trackers and sun sensors, and is steered with eight hydrazine thrusters.[2]
Launch, trajectory, and orbit The WMAP spacecraft arrived at the Kennedy Space Center on April 20, 2001. After being tested for two months, it was launched via Delta II 7425 rocket on June 30, 2001.[3][4] It began operating on its internal power five minutes before its launching, and so continued operating until the solar panel array deployed. The WMAP was activated and monitored while it cooled. On July 2, it began working, first with in-flight testing (from launching until August 17), then began constant, formal work.[3] Afterwards, it effected three Earth-Moon phase loops, measuring its sidelobes, then flew by the Moon on July 30, enroute to The WMAP's trajectory and orbit. the Sun-Earth L2 Lagrangian point, arriving there on October 1, 2001, becoming, thereby, the first CMB observation mission permanently posted there.[4]
Wilkinson Microwave Anisotropy Probe
14
WMAP launches from Kennedy Space Center, June 30, 2001.
The spacecraft's location at Lagrange 2, (1.5 million kilometers from Earth) minimizes the amount of contaminating solar, terrestrial, and lunar emissions registered, and thermally stabilizes it. To view the entire sky, without looking to the sun, the WMAP traces a path around L2 in a Lissajous orbit ca. 1.0 degree to 10 degrees,[2] with a 6-month period.[4] The telescope rotates once every 2 minutes, 9 seconds" (0.464 rpm) and precesses at the rate of 1 revolution per hour.[2] WMAP measures the entire sky every six months, and completed its first, full-sky observation in April 2002.[16]
WMAP's orbit and sky scan strategy
Foreground radiation subtraction The WMAP observes in five frequencies, permitting the measurement and subtraction of foreground contamination (from the Milky Way and extra-galactic sources) of the CMB. The main emission mechanisms are synchrotron radiation and free-free emission (dominating the lower frequencies), and astrophysical dust emissions (dominating the higher frequencies). The spectral properties of these emissions contribute different amounts to the five frequencies, thus permitting their identification and subtraction.[2] Foreground contamination is removed in several ways. First, subtract extant emission maps from the WMAP's measurements; second, use the components' known, spectral values to identify them; third, simultaneously fit the position and spectra data of the foreground emission, using extra data sets. Foreground contamination also is reduced by using only the full-sky map portions with the least foreground contamination, whilst masking the remaining map portions.[2]
Wilkinson Microwave Anisotropy Probe
15
The five-year models of foreground emission, at different frequencies. Red = Synchrotron; Green = free-free; Blue = thermal dust.
23 GHz
33 GHz
41 GHz
61 GHz
94 GHz
Measurements and discoveries One-year data release On February 11, 2003, based upon one year's worth of WMAP data, NASA published the latest calculated age, composition, and image of the universe to date, that "contains such stunning detail, that it may be one of the most important scientific results of recent years"; the data surpass previous CMB measurements.[7] Based upon the Lambda-CDM model, the WMAP team produced The first-year map of the CMB. cosmological parameters from the WMAP's first-year results. Three sets are given below; the first and second sets are WMAP data; the difference is the addition of spectral indices, predictions of some inflationary models. The third data set combines the WMAP constraints with those from other CMB experiments (ACBAR and CBI), and constraints from the 2dF Galaxy Redshift Survey and Lyman alpha forest measurements. Note that there are degenerations among the parameters, the most significant is between and ; the errors given are at 68% confidence.[17] Parameter
Symbol
Best fit (WMAP only) Best fit (WMAP, extra parameter) Best fit (all data)
Hubble's constant ( km⁄Mpc·s )
72 ± 5
70 ± 5
Baryonic content
0.024 ± 0.001
0.023 ± 0.002
Matter content
0.14 ± 0.02
0.14 ± 0.02
Optical depth to reionization Amplitude
0.166 A
0.9 ± 0.1
71 0.0224 ± 0.0009 0.135
0.20 ± 0.07
0.17 ± 0.06
0.92 ± 0.12
0.83
0.93
0.93 ± 0.03
Scalar spectral index
0.99 ± 0.04
Running of spectral index
—
−0.047 ± 0.04
Fluctuation amplitude at 8h−1 Mpc
0.9 ± 0.1
—
0.84 ± 0.04
Age of the universe (Ga)
13.4 ± 0.3
–
13.7 ± 0.2
Total density of the universe
–
–
1.02 ± 0.02
−0.031
|+ Best-fit cosmological parameters from WMAP one-year results[17] Using the best-fit data and theoretical models, the WMAP team determined the times of important universal events, including the redshift of reionization, 17 ± 4; the redshift of decoupling, 1089 ± 1 (and the universe's age at decoupling, 379 ka); and the redshift of matter/radiation equality, 3233 . They determined the thickness of the surface of last scattering to be 195 ± 2 in redshift, or 118 −7
−1
2.5 ± 0.1 × 10 cm , and the ratio of baryons to photons, 6.1 reionization excluded warm dark matter.[17]
ka. They determined the current density of baryons, × 10−10. The WMAP's detection of an early
Wilkinson Microwave Anisotropy Probe
16
The team also examined Milky Way emissions at the WMAP frequencies, producing a 208-point source catalogue. Also, they observed the Sunyaev-Zel'dovich effect at 2.5 σ the strongest source is the Coma cluster.[15]
Three-year data release The three-year WMAP data were released on March 17, 2006. The data included temperature and polarization measurements of the CMB, which provided further confirmation of the standard flat Lambda-CDM model and new evidence in support of inflation. The 3-year WMAP data alone shows that the universe must have dark matter. Results were computed both only using WMAP data, and also with a mix of parameter constraints from other instruments, including other CMB experiments (ACBAR, CBI and BOOMERANG), SDSS, the 2dF Galaxy Redshift Survey, the Supernova Legacy Survey and constraints on the Hubble constant from the Hubble Space Telescope.[18] Parameter
A map of the polarization from the 3rd year results
Symbol Best fit (WMAP only)
Hubble's constant ( km⁄Mpc·s )
73.2
Baryonic content
0.0229 ± 0.00073
Matter content
0.1277
Optical depth to reionization [a]
0.089 ± 0.030
Scalar spectral index
0.958 ± 0.016
Fluctuation amplitude at 8h−1 Mpc
0.761
Age of the universe (Ga)
13.73
Tensor-to-scalar ratio [b]
r
< 0.65
|+ Best-fit cosmological parameters from WMAP three-year results[18] [a] Optical depth to reionization improved due to polarization measurements.[19] [b] < 0.30 when combined with SDSS data. No indication of non-gaussianity.[18]
Five-year data release The five-year WMAP data were released on February 28, 2008. The data included new evidence for the cosmic neutrino background, evidence that it took over half a billion years for the first stars to reionize the universe, and new constraints on cosmic inflation.[20] The improvement in the results came from both having an extra 2 years of measurements (the data set runs between midnight on August 10, 5 year WMAP image of background cosmic 2001 to midnight of August 9, 2006), as well as using improved data radiation (2008) processing techniques and a better characterization of the instrument, most notably of the beam shapes. They also make use of the 33 GHz observations for estimating cosmological parameters; previously only the 41 GHz and 61 GHz channels had been used. Finally, improved masks were used to remove foregrounds.[8]
Wilkinson Microwave Anisotropy Probe
17
Improvements to the spectra were in the 3rd acoustic peak, and the polarization spectra.[8] The measurements put constraints on the content of the universe at the time that the CMB was emitted; at the time 10% of the universe was made up of neutrinos, 12% of atoms, 15% of photons and 63% dark matter. The contribution of dark energy at the time was negligible.[20] It also constrained the content of the present-day universe; 4.6% atoms, 23% dark matter and 72% dark energy.[8] The WMAP five-year data was combined with measurements from Type Ia supernova (SNe) and Baryon acoustic oscillations (BAO).[8] The elliptical shape of the WMAP skymap is the result of a Mollweide projection.[21] The five-year total-intensity and polarization spectra from WMAP
Matter/energy content in the current universe (top) and at the time of photon decoupling in the recombination epoch 380,000 years after the Big Bang (bottom)
Wilkinson Microwave Anisotropy Probe
18
Parameter
Symbol
Best fit (WMAP only) Best fit (WMAP + SNe + BAO)
Hubble's constant ( km⁄Mpc·s )
70.5 ± 1.3
71.9
Baryonic content
0.02273 ± 0.00062
0.02267
Cold dark matter content
0.1099 ± 0.0062
0.1131 ± 0.0034
Dark energy content
0.742 ± 0.030
0.726 ± 0.015
Optical depth to reionization
0.087 ± 0.017
0.084 ± 0.016
Scalar spectral index
0.960 ± 0.013
0.963
Running of spectral index
−0.037 ± 0.028
−0.028 ± 0.020
Fluctuation amplitude at 8h−1 Mpc
0.796 ± 0.036
0.812 ± 0.026
Age of the universe (Ga)
13.69 ± 0.13
13.72 ± 0.12
Total density of the universe Tensor-to-scalar ratio
1.099 r
1.0050
< 0.43
< 0.22
|+ Best-fit cosmological parameters from WMAP five-year results[8] The data puts a limits on the value of the tensor-to-scalar ratio, r < 0.22 (95% certainty), which determines the level at which gravitational waves affect the polarization of the CMB, and also puts limits on the amount of primordial non-gaussianity. Improved constraints were put on the redshift of reionization, which is 10.9 ± 1.4, the redshift of decoupling, 1090.88 ± 0.72 (as well as age of universe at decoupling, 376.971 ka) and the redshift of matter/radiation equality, 3253
.[8]
The extragalactic source catalogue was expanded to include 390 sources, and variability was detected in the emission from Mars and Saturn.[8]
23 GHz
33 GHz
41 GHz
61 GHz
94 GHz
|+ The five-year maps at different frequencies from WMAP with foregrounds (the red band)
Seven-year data release The Seven-year WMAP data were released on January 26, 2010. According to this data the Universe is 13.75 ±0.11 bln. years old. As part of this release, claims for inconsistencies with the standard model were investigated.[22] Most were shown not to be statistically significant, and likely due to a posteriori selection (where one sees a weird deviation, but fails to consider properly how hard one has been 7 year WMAP image of background cosmic looking; a deviation with 1:1000 likelihood will typically be found if radiation (2010) one tries one thousand times). For the deviations that do remain, there are no alternative cosmological ideas (for instance, there seem to be correlations with the ecliptic pole). It seems most likely these are due to other effects, with the report mentioning uncertainties in the precise beam shape and other possible small remaining instrumental and analysis issues. The other confirmation of major significance is of the total amount of matter/energy in the Universe in the form of Dark Energy – 72.8% (within 1.6%) as non 'particle' background, and Dark Matter – 22.7% (within 1.4%) of non baryonic (sub atomic) 'particle' energy. This leaves matter, or baryonic particles (atoms) at only 4.56% (within
Wilkinson Microwave Anisotropy Probe
19
0.16%). Symbol Best fit (WMAP only) Best fit (WMAP + BAO[23] + H [24]) 0
Parameter Age of the universe (Ga)
13.75 ± 0.13
13.75 ± 0.11
Hubble's constant ( km⁄Mpc·s )
71.0 ± 2.5
Baryon density
0.0449 ± 0.0028
0.0456 ± 0.0016
Physical baryon density
0.02258
0.02260 ± 0.00053
Dark matter density
0.222 ± 0.026
0.227 ± 0.014
Physical dark matter density
0.1109 ± 0.0056
0.1123 ± 0.0035
Dark energy density
0.734 ± 0.029
Fluctuation amplitude at 8h−1 Mpc
0.801 ± 0.030
0.809 ± 0.024
Scalar spectral index
0.963 ± 0.014
0.963 ± 0.012
Reionization optical depth
0.088 ± 0.015
0.087 ± 0.014
70.4
0.728
|+ Best-fit cosmological parameters from WMAP seven-year results[25] Parameter
Symbol
Best fit (WMAP only) Best fit (WMAP + BAO[23] + H [24]) 0
Total density of the universe Tensor-to-scalar ratio, k0 = 0.002 Mpc−1
1.080 r
Running of spectral index, k0 = 0.002 Mpc−1
1.0023
< 0.36 (95% CL)
< 0.24 (95% CL)
−0.034 ± 0.026
−0.022 ± 0.020
|+ Parameters for extended models (parameters place limits on deviations from the Lambda-CDM model[25])
23 GHz
33 GHz
41 GHz
61 GHz
94 GHz
|+ The Seven-year maps at different frequencies from WMAP with foregrounds (the red band)
Main result The main result of the mission is contained in the various oval maps of the CMB spectrum over the years. These oval images present the temperature distribution gained by the WMAP team from the observations by the telescope of the mission. Measured is the temperature obtained from a Planck's law interpretation of the microwave background. The oval map covers the whole sky. The results describe the state of the universe only some hundred-thousand years after the "big bang", which happened roughly 13.7 billion years before our time. The microwave background is very homogeneous in temperature (the relative variations from the mean, which presently is still 2.7 kelvins, are only of the order of 5x10−5. The temperature variations corresponding to the local directions are presented through different colours (the "red" directions are hotter, the "blue" directions cooler than the average).
Wilkinson Microwave Anisotropy Probe
20
Follow-on missions and future measurements The original timeline for WMAP gave it two years of observations; these were completed by September 2003. Mission extensions were granted in 2002, 2004, 2006, and 2008 giving the spacecraft a total of 9 observing years, which ended August 2010[4] and in October 2010 the spacecraft was moved to a special graveyard orbit.[12] outside of L2, in which it orbits the sun 14 times every 15 years. The Planck spacecraft, launched on the May 14, 2009, also measures the CMB and aims to refine the measurements made by WMAP, both in total intensity and polarization. Various ground- and balloon-based instruments have also made CMB contributions or are being constructed to do so. Many are aimed at searching for the B-mode polarization expected from the simplest models of inflation, including EBEX, Spider, BICEP2, Keck, QUIET, CLASS, SPTpol and others.
Artist's impression of the Planck spacecraft
References Footnotes [1] [2] [3] [4] [5]
http:/ / nssdc. gsfc. nasa. gov/ nmc/ masterCatalog. do?sc=2001-027A Bennett et al. (2003a) Limon et al. (2008) "WMAP News: Facts" (http:/ / map. gsfc. nasa. gov/ news/ facts. html). NASA. April 22, 2008. . Retrieved April 27, 2008. "Wilkinson Microwave Anisotropy Probe: Overview" (http:/ / lambda. gsfc. nasa. gov/ product/ map/ current/ ). Legacy Archive for Background Data Analysis (LAMBDA). Greenbelt, Maryland: NASA's High Energy Astrophysics Science Archive Research Center (HEASARC). August 4, 2009. . Retrieved September 24, 2009. "The WMAP (Wilkinson Microwave Anisotropy Probe) mission is designed to determine the geometry, content, and evolution of the universe via a 13 arcminute FWHM resolution full sky map of the temperature anisotropy of the cosmic microwave background radiation." [6] "Tests of Big Bang: The CMB" (http:/ / map. gsfc. nasa. gov/ universe/ bb_tests_cmb. html). Universe 101: Our Universe. NASA. July, 2009. . Retrieved September 24, 2009. "Only with very sensitive instruments, such as COBE and WMAP, can cosmologists detect fluctuations in the cosmic microwave background temperature. By studying these fluctuations, cosmologists can learn about the origin of galaxies and large scale structures of galaxies and they can measure the basic parameters of the Big Bang theory." [7] "New image of infant universe reveals era of first stars, age of cosmos, and more" (http:/ / web. archive. org/ web/ 20080227175308/ http:/ / www. gsfc. nasa. gov/ topstory/ 2003/ 0206mapresults. html). NASA / WMAP team. February 11, 2003. Archived from the original (http:/ / www. gsfc. nasa. gov/ topstory/ 2003/ 0206mapresults. html) on February 27, 2008. . Retrieved April 27, 2008. [8] Hinshaw et al. (2009) [9] Seife (2003) [10] ""Super Hot" Papers in Science" (http:/ / www. in-cites. com/ hotpapers/ shp/ 1-50. html). in-cites. October 2005. . Retrieved April 26, 2008. [11] "Announcement of the Shaw Laureates 2010" (http:/ / www. shawprize. org/ en/ shawprize2010/ announcement/ announcement. html). . [12] "MISSION COMPLETE! WMAP FIRES ITS THRUSTERS FOR THE LAST TIME" (http:/ / news. discovery. com/ space/ mission-complete-wmap-fires-its-thrusters-for-the-last-time. html). . [13] Li, H. and Liu, T-P. (2011). "Pseudo-dipole signal removal from WMAP data". Chinese Sci. Bull. 56: 29-33. [14] Roukema, B. F. (2010). "On the suspected timing error in Wilkinson microwave anisotropy probe map-making". Astron. & Astrophys. 518: A34. [15] Bennett et al. (2003b) [16] "WMAP News: Events" (http:/ / map. gsfc. nasa. gov/ news/ events. html). NASA. April 17, 2008. . Retrieved April 27, 2008. [17] Spergel et al. (2003) [18] Spergel et al. (2007) [19] Hinshaw et al. (2007) [20] "WMAP Press Release — WMAP reveals neutrinos, end of dark ages, first second of universe" (http:/ / map. gsfc. nasa. gov/ news/ ). NASA / WMAP team. March 7, 2008. . Retrieved April 27, 2008. [21] WMAP 1-year Paper Figures (http:/ / lambda. gsfc. nasa. gov/ product/ map/ pub_papers/ firstyear/ basic/ wmap_cb1_images. cfm), Bennett, et al.
Wilkinson Microwave Anisotropy Probe [22] (http:/ / arxiv. org/ abs/ 1001. 4758) Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Are There Cosmic Microwave Background Anomalies? [23] Percival, Will J. et.al. (February 2010). "Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample". Monthly Notices of the Royal Astronomical Society 401 (4): 2148–2168. arXiv:0907.1660. Bibcode 2010MNRAS.401.2148P. doi:10.1111/j.1365-2966.2009.15812.x. [24] Riess, Adam G. et.al.. "A Redetermination of the Hubble Constant with the Hubble Space Telescope from a Differential Distance Ladder" (http:/ / hubblesite. org/ pubinfo/ pdf/ 2009/ 08/ pdf. pdf) (PDF). hubblesite.org. . Retrieved December 4, 2010. [25] Table 8 on p. 39 of Jarosik, N., et.al. (WMAP Collaboration). "Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results" (http:/ / lambda. gsfc. nasa. gov/ product/ map/ dr4/ pub_papers/ sevenyear/ basic_results/ wmap_7yr_basic_results. pdf) (PDF). nasa.gov. . Retrieved December 4, 2010. (from NASA's WMAP Documents (http:/ / lambda. gsfc. nasa. gov/ product/ map/ dr4/ map_bibliography. cfm) page)
Primary sources • Bennett, C.; et al. (2003a). "The Microwave Anisotropy Probe (MAP) Mission". Astrophysical Journal 583 (1): 1–23. arXiv:astro-ph/0301158. Bibcode 2003ApJ...583....1B. doi:10.1086/345346. • Bennett, C.; et al. (2003b). "First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission". Astrophysical Journal Supplement 148 (1): 97–117. arXiv:astro-ph/0302208. Bibcode 2003ApJS..148...97B. doi:10.1086/377252. • Hinshaw, G.; et al. (2007). "Three-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Temperature Analysis". Astrophysical Journal Supplement 170 (2): 288–334. arXiv:astro-ph/0603451. Bibcode 2007ApJS..170..288H. doi:10.1086/513698. • Hinshaw, G. et al. (WMAP Collaboration). (feb 2009). "Five-Year Wilkinson Microwave Anisotropy Probe Observations: Data Processing, Sky Maps, and Basic Results". The Astrophysical Journal Supplement 180 (2): 225–245. arXiv:astro-ph/id=0803.0732. Bibcode 2009ApJS..180..225H. doi:10.1088/0067-0049/180/2/225. • Limon, M.; et al. (March 20, 2008). "Wilkinson Microwave Anisotropy Probe (WMAP): Five–Year Explanatory Supplement" (http://lambda.gsfc.nasa.gov/product/map/dr3/pub_papers/fiveyear/supplement/ WMAP_supplement.pdf) (PDF). • Seife, Charles (2003). "Breakthrough of the Year: Illuminating the Dark Universe" (http://www.sciencemag. org/cgi/content/full/302/5653/2038). Science 302 (5653): 2038–2039. doi:10.1126/science.302.5653.2038. PMID 14684787. • Spergel, D. N.; et al. (2003). "First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters". Astrophysical Journal Supplement 148 (1): 175–194. arXiv:astro-ph/0302209. Bibcode 2003ApJS..148..175S. doi:10.1086/377226. • Sergel, D. N.; et al. (2007). "Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology". Astrophysical Journal Supplement 170 (2): 377–408. arXiv:astro-ph/0603449. Bibcode 2007ApJS..170..377S. doi:10.1086/513700. • Komatsu; Dunkley; Nolta; Bennett; Gold; Hinshaw; Jarosik; Larson et al. (2009). "Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation". The Astrophysical Journal Supplement Series 180 (2): 330–376. arXiv:0803.0547. Bibcode 2009ApJS..180..330K. doi:10.1088/0067-0049/180/2/330.
21
Wilkinson Microwave Anisotropy Probe
External links • Sizing up the universe (http://www.bioedonline.org/news/news.cfm?art=977) • About WMAP and the Cosmic Microwave Background (http://www.space.com/scienceastronomy/ map_mission_basics_030211.html) – Article at Space.com • Big Bang glow hints at funnel-shaped Universe (http://www.newscientist.com/article.ns?id=dn4879), NewScientist, April 15, 2004 • NASA March 16, 2006 WMAP inflation related press release (http://www.nasa.gov/home/hqnews/2006/mar/ HQ_06097_first_trillionth_WMAP.html) • Seife, Charles (2003). "With Its Ingredients MAPped, Universe's Recipe Beckons". Science 300 (5620): 730–731. doi:10.1126/science.300.5620.730. PMID 12730575.
22
23
Electromagnetism & Special Relativity Fizeau experiment The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. Albert Einstein later pointed out the importance of the experiment for special relativity.[1][2] Although it is referred to as the Fizeau experiment, Fizeau was an active experimenter who carried out a wide variety of different experiments involving measuring the speed of light in different situations.
Significance In 1851, Fizeau used a special interferometer arrangement to measure the effect of movement of a medium upon the speed of light.[3][4] According to the theories prevailing at the time, light traveling through a moving medium would be dragged along by the medium, so that the measured speed of the light would be a simple sum of its speed through the medium plus the speed of the medium. Fizeau indeed detected a dragging effect, but the magnitude of the effect that he observed was far lower than expected. His results seemingly supported the partial aether-drag hypothesis of Fresnel, a situation that was disconcerting to most physicists. Over half a century passed before a satisfactory explanation of Fizeau's unexpected measurement was developed with the advent of Einstein's theory of special relativity.
Experimental setup
A light ray emanating from the source S' is reflected by a beam splitter G and is collimated into a parallel beam by lens L. After passing the slits O1 and O2, two rays of light travel through the tubes A1 and A2, through which water is streaming back and forth as shown by the arrows. The rays reflect off a mirror m at the focus of lens L', so that one ray always propagates in the same direction as the water stream, and the other ray opposite to the direction of the water stream. After passing back and forth through the tubes, both rays unite at S, where they produce interference fringes that can be visualized through the illustrated eyepiece.
Fizeau experiment The interference pattern can be analyzed to determine the speed of light traveling along each leg of the tube.
Fresnel drag coefficient Assume that water flows in the pipes at velocity v. According to the non-relativistic theory of the luminiferous aether, the speed of light should be increased when "dragged" along by the water, and decreased when "overcoming" the resistance of the water. The overall speed of a beam of light should be a simple additive sum of its speed through the water plus the speed of the water. That is, if n is the index of refraction of water, so that c/n is the velocity of light in stationary water, then the predicted speed of light w in one arm would be
and the predicted speed in the other arm would be
Light traveling against the flow of water should be slower than light traveling with the flow of water. The interference pattern between the two beams when the light is recombined at the observer depends upon the transit times over the two paths, and can be used to calculate the speed of light as a function of the speed of the water.[5] Fizeau found that
In other words, light appeared to be dragged by the water, but the magnitude of the dragging was much lower than expected. The Fizeau experiment forced physicists to accept the empirical validity of an old, theoretically unsatisfactory theory of Augustin Fresnel (1818) that had been invoked to explain an 1810 experiment by Arago, namely, that a medium moving through the stationary aether drags light propagating through it with only a fraction of the medium's speed, with a dragging coefficient f given by
In 1895, Lorentz predicted the existence of an extra term due to dispersion:[6]
Repetitions Albert Michelson and Edward Morley (1886),[7] repeated Fizeau's experiment with improved accuracy. Another experiment was conducted by Zeeman in 1914, who confirmed Lorentz's modified coefficient.[8][9] In 1910, Franz Harress (1910) used a rotating device and overall confirmed Fresnel's dragging coefficient. However, he additionally found a "systematic bias" in the data, which later turned out to be the Sagnac effect.[10]
Controversy Although Fresnel's hypothesis was empirically successful in explaining Fizeau's results, many leading experts in the field, including Fizeau (1851), Éleuthère Mascart (1872), Ketteler (1873), Veltmann (1873), and Lorentz (1886) were united in considering Fresnel's partial aether-dragging hypothesis to be on shaky theoretical grounds. For example, Veltmann (1870) demonstrated that Fresnel's formula implies that the aether would have to be dragged by different amounts for different colors of light, since the index of refraction depends on wavelength; Mascart (1872)
24
Fizeau experiment demonstrated a similar result for polarized light traveling through a birefringent medium. In other words, the aether must be capable of sustaining different motions at the same time.[11] Fizeau's dissatisfaction with the result of his own experiment is easily discerned in the conclusion to his report: The success of the experiment seems to me to render the adoption of Fresnel's hypothesis necessary, or at least the law which he found for the expression of the alteration of the velocity of light by the effect of motion of a body; for although that law being found true may be a very strong proof in favour of the hypothesis of which it is only a consequence, perhaps the conception of Fresnel may appear so extraordinary, and in some respects so difficult, to admit, that other proofs and a profound examination on the part of geometricians will still be necessary before adopting it as an expression of the real facts of the case.[3] Despite the dissatisfaction of most physicists with Fresnel's partial aether-dragging hypothesis, repetitions and improvements to his experiment (see section above) by others confirmed his results to high accuracy. Besides the problems of the partial aether-dragging hypothesis, another major problem arose with the Michelson-Morley experiment (1887). In Fresnel's theory, the aether is almost stationary, so the experiment should have given a positive result. However, the result of this experiment was negative. Thus from the viewpoint of the aether models at that time, the experimental situation was contradictory: On one hand, the Fizeau experiment and the repetition by Michelson and Morley in 1886 appeared to prove the (almost) stationary aether with partial aether-dragging. On the other hand, the Michelson-Morley experiment of 1887 appeared to prove that the aether is at rest with respect to Earth, apparently supporting the idea of complete aether-dragging (see aether drag hypothesis).[12] So the very success of Fresnel's hypothesis in explaining Fizeau's results helped lead to a theoretical crisis, which was not resolved until the development of the theory of special relativity.[11]
Lorentz's interpretation In 1892, Hendrik Lorentz proposed a modification of Fresnel's model, in which the aether is completely stationary. He succeeded in deriving Fresnel's dragging coefficient by the reaction of the moving water upon the interfering waves, without the need of any aether entrainment.[1][12] He also discovered that the transition from one to another reference frame could be simplified by using a auxiliary time variable which he called local time:
In 1895, Lorentz more generally explained Fresnel's coefficient based on the concept of local time. However, Lorentz's theory had the same fundamental problem as Fresnel's: a stationary aether contradicted the Michelson-Morley experiment. So in 1892 Lorentz proposed that moving bodies contract in the direction of motion (FitzGerald-Lorentz Contraction hypothesis, since George FitzGerald had already arrived in 1889 at this conclusion).[1][12] The equations that he used to describe these effects were further developed by him until 1904. These are now called the Lorentz transformations in his honor, and are identical in form to the equations that Einstein were later to derive from first principles. Unlike Einstein's equations, however, Lorentz's transformations were strictly ad hoc, their only justification being that they seemed to work.
Derivation in special relativity Einstein showed how Lorentz's equations could be derived as the logical outcome of a set of two simple starting postulates. In addition Einstein recognized that the stationary aether concept has no place in special relativity, and that the Lorentz transformation concerns the nature of space and time. The Fizeau experiment was one of the key experimental results that shaped Einstein's thinking about relativity. Robert S. Shankland reported some conversations with Einstein, in which Einstein emphasized the importance of the Fizeau experiment:[13]
25
Fizeau experiment He continued to say the experimental results which had influenced him most were the observations of stellar aberration and Fizeau’s measurements on the speed of light in moving water. “They were enough,” he said. Max von Laue (1907) demonstrated that the Fresnel drag coefficient can be easily explained as a natural consequence of the relativistic formula for addition of velocities,[14] namely: The speed of light in immobile water is c/n. From the velocity composition law it follows that the speed of light observed in the laboratory, where water is flowing with speed v (in the same direction as light) is
Thus the difference in speed is (assuming v is small comparing to c, approximating to the first non-trivial correction)
This is accurate when v/c << 1, and agrees with the formula based upon Fizeau's measurements, which satisfied the condition v/c << 1. Fizeau's experiment is hence supporting evidence for the collinear case of Einstein's velocity addition formula.[15] and the earliest refutation of the emission theory of light.
References [1] Miller, A.I. (1981). Albert Einstein’s special theory of relativity. Emergence (1905) and early interpretation (1905–1911). Reading: Addison–Wesley. ISBN 0-201-04679-2. [2] Lahaye, Thierry; Labastie, Pierre; Mathevet, Renaud (2012). "Fizeau's "aether-drag" experiment in the undergraduate laboratory". arXiv:1201.0501. [3] Fizeau, H. (1851). "Sur les hypothèses relatives à l’éther lumineux" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k29901/ f351. chemindefer). Comptes Rendus 33: 349–355. .
English: Fizeau, H. (1851). "The Hypotheses Relating to the Luminous Aether, and an Experiment which Appears to Demonstrate that the Motion of Bodies Alters the Velocity with which Light Propagates itself in their Interior". Philosophical Magazine 2: 568–573. [4] Fizeau, H. (1859). "Sur les hypothèses relatives à l’éther lumineux" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k347981/ f381. table). Ann. de Chim. et de Phys. 57: 385–404. .
English: Fizeau, H. (1860). "On the Effect of the Motion of a Body upon the Velocity with which it is traversed by Light". Philosophical Magazine 19: 245–260. [5] Robert Williams Wood (1905). Physical Optics (http:/ / books. google. com/ books?id=Ohp5AAAAIAAJ& pg=PA514). The Macmillan Company. p. 514. . [6] Pauli, Wolfgang (1921/1981). Theory of Relativity. New York: Dover. ISBN 0-486-64152-X. [7] Michelson, A. A. and Morley, E.W. (1886). "Influence of Motion of the Medium on the Velocity of Light". Am. J. Science 31: 377–386. [8] Zeeman, Pieter (1914). "Fresnel's coefficient for light of different colours. (First part)" (http:/ / www. archive. org/ details/ p1proceedingsofs17akad). Proc. Kon. Acad. Van Weten. 17: 445–451. . [9] Zeeman, Pieter (1915). "Fresnel's coefficient for light of different colours. (Second part)" (http:/ / www. archive. org/ details/ proceedingsofsec181koni). Proc. Kon. Acad. Van Weten. 18: 398–408. . [10] Anderson, R., Bilger, H.R., Stedman, G.E. (1994). "Sagnac effect: A century of Earth-rotated interferometers". Am. J. Phys. 62 (11): 975–985. Bibcode 1994AmJPh..62..975A. doi:10.1119/1.17656. [11] Stachel, J. (2005). "Fresnel's (dragging) coefficient as a challenge to 19th century optics of moving bodies" (http:/ / books. google. com/ books?id=-KlBhDwUKF8C& pg=PA1& lpg=PA1#v=onepage& q& f=false). In Kox, A.J.; Eisenstaedt, J. The universe of general relativity. Boston: Birkhäuser. pp. 1–13. ISBN 0-8176-4380-X. . Retrieved 17 April 2012. [12] Janssen, Michel & Stachel, John (2010), "The Optics and Electrodynamics of Moving Bodies" (http:/ / www. mpiwg-berlin. mpg. de/ Preprints/ P265. PDF), in John Stachel, Going Critical, Springer, ISBN 1-4020-1308-6, [13] Shankland, R. S. (1963). "Conversations with Albert Einstein". American Journal of Physics 31 (1): 47–57. Bibcode 1963AmJPh..31...47S. doi:10.1119/1.1969236.
26
Fizeau experiment
27
[14] N David Mermin (2005). It's about time: understanding Einstein's relativity (http:/ / books. google. com/ books?id=rKFhqlzjv-IC& pg=PA41). Princeton University Press. pp. 39 ff. ISBN 0-691-12201-6. . [15] Laue, Max von (1907). "The Entrainment of Light by Moving Bodies According to the Principle of Relativity". Annalen der Physik 23: 989–990.
Secondary sources Primary sources
Fizeau–Foucault apparatus The Fizeau–Foucault apparatus (1850) (Figure 1) was designed by the French physicists Hippolyte Fizeau and Léon Foucault for measuring the speed of light. The apparatus involves light reflecting off a rotating mirror, toward a stationary mirror some 20 miles (35 kilometers) away. As the rotating mirror will have moved slightly in the time it takes for the light to bounce off the stationary mirror (and return to the rotating mirror), it will thus be deflected away from the original source, by a small angle.[1] If the distance between mirrors is h, the time between the first and second reflections on the rotating mirror is 2h/c (c = speed of light). If the mirror rotates at a known constant angular rate dθ/dt, the angle θ is given by:
Figure 1: Schematic of the Foucault apparatus. Left panel: Light is reflected by a rotating mirror (left) toward a stationary mirror (top). Right panel: The reflected light from the stationary mirror bounces from the rotating mirror that has advanced an angle θ during the transit of the light. The telescope at an angle 2θ from the source picks up the reflected beam from the rotating mirror.
In other words the speed of light is calculated from the observed angle θ, known rate of rotation, and measured distance h as
The detector is at an angle 2θ from the source direction because the normal to the rotating mirror rotates by θ, decreasing by θ both the angle of incidence of the beam and its angle of reflection. Figure 2: Schematic of the Fizeau apparatus. The light passes on one side of a tooth
Foucault based his apparatus on an earlier on the way out, and the other side on the way back, assuming the cog rotates one tooth during transit of the light. experiment by Fizeau (Figure 2) who, in 1849, used two fixed mirrors, one partially obscured by a rotating cogwheel.[2] Fizeau's value for light's speed was about 5% too high.
FizeauFoucault apparatus The Fizeau experiment to measure the speed of light in water has been viewed as "driving the last nail in the coffin" of Newton's corpuscle theory of light when it showed that light travels more slowly through water than through air.[3] Newton predicted refraction as a pull of the medium upon the light, implying an increased speed of light in the medium. However, Fizeau showed the speed of light in water to be less than in air, not more, by inserting a tube of water in the light path.[4]
References [1] Ralph Baierlein (2001). Newton to Einstein: the trail of light : an excursion to the wave-particle duality and the special theory of relativity (http:/ / books. google. com/ books?id=wrmZrcE0fPMC& pg=PA44). Cambridge University Press. p. 44; Figure 2.6 and discussion. ISBN 0-521-42323-6. . [2] Abdul Al-Azzawi (2006). Photonics: principles and practices (http:/ / books. google. com/ books?id=H3dtlDZrfwkC& pg=PA9). CRC Press. p. 9. ISBN 0-8493-8290-4. . [3] David Cassidy, Gerald Holton, James Rutherford (2002). Understanding Physics (http:/ / books. google. com/ books?id=rpQo7f9F1xUC& pg=PA382& dq=Foucault+ speed-of-light+ wave+ theory). Birkhäuser. ISBN 0-387-98756-8. . [4] Bruce H Walker (1998). Optical Engineering Fundamentals (http:/ / books. google. com/ books?id=Ccx9OM7iph8C& pg=PA13). SPIE Press. p. 13. ISBN 0-8194-2764-0. .
External links • Diagram (http://imgbase-scd-ulp.u-strasbg.fr/displayimage.php?album=648&pos=24) showing the original experimental design found in the second volume of Foucalt's collected works: Volume Two - Recueil des travaux scientifiques de Léon Foucault (http://num-scd-ulp.u-strasbg.fr:8080/527/) 1878. • Speed of Light Formal Report (The Foucault Method) (http://www.njsas.org/projects/speed_of_light/cache/ 2/lightspeedformal.htm) • Light in moving media (http://www.st-andrews.ac.uk/~ulf/media.html)
Hafele–Keating experiment The Hafele–Keating experiment was a test of the theory of relativity. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners and flew twice around the world, first eastward, then westward, and compared the clocks against those of the United States Naval Observatory. According to special relativity, the rate of a clock is greatest according to an observer who is at rest with respect to the clock. In a frame of reference in which the clock is not at rest, the clock runs slower, expressed by the Lorentz factor. This effect called time dilation was confirmed in many tests of special relativity, such as the Ives–Stilwell experiment or Time dilation of moving particles. According to general relativity, a slight increase in gravitational potential due to altitude speeds the clocks up. That is, clocks at higher altitude are ticking faster than clocks on Earth's surface. Also this effect was confirmed in many tests of general relativity, such as the Pound–Rebka experiment or Gravity Probe A. The Hafele–Keating experiment tests both effects simultaneously. Similar experiments were conducted with higher precision in the Maryland experiment. In particular, both effects must be considered in the operation of GPS.
28
HafeleKeating experiment
29
Overview In a frame of reference at rest with respect to the center of the earth, the clock aboard the plane moving eastward, in the direction of the Earth's rotation, has a greater velocity (resulting in a relative time loss) than a clock that remains on the ground, while the clock aboard the plane moving westward, against the Earth's rotation, has a lower velocity than the one on the ground. According to special relativity, this is resulting in a relative time gain. Also general relativity comes into play: the slight increase in gravitational potential due to altitude that speeds the clocks back up. Since the aircraft are flying at roughly the same altitude in both directions, this effect is more "constant" between the two clocks, but nevertheless it causes a difference in comparison to the clock on the ground. The results were published in Science in 1972:[1][2] nanoseconds gained predicted gravitational kinematic (general relativity) (special relativity)
measured total
eastward 144±14
−184 ± 18
−40 ± 23 −59 ± 10
westward 179±18
96±10
275±21
273±7
The published outcome of the experiment was consistent with special and general relativity. The observed time gains and losses were different from zero to a high degree of confidence, and were in agreement with relativistic predictions to within the ~10% precision of the experiment.
Repetitions The results were verified in an improved experiment in 1976 by the University of Maryland, this time agreeing with the relativistic predictions to a precision of about 1%.[3][4] Versions of the experiment have also been done in which the only effect was gravitational[5][6] and in which the only effect was kinematic.[7] A reenactment of the original experiment by the NPL took place in 1996 on the 25th anniversary of the original experiment, using more precise atomic clocks during a flight from London to Washington, D.C. and back again. The results were verified to a higher degree of accuracy. A time gain of 39 ± 2 ns was observed, compared to a relativistic prediction of 39.8 ns.[8] In June 2010, NPL again repeated the experiment, this time around the globe (London - Los Angeles - Auckland - Hongkong - London). The predicted value was 246 ± 3 ns, the measured value was 230 ± 20 ns.[9] Nowadays such relativistic effects are, for example, routinely incorporated into the calculations used for the Global Positioning System.[10] Because the experiment was reproduced by increasingly accurate methods, there has been a consensus among physicists since at least the 1970s that the relativistic predictions of gravitational and kinematic effects on time have been conclusively verified.[11] Criticisms of the experiment did not address the subsequent verification of the result by more accurate methods, and have been shown to be in error.[12]
HafeleKeating experiment
Equations The equations and effects involved in the experiment are: Total time dilation
Velocity
Gravitation
Sagnac effect
Where c = speed of light, h = height, g=acceleration of gravity, v = velocity, = angular velocity of Earth's rotation and τ represents the duration/distance of a section of the flight. The effects are summed over the entire flight, since the parameters will change with time.
Historical and scientific background In his original 1905 paper on special relativity,[13] Einstein suggested a possible test of the theory: "Thence we conclude that a spring-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions." Because he had not yet developed the general theory, he did not realize that the results of such a test would in fact be null, since the surface of the earth is a gravitational equipotential, and therefore the effects of kinematic and gravitational time dilation would precisely cancel. The kinematic effect was verified in the 1938 Ives–Stilwell experiment and in the 1940 Rossi-Hall experiment. General relativity's prediction of the gravitational effect was confirmed in 1959 by Pound and Rebka. These experiments, however, used subatomic particles, and were therefore less direct than the type of measurement with actual clocks as originally envisioned by Einstein. Even as late as 1970, physicists such as Herbert Dingle and Mendel Sachs maintained vocally that the twin paradox was an erroneous prediction of special relativity, and that a null result would be observed with clocks. Hafele, an assistant professor of physics at Washington University in St. Louis, was preparing notes for a physics lecture when he did a back-of-the-envelope calculation showing that an atomic clock aboard a commercial airliner should have sufficient precision to detect the predicted relativistic effects.[14] He spent a year in fruitless attempts to get funding for such an experiment, until he was approached after a talk on the topic by Keating, an astronomer at the United States Naval Observatory who worked with atomic clocks.[14] Hafele and Keating obtained $8000 in funding from the Office of Naval Research[15] for one of the most inexpensive tests ever conducted of general relativity. Of this amount, $7600 was spent on the eight round-the-world plane tickets,[16] including two seats on each flight for "Mr. Clock." They flew eastward around the world, ran the clocks side by side for a week, and then flew westward. The crew of each flight helped by supplying the navigational data needed for the comparison with theory. In addition to the scientific papers published in Science, there were several accounts published in the popular press and other publications,[14][17] including one with a photo showing a stewardess ironically checking her wristwatch while standing behind the instruments.[18]
30
HafeleKeating experiment
References [1] Hafele, J.; Keating, R. (July 14, 1972). "Around the world atomic clocks:predicted relativistic time gains" (http:/ / www. sciencemag. org/ cgi/ content/ abstract/ 177/ 4044/ 166). Science 177 (4044): 166–168. Bibcode 1972Sci...177..166H. doi:10.1126/science.177.4044.166. PMID 17779917. . Retrieved 2006-09-18. [2] Hafele, J.; Keating, R. (July 14, 1972). "Around the world atomic clocks:observed relativistic time gains" (http:/ / www. sciencemag. org/ cgi/ content/ abstract/ 177/ 4044/ 168). Science 177 (4044): 168–170. Bibcode 1972Sci...177..168H. doi:10.1126/science.177.4044.168. PMID 17779918. . Retrieved 2006-09-18. [3] C.O. Alley, in NASA Goddard Space Flight Center, Proc. of the 13th Ann. Precise Time and Time Interval (PTTI) Appl. and Planning Meeting, p. 687-724, 1981, available online at http:/ / www. pttimeeting. org/ archivemeetings/ index9. html [4] C. Alley, "Proper Time Experiments in Gravitational Fields with Atomic Clocks, Aircraft, and Laser Light Pulses," in Quantum Optics, Experimental Gravity, and Measurement Theory, eds. Pierre Meystre and Marlan O. Scully, Proceedings Conf. Bad Windsheim 1981, 1983, Plenum Press, New York, pp. 363–427. [5] S. Iijima and K. Fujiwara, An experiment for the potential blue shift at the Norikura Corona Station, Annals of the Tokyo Astronomical Observatory, Second Series, Vol. XVII, 2 (1978) 68. [6] L. Briatore and S. Leschiutta, Evidence for the earth gravitational shift by direct atomic-time-scale comparison, Il Nuovo Cimento B, 37B (2): 219 (1979) [7] Chou et al., Science 329 (2010) 1630. Nontechnical explanation at http:/ / www. scientificamerican. com/ article. cfm?id=time-dilation [8] NPL Metromnia, Issue 18 - Spring 2005 (http:/ / resource. npl. co. uk/ docs/ publications/ newsletters/ metromnia/ issue18_einstein. pdf) [9] NPL news, Time flies, 1 Feb. 2011 (http:/ / www. npl. co. uk/ news/ time-flies) [10] Deines, "Uncompensated relativity effects for a ground-based GPSA receiver", Position Location and Navigation Symposium, 1992. Record. '500 Years After Columbus - Navigation Challenges of Tomorrow'. IEEE PLANS '92. [11] Wolfgang Rindler, Essential Relativity: Special, General, and Cosmological, Springer-Verlag, 1979, p. 45 [12] Roberts and Schleif, What is the experimental basis of Special Relativity? (http:/ / math. ucr. edu/ home/ baez/ physics/ Relativity/ SR/ experiments. html#Twin_paradox) [13] A. Einstein, "On the electrodynamics of moving bodies," Annalen der Physik 17 (10): 891, tr. W. Perrett and G.B. Jeffery, 1923 [14] New Scientist, February 3, 1972, "The clock paradox resolved" [15] Hafele, "Performance and results of portable clocks in aircraft," PTTI, 3rd Annual Meeting, 1971; http:/ / www. pttimeeting. org/ archivemeetings/ ptti1971. html [16] Martin Gardner, Relativity Simply Explained, Dover, 1997, p. 117 [17] Time Magazine, October 18, 1971; http:/ / www. time. com/ time/ magazine/ article/ 0,9171,910115,00. html [18] John Pearson, " Science Worldwide (http:/ / books. google. com/ books?id=iNQDAAAAMBAJ& lpg=PP1& lr& rview=1& pg=PA30)", Popular Mechanics, January 1972, p. 30.
31
Hammar experiment
Hammar experiment The Hammar experiment was an experiment designed and conducted by Gustaf Wilhelm Hammar (1935) to test the aether drag hypothesis. Its negative result refuted some specific aether drag models, and confirmed special relativity.
Overview Experiments such as the Michelson-Morley experiment of 1887 (and later other experiments such as the Trouton-Noble experiment in 1903 or the Trouton-Rankine experiment in 1908), presented evidence against the theory of a medium for light propagation known as the Luminiferous aether; a theory that had been an established part of science for nearly one hundred years at the time. These results cast doubts on what was then a very central assumption of modern science, and later led to the development of special relativity. In an attempt to explain the results of the Michelson-Morley experiment in the context of the assumed medium, aether, many new hypotheses were examined. One of the proposals was that instead of passing through a static and unmoving aether, massive objects at the Earth's surface may drag some of the aether along with them, making it impossible to detect a "wind". Oliver Lodge (1893-1897) was one of the first to perform a test of this theory by using rotating and massive lead blocks in an experiment that attempted to cause an asymmetrical aether wind. His tests yielded no appreciable results differing from previous tests for the aether wind.[1][2] In the 1920s, Dayton Miller conducted repetitions of the Michelson–Morley experiments, which allegedly gave a positive result. However, several experiments conducted afterwards by others gave negative results. Miller claimed that this is due to entrainment of the aether, because the other experiments used heavily enclosed equipments. To test Miller's assertion, Hammar conducted the following experiment using a common path interferometer in 1935.[3][4]
The experiment Using a half-silvered mirror A, he divided a ray of white light into two half-rays. One half-ray was sent in the transverse direction into a pipe surrounded by massive lead blocks. In this pipe, the ray was reflected by mirror D and sent into the longitudinal direction to another mirror C at the other end of the pipe. There it was reflected and sent in the transverse direction to a mirror B outside of the pipe. From B it traveled back to A in the longitudinal direction. The other half-ray traversed the same path in the opposite direction. Similar to Lodge's, this experiment should cause an asymmetry in any proposed aether wind. Hammar's expectation of the results was that: In an experiment without lead blocks, both arms would be equally affected by aether entrainment. While in an experiment with lead blocks in place on one arm, one arm would be more affected by aether entrainment than the other. The following expected propagation times for the counter-propagating rays were given by Robertson/Noonan[4]:
where
is the velocity of the entrained aether. This gives an expected time difference:
The reported result of the Hammar experiment was that, even with the lead blocks in place, the fringe displacements were equal to the ones without any lead block, corresponding to an upper limit of km/s. This is considered a proof against the aether drag hypothesis, as it was proposed by Miller.
32
Hammar experiment
Consequences for Aether drag hypothesis Because differing ideas of "aether drag" existed, the interpretation of all aether drag experiments can be done in the context of each version of the hypothesis. 1. None or partial entrainment by any object with mass. This was discussed by scientists such as Augustin-Jean Fresnel and François Arago. It was refuted by the Michelson-Morley experiment. 2. Complete entrainment within or in the vicinity of all masses. It was refuted by the Aberration of light, Sagnac effect, Oliver Lodge's experiments, and Hammar's experiment. 3. Complete entrainment within or in the vicinity of only very large masses such as Earth. It was refuted by the Aberration of light, Michelson–Gale–Pearson experiment.
References [1] Lodge, Oliver J. (1893). "Aberration Problems" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k559898/ f781). Philosophical Transactions of the Royal Society of London. A 184: 727-804. doi:10.1098/rsta.1893.0015. . [2] Lodge, Oliver J. (1897). "Experiments on the Absence of Mechanical Connexion between Ether and Matter". Philosophical Transactions of the Royal Society of London. A 189: 149-166. [3] G. W. Hammar (1935). "The Velocity of Light Within a Massive Enclosure". Physical Review 48 (5): 462–463. Bibcode 1935PhRv...48..462H. doi:10.1103/PhysRev.48.462.2. [4] H. P. Robertson and Thomas W. Noonan (1968). "Hammar's experiment". Relativity and Cosmology. Philadelphia: Saunders. pp. 36–38.
Ives–Stilwell experiment The Ives–Stilwell experiment exploits the transverse Doppler effect (TDE). This was the first direct, quantitative confirmation of the time dilation factor. Together with the Michelson–Morley and Kennedy–Thorndike experiments, it forms one of the fundamental tests of special relativity theory.[1] Other tests confirming the relativistic Doppler effect, are the Mössbauer rotor experiment and modern Ives–Stilwell experiments. For other time dilation experiments, see Time dilation of moving particles. For general overview, see Tests of special relativity.
Ives–Stilwell experiment The TDE was described by Albert Einstein in his seminal 1905 paper.[2] Einstein subsequently suggested an experiment based on the measurement of the relative frequencies of light perceived as arriving from a light source in motion with respect to the observer. Herbert E. Ives and G. R. Stilwell (although they referred to time dilation as following from the "theory of Lorentz and Larmor") undertook the task of executing the experiment and they came up with a very clever way of separating the much smaller TDE from the much bigger longitudinal Doppler effect. The experiment was executed in 1938[3] and it was reprised multiple times (see, e.g.[4]). Similar experiments were conducted several times with increased precision, by Otting (1939),[5] Mandelberg et al. (1962),[6] Hasselkamp et al. (1979),[7] Ives remarked, that it is nearly impossible to measure the transverse Doppler effect with respect to light rays emitted by canal rays, at right angles to the direction of motion of the canal rays (as it was considered earlier by Einstein), because the influence of the longitudinal effect can hardly be excluded. Therefore he developed a method, to observe the effect in the longitudinal direction of the canal rays' motion. If it is assumed that the speed of light is fixed with respect to the observer (“Classical Theory”), then the forward and rearward Doppler-shifted frequencies seen on a moving object will be f'/f = c/(c±v), where v is recession velocity. Under special relativity, the two frequencies will also include an additional “Lorentz factor” redshift correction. When we invert these relationships so that they relate to wavelengths rather than frequencies, “Classical Theory” predicts redshifted and blueshifted wavelength values of 1+v/c and 1-v/c, so if all three wavelengths (redshifted, blueshifted and original) are marked on a linear scale, according to Classical Theory the three marks should be
33
IvesStilwell experiment
34
perfectly evenly spaced. |.....|.....| But if the light is shifted by special relativity's predictions, the additional Lorentz offset means that the two outer marks will be offset in the same direction with respect to the central mark. |....|......| Ives and Stilwell found that there was a significant offset of the centre of gravity of the three marks, and therefore the Doppler relationship was not that of "Classical Theory". This approach had two main advantages: 1. didn't require us to commit to an exact value for the velocity involved (which might have been theory-dependent), and 2. it didn't require an understanding or interpretation of angular aberration effects, as might have been required for the analysis of a "true" transverse test. A "true transverse test" has been run almost 40 years later, by Hasselkamp in 1979.[7]
Mössbauer rotor experiments Relativistic Doppler effect A more precise confirmation of the relativistic Doppler effect was achieved by the Mössbauer rotor experiments. From a source in the middle of a rotating disk, gamma rays are being sent to a receiver at the rim (in some variations this scheme was reversed). Due to the rotation velocity of the receiver, the absorption frequency decreases if the transverse Doppler effect exists. This effect was actually observed using the Mössbauer effect. The maximal deviation from time dilation was , thus the precision was much higher than that ( ) of the Ives–Stilwell experiments. Such experiments were performed by Hay et al. (1960),[8] Champeney et al. (1963, 1965),[9][10] Kündig (1963).[11] Isotropy of the speed of light Moessbauer rotor experiments were also used to measure a possible anisotropy of the speed of light. That is, a possible aether wind should exert a disturbing influence on the absorption frequency. However, like in all other aether drift experiments (Michelson–Morley experiment), the result was negative, putting an upper limit to aether drift of 3–4 m/s. Experiments of that kind were performed by Champeney & Moon (1961),[12] Champeney et al. (1963)[13] and Turner & Hill (1964).[14]
Modern experiments Further information: Modern searches for Lorentz violation
Fast moving clocks A considerably higher precision has been achieved in modern variations of Ives–Stilwell experiments. In heavy ion storage rings, as the TSR at the MPIK, the Doppler shift of lithium ions traveling at high speeds is evaluated by using Saturated spectroscopy. Due to their frequencies emitted, these ions can be considered as optical atomic clocks of high precision.
IvesStilwell experiment
35
Author
Year Speed
[15]
Grieser et al.
[16]
Saathoff et al.
Maximum deviation from time dilation
1994 0,064c 2003 0,064c
[17] 2007 0,064c
Reinhardt et al.
[18]
Novotny et al.
2009 0,34c
Slow moving clocks Meanwhile, the measurement of time dilation at every day's speeds has been accomplished as well. For that purpose, Chou et al. (2010) used aluminium ions, moving within a 75 m long, phase-stabilized optical fiber. These optical atomic clocks emitted frequencies of a certain frequency, and the sensitivity of this experiment was . Therefore, it was possible to measure a frequency shift due to time dilation of
at speeds below 36 km/h (<
[19]
10 m/s), by comparison of the rates of moving and resting clocks.
References [1] Robertson, H. P. (1949). "Postulate versus Observation in the Special Theory of Relativity". Reviews of Modern Physics 21 (3): 378–382. Bibcode 1949RvMP...21..378R. doi:10.1103/RevModPhys.21.378. [2] Einstein, Albert (1905). "Zur Elektrodynamik bewegter Körper". Annalen der Physik 322 (10): 891–921. Bibcode 1905AnP...322..891E. doi:10.1002/andp.19053221004. English translation: ‘On the Electrodynamics of Moving Bodies’ (http:/ / www. fourmilab. ch/ etexts/ einstein/ specrel/ www/ ) [3] Ives, H. E.; Stilwell, G. R. (1938). "An experimental study of the rate of a moving atomic clock". Journal of the Optical Society of America 28 (7): 215. Bibcode 1938JOSA...28..215I. doi:10.1364/JOSA.28.000215. [4] Ives, H. E.; Stilwell, G. R. (1941). "An experimental study of the rate of a moving atomic clock. II". Journal of the Optical Society of America 31 (5): 369. Bibcode 1941JOSA...31..369I. doi:10.1364/JOSA.31.000369. [5] Otting, G. (1939). "Der quadratische Dopplereffekt". Physikalische Zeitschrift 40: 681–687. [6] Mandelberg, Hirsch I.; Witten, Louis (1962). "Experimental verification of the relativistic doppler effect". Journal of the Optical Society of America 52 (5): 529. Bibcode 1962JOSA...52..529M. [7] Hasselkamp, D.; E. Mondry, A. Scharmann (1979-06-01). "Direct observation of the transversal Doppler-shift". Zeitschrift für Physik A 289 (2): 151–155. Bibcode 1979ZPhyA.289..151H. doi:10.1007/BF01435932. [8] Hay, H. J.; Schiffer, J. P.; Cranshaw, T. E.; Egelstaff, P. A. (1960). "Measurement of the Red Shift in an Accelerated System Using the Mössbauer Effect in Fe57". Physical Review Letters 4 (4): 165–166. Bibcode 1960PhRvL...4..165H. doi:10.1103/PhysRevLett.4.165. [9] Champeney, D. C.; Isaak, G. R.; Khan, A. M. (1963). "Measurement of Relativistic Time Dilatation using the Mössbauer Effect". Nature 198 (4886): 1186–1187. doi:10.1038/1981186b0. [10] Champeney, D. C.; Isaak, G. R.; Khan, A. M. (1965). "A time dilatation experiment based on the Mössbauer effect". Proceedings of the Physical Society 85 (3): 583–593. doi:10.1088/0370-1328/85/3/317. [11] Kündig, Walter (1963). "Measurement of the Transverse Doppler Effect in an Accelerated System". Physical Review 129 (6): 2371–2375. doi:10.1103/PhysRev.129.2371. [12] Champeney, D. C.; Moon, P. B. (1961). "Absence of Doppler Shift for Gamma Ray Source and Detector on Same Circular Orbit". Proceedings of the Physical Society 77 (2): 350–352. doi:10.1088/0370-1328/77/2/318. [13] Champeney, D. C.; Isaak, G. R.; Khan, A. M. (1963). "An 'aether drift' experiment based on the Mössbauer effect". Physics Letters 7 (4): 241–243. doi:10.1016/0031-9163(63)90312-3. [14] Turner, K. C.; Hill, H. A. (1964). "New Experimental Limit on Velocity-Dependent Interactions of Clocks and Distant Matter". Physical Review 134 (1B): 252–256. doi:10.1103/PhysRev.134.B252. [15] Grieser, R.; Klein, R.; Huber, G.; Dickopf, S.; Klaft, I.; Knobloch, P.; Merz, P.; Albrecht, F.; Grieser, M.; Habs, D.; Schwalm, D.; Kühl, T. (1994). "A test of special relativity with stored lithium ions". Applied Physics B Lasers and Optics 59 (2): 127–133. doi:10.1007/BF01081163. [16] Saathoff, G.; Karpuk, S.; Eisenbarth, U.; Huber, G.; Krohn, S.; Horta, R. Muñoz; Reinhardt, S.; Schwalm, D.; Wolf, A.; Gwinner, G. (2003). "Improved Test of Time Dilation in Special Relativity". Phys. Rev. Lett. 91 (19): 190403. Bibcode 2003PhRvL..91s0403S. doi:10.1103/PhysRevLett.91.190403. [17] Reinhardt, S.; Saathoff, G.; Buhr, H.; Carlson, L. A.; Wolf, A.; Schwalm, D.; Karpuk, S.; Novotny, C.; Huber, G.; Zimmermann, M.; Holzwarth, R.; Udem, T.; Hänsch, T. W.; Gwinner, G. (2007). "Test of relativistic time dilation with fast optical atomic clocks at different
IvesStilwell experiment
36
velocities". Nature Physics 3 (12): 861–864. Bibcode 2007NatPh...3..861R. doi:10.1038/nphys778. [18] Novotny, C. et al. (2009). "Sub-Doppler laser spectroscopy on relativistic beams and tests of Lorentz invariance". Physical Review A 80 (2): 022107. doi:10.1103/PhysRevA.80.022107. [19] Chou, C. W.; Hume, D. B.; Rosenband, T.; Wineland, D. J. (2010). "Optical Clocks and Relativity". Science 329 (5999): 1630–1633. Bibcode 2010Sci...329.1630C. doi:10.1126/science.1192720. PMID 20929843.
External links • Roberts, T; Schleif, S; Dlugosz, JM (ed.) (2007). "What is the experimental basis of Special Relativity?" (http:// math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html). Usenet Physics FAQ. University of California, Riverside. • Modern Reenactments of Relativity Tests (http://www.exphy.uni-duesseldorf.de/ResearchInst/FundPhys. html) • M Moriconi, 2006, Special theory of relativity through the Doppler effect (http://www.iop.org/EJ/abstract/ 0143-0807/27/6/015) • Warp Special Relativity Simulator (http://adamauton.com/warp/) Computer program demonstrating the relativistic doppler effect. • The Doppler Effect (http://mathpages.com/home/kmath587/kmath587.htm) at MathPages
Lunar Laser Ranging experiment The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Lasers on Earth are aimed at retroreflectors planted on the Moon during the Apollo program, and the time for the reflected light to return is determined.
The Lunar Laser Ranging Experiment from the Apollo 11 mission.
Lunar Laser Ranging experiment
37
Early tests, Apollo, and Lunokhod The first successful tests were carried out in 1962 when a team from the Massachusetts Institute of Technology succeeded in observing reflected laser pulses using a laser with a millisecond pulse length. Similar measurements were obtained later the same year by a Soviet team at the Crimean Astrophysical Observatory using a Q-switched ruby laser.[1] Greater accuracy was achieved following the installation of a retroreflector array on July 21, 1969, by the crew of Apollo 11, while two more retroreflector arrays left by the Apollo 14 and Apollo 15 missions have also contributed to the experiment. The unmanned Soviet Lunokhod 1 and Lunokhod 2 rovers carried smaller arrays. Reflected signals were initially received from Lunokhod 1, but no return signals were detected after 1971 until a team from University of California rediscovered the array in April 2010 using images from NASA’s Lunar Reconnaissance Orbiter.[2] Lunokhod 2's array continues to return signals to Earth.[3] The Lunokhod arrays suffer from decreased performance in direct sunlight, a factor which was considered in the reflectors placed during the Apollo missions.[4]
Apollo 15 LRRR.
The Apollo 15 array is three times the size of the arrays left by the two earlier Apollo missions. Its size made it the target of three-quarters of the sample measurements taken in the first 25 years of the experiment. Improvements in technology since then have resulted in greater use of the smaller arrays, by sites such as the Côte d'Azur Observatory in Apollo 15 LRRR schematic. Grasse, France, and the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) at the Apache Point Observatory in New Mexico. The first measurements were made by the McDonald Observatory in Texas, although lunar laser ranging at this site stopped in 2009.[5] Although this (i.e., the report that lunar laser ranging was discontinued at McDonald Observatory) was the case at the time of that interview, temporary and interim funding has been procured and lunar laser ranging at McDonald Observatory continues into its fourth decade of operation.
Details The distance to the Moon is calculated approximately using this equation: Distance = (Speed of light × Time taken for light to reflect) / 2. In actuality, the round-trip time of about 2½ seconds is affected by the relative motion of the Earth and the Moon, the rotation of the Earth, lunar libration, weather, polar motion, propagation delay through Earth's atmosphere, the motion of the observing station due to crustal motion and tides, velocity of light in various parts of air and relativistic effects.[6] Nonetheless, the Earth-Moon distance has been measured with increasing accuracy for more than 35 years. The distance continually changes for a number of reasons, but averages about 384,467 kilometers (238,897 miles). At the Moon's surface, the beam is only about 6.5 kilometers (four miles) wide[7] and scientists liken the task of aiming the beam to using a rifle to hit a moving dime 3 kilometers (approximately two miles) away. The reflected light is too weak to be seen with the human eye: out of 1017 photons aimed at the reflector, only one will be received back on Earth every few seconds, even under good conditions. They can be identified as originating from the laser because the laser is highly monochromatic. This is one of the most precise distance measurements ever made, and is equivalent in accuracy to determining the distance between Los Angeles and New York to one hundredth of an
Lunar Laser Ranging experiment
38
inch.[4][8] As of 2002 work is progressing on increasing the accuracy of the Earth-Moon measurements to near millimeter accuracy, though the performance of the reflectors continues to degrade with age.[4]
Results Some of the findings of this long-term experiment are: • The Moon is spiraling away from Earth at a rate of 3.8 cm per year.[7] This rate has been described as anomalously high.[9] • The Moon probably has a liquid core of about 20% of the Moon's radius.[3] • The universal force of gravity is very stable. The experiments have put an upper limit on the change in Newton's gravitational constant G of less than 1 part in 1011 since 1969.[3] • The likelihood of any "Nordtvedt effect" (a composition-dependent differential acceleration of the Moon and Earth towards the Sun) has been ruled out to high precision,[10][11] strongly supporting the validity of the Strong Equivalence Principle. • Einstein's theory of gravity (the general theory of relativity) predicts the Moon's orbit to within the accuracy of the laser ranging measurements.[3] The presence of reflectors on the Moon has been used to rebut claims that the Apollo landings were faked. For example, the APOLLO Collaboration photon pulse return graph, shown here, has a pattern consistent with a retroreflector array near a known landing site.
Photo gallery
Apollo 14 Lunar Ranging Retro Reflector (LRRR).
APOLLO Collaboration photon pulse return times
Lunar Laser Ranging ground station in Wetzell, Bavaria, Germany.
The Laser Ranging Facility.
Lunokhod 1 – the small structure on the left is the retroreflector.
Lunar Laser Ranging experiment
References [1] Bender, P. L., The Lunar Laser Ranging Experiment, UCSD (http:/ / www. physics. ucsd. edu/ ~tmurphy/ apollo/ doc/ Bender. pdf) [2] McDonald, Kim (April 26, 2010). "UC San Diego Physicists Locate Long Lost Soviet Reflector on Moon" (http:/ / ucsdnews. ucsd. edu/ newsrel/ science/ 04-26SovietReflector. asp). UCSD. . Retrieved 27 April 2010. [3] James G. Williams and Jean O. Dickey. "Lunar Geophysics, Geodesy, and Dynamics" (http:/ / ilrs. gsfc. nasa. gov/ docs/ williams_lw13. pdf) (PDF). ilrs.gsfc.nasa.gov. . Retrieved 2008-05-04. 13th International Workshop on Laser Ranging, October 7–11, 2002, Washington, D. C. [4] "It’s Not Just The Astronauts That Are Getting Older" (http:/ / www. universetoday. com/ 2010/ 03/ 10/ itâs-not-just-the-astronauts-that-are-getting-older/ ). Universe Today. March 10, 2010. . Retrieved 10 March 2010. [5] McKie, Robin (June 21, 2009), "After 40 years' reflection, laser Moon mirror project is axed" (http:/ / www. guardian. co. uk/ technology/ 2009/ jun/ 21/ mcdonald-observatory-space-laser-funding), The Guardian, . [6] Seeber, Gunter. Satellite Geodesy 2nd Edition. de Gruyter, 2003, p. 439 [7] Fred Espenek (August 1994). "NASA - Accuracy of Eclipse Predictions" (http:/ / eclipse. gsfc. nasa. gov/ SEhelp/ ApolloLaser. html). eclipse.gsfc.nasa.gov. . Retrieved 2008-05-04. [8] "Apollo 11 Experiment Still Going Strong after 35 Years" (http:/ / www. jpl. nasa. gov/ news/ features. cfm?feature=605). www.jpl.nasa.gov. July 20, 2004. . Retrieved 2008-05-04. [9] Bills, B.G., and Ray, R.D. (1999), "Lunar Orbital Evolution: A Synthesis of Recent Results" (http:/ / www. agu. org/ pubs/ crossref/ 1999/ 1999GL008348. shtml), Geophysical Research Letters 26 (19): 3045-3048, doi:10.1029/1999GL008348, [10] Adelberger, E.G., Heckel, B.R., Smith, G., Su, Y., and Swanson, H.E. (1990-Sep-20), "Eötvös experiments, lunar ranging and the strong equivalence principle" (http:/ / www. nature. com/ nature/ journal/ v347/ n6290/ abs/ 347261a0. html), Nature 347 (6290): 261–263, Bibcode 1990Natur.347..261A, doi:10.1038/347261a0, [11] Williams, J.G., Newhall, X.X., and Dickey, J.O. (1996), "Relativity parameters determined from lunar laser ranging" (http:/ / prola. aps. org/ abstract/ PRD/ v53/ p6730_1), Phys. Rev. D 53: 6730–6739, Bibcode 1996PhRvD..53.6730W, doi:10.1103/PhysRevD.53.6730,
External links • Apollo 14 Laser Ranging Retroreflector Experiment (http://www.lpi.usra.edu/expmoon/Apollo15/ A15_Experiments_LRRR.html) • History of Laser Ranging (http://www.csr.utexas.edu/mlrs/history.html) • Lunar Retroreflectors History and Position (http://physics.ucsd.edu/~tmurphy/apollo/lrrr.html) • Station de Télémétrie Laser-Lune (http://www.obs-azur.fr/cerga/laser/laslune/llr.htm) in Grasse, France • 2002 article about "UW researcher plans project to pin down moon's distance from Earth" (http://www. washington.edu/newsroom/news/2002archive/01-02archive/k011402.html) • NASA: What Neil & Buzz Left on the Moon (http://science.nasa.gov/science-news/science-at-nasa/2004/ 21jul_llr/) • CNN: Apollo 11 Experiment Still Returning Results after 30 Years (http://www.cnn.com/TECH/space/9907/ 21/apollo.experiment/)
39
KennedyThorndike experiment
Kennedy–Thorndike experiment The Kennedy–Thorndike experiment first conducted in 1932, is a modified form of the Michelson–Morley experimental procedure, and tests special relativity.[1] [2] The modification is to make one arm of the classical Michelson–Morley (MM) apparatus shorter than the other one. While the Michelson-Morley experiment showed, that the speed of light is independent of the orientation of the apparatus, the Kennedy–Thorndike experiment showed that it is also independent of the velocity of the apparatus in different inertial frames. It also served as a test to indirectly verify time dilation: while the negative result of the Michelson-Morley experiment can be explained by length contraction alone, the negative result of the Kennedy–Thorndike experiment also requires time dilation besides length contraction to explain why no phase shifts will be detected while the earth moves around the sun. The first direct confirmation of time dilation was achieved by the Ives–Stilwell experiment. See also Tests of special relativity.
The experiment The original Michelson–Morley experiment was useful for testing the Lorentz–FitzGerald contraction hypothesis only. Kennedy had already made several increasingly sophisticated versions of the MM experiment through the 1920s when he struck upon a way to test time dilation as well. In their own words: The principle on which this experiment is based is the simple proposition that if a beam of homogeneous light is split [...] into two beams which after traversing paths of different lengths are brought together again, then the relative phases […] will depend [] on the velocity of the apparatus unless the frequency of the light depends […] on the velocity in the way required by relativity. By making one arm of the experiment much shorter than the other, a change in speed of the earth would cause changes in the travel times of the light rays, from which a fringe shift would result except if the frequency of the light source would change to the same degree. In order to determine if such a fringe shift took place, the interferometer was made extremely stable and the interference patterns were photographed for later comparison. The tests were done over a period of many months. As no significant fringe shift was found, the experimenters concluded that time dilation occurs as predicted by Special relativity.
Recent experiments Further information: Modern searches for Lorentz violation Such experiments have been repeated with increased precision until today, using laser, maser, cryogenic optical resonators, etc.. Examples that considerably reduce the possibility of anisotropy, are Hils and Hall (1990),[3] Braxmeier et al. (2002),[4] Wolf et al. (2004).[5] Tobar et al. (2009)[6] which gave an upper limit of the velocity dependence of the speed of light of . Besides those terrestrial measurements, a Kennedy–Thorndike experiment was carried out by Müller & Soffel (1995) using Lunar Laser Ranging, i.e., signals between Earth and Moon have been evaluated. This experiment gave a negative result as well.[7]
40
KennedyThorndike experiment
41
References [1] Kennedy, R. J.; Thorndike, E. M. (1932). "Experimental Establishment of the Relativity of Time". Physical Review 42 (3): 400–418. Bibcode 1932PhRv...42..400K. doi:10.1103/PhysRev.42.400. [2] Robertson, H. P. (1949). "Postulate versus Observation in the Special Theory of Relativity". Reviews of Modern Physics 21 (3): 378–382. Bibcode 1949RvMP...21..378R. doi:10.1103/RevModPhys.21.378. [3] Hils, Dieter; Hall, J. L. (1990). "Improved Kennedy-Thorndike experiment to test special relativity". Phys. Rev. Lett. 64 (15): 1697–1700. Bibcode 1990PhRvL..64.1697H. doi:10.1103/PhysRevLett.64.1697. PMID 10041466. [4] Braxmaier, C.; Müller, H.; Pradl, O.; Mlynek, J.; Peters, A.; Schiller, S. (2002). "Tests of Relativity Using a Cryogenic Optical Resonator". Phys. Rev. Lett. 88 (1): 010401. Bibcode 2002PhRvL..88a0401B. doi:10.1103/PhysRevLett.88.010401. PMID 11800924. [5] Wolf, P.; Tobar, M. E.; Bize, S.; Clairon, A.; Luiten, A. N.; Santarelli, G. (2004). "Whispering Gallery Resonators and Tests of Lorentz Invariance". General Relativity and Gravitation 36 (10): 2351–2372. arXiv:gr-qc/0401017. Bibcode 2004GReGr..36.2351W. doi:10.1023/B:GERG.0000046188.87741.51. [6] Tobar, M. E.; Wolf, P.; Bize, S.; Santarelli, G.; Flambaum, V. (2010). "Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser". Physical Review D 81 (2): 022003. arXiv:0912.2803. Bibcode 2010PhRvD..81b2003T. doi:10.1103/PhysRevD.81.022003. [7] Müller, J.; Soffel, M. H. (1995). "A Kennedy-Thorndike experiment using LLR data". Physics Letters A 198 (2): 71–73. Bibcode 1995PhLA..198...71M. doi:10.1016/0375-9601(94)01001-B.
Michelson–Gale–Pearson experiment The Michelson–Gale–Pearson experiment (1925) is a modified version of the Michelson-Morley experiment and the Sagnac-Interferometer. It measured the Sagnac effect due to Earth's rotation, and thus tests the theories of special relativity and luminiferous ether along the rotating frame of Earth.
Experiment The aim, as it was first proposed by Albert Abraham Michelson in 1904 and then executed in 1925, was to find out whether the rotation of the Earth has an effect on the propagation of light in the vicinity of the Earth.[1][2] [3] The Michelson-Gale experiment was a very large ring interferometer, (a perimeter of 1.9 kilometer), large enough to detect the angular velocity of the Earth. Like the original Michelson-Morley experiment, the Michelson-Gale-Pearson version compared the light from a single source (carbon arc) after travelling in two directions. The major change was to replace the two "arms" of the original MM version with two rectangles, one much larger than the other. Light was sent into the rectangles, reflecting off mirrors at the corners, and returned to the starting point. Light exiting the two rectangles was compared on a screen just as the light returning from the two arms would be in a standard MM experiment. The expected fringe shift in accordance with the stationary aether and special relativity was given by Michelson as:
where light,
is the displacement in fringes, the angular velocity of Earth,
the area in square kilometers,
the latitude (41° 46'),
the speed of
the effective wave-length used. In other words, this experiment was aimed
to detect the Sagnac effect due to Earth's rotation.[4][5]
Result The outcome of the experiment was that the angular velocity of the Earth as measured by astronomy was confirmed to within measuring accuracy. The ring interferometer of the Michelson-Gale experiment was not calibrated by comparison with an outside reference (which was not possible, because the setup was fixed to the Earth). From its design it could be deduced where the central interference fringe ought to be if there would be zero shift. The measured shift was 230 parts in 1000, with an accuracy of 5 parts in 1000. The predicted shift was 237 parts in 1000. According to Michelson/Gale, the experiment is compatible with both the idea of a stationary ether and special
MichelsonGalePearson experiment
42
relativity. As it was already pointed out by Michelson in 1904, a positive result in such experiments contradicts the hypothesis of complete aether drag. On the other hand, the stationary ether concept is in agreement with this result, yet it contradicts (with the exception of Lorentz's ether) the Michelson-Morley experiment. Thus special relativity is the only theory which explains both experiments[6]. The experiment is consistent with relativity for the same reason as all other Sagnac type experiments (see Sagnac effect). That is, rotation is absolute in special relativity, because there is no inertial frame of reference in which the whole device is at rest during the complete process of rotation, thus the light paths of the two rays are different in all of those frames, consequently a positive result must occur. It's also possible to define rotating frames in special relativity (Born coordinates), yet in those frames the speed of light is not constant in extended areas any more, thus also in this view a positive result must occur. Today, Sagnac type effects due to Earth's rotation are routinely incorporated into GPS.
References [1] Michelson, A.A. (1904). "Relative Motion of Earth and Aether". Philosophical Magazine 8 (48): 716–719. [2] Michelson, A. A. (1925). "The Effect of the Earth's Rotation on the Velocity of Light, I.". Astrophysical Journal 61: 137. Bibcode 1925ApJ....61..137M. doi:10.1086/142878. [3] Michelson, A. A.; Gale, Henry G. (1925). "The Effect of the Earth's Rotation on the Velocity of Light, II.". Astrophysical Journal 61: 140. Bibcode 1925ApJ....61..140M. doi:10.1086/142879. [4] Anderson, R., Bilger, H.R., Stedman, G.E. (1994). "Sagnac effect: A century of Earth-rotated interferometers". Am. J. Phys. 62 (11): 975–985. Bibcode 1994AmJPh..62..975A. doi:10.1119/1.17656. [5] Stedman, G. E. (1997). "Ring-laser tests of fundamental physics and geophysics". Reports on Progress in Physics 60 (6): 615–688. Bibcode 1997RPPh...60..615S. doi:10.1088/0034-4885/60/6/001. [6] Georg Joos: Lehrbuch der theoretischen Physik. 12. edition, 1959, page 448
Michelson–Morley experiment The Michelson–Morley experiment was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University in Cleveland, Ohio.[1] It was aimed at detecting the relative motion of matter relative to the stationary luminiferous aether ("aether wind"). The negative results are generally considered to be the first strong evidence against the then prevalent aether theory, and initiated a line of research that eventually led to special relativity, in which the classical aether concept has no role.[2] The experiment has also been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution".[3]
Figure 1. Michelson and Morley's interferometric setup, mounted on a stone slab and floating in a pool of mercury.
Michelson-Morley type experiments have been constantly repeated. For instance, modern resonator experiments confirmed the absence of any aether wind at the level.[4][5] For a general overview, see also Tests of special relativity.
MichelsonMorley experiment
43
Measuring aether Physics theories of the late 19th century assumed that just as water waves must have an intervening substance, i.e. a "medium", to move across (in this case water), and audible sound requires a medium to transmit its wave motions (such as air or water), so light must also require a medium, the "luminiferous aether", to transmit its wave motions. Because light can travel through a vacuum, it was assumed that even a vacuum must be filled with aether. Because the speed of light is so great, and because material bodies pass through the aether without obvious friction or drag, the aether was assumed to have a highly unusual combination of properties. Designing experiments to test the properties of the aether was a high priority of 19th century physics. Earth travels a tremendous distance in its orbit around the Sun, at a speed of around 30 km/s (18.75 mi/s) or over 108,000 km/hr (67,500 mi/hr). The Sun itself is travelling about the Galactic Center at even greater speeds, and there are other motions at higher levels of the structure of the universe. Since the Earth is in motion, two main possibilities were considered. a) That the aether is stationary and only partially dragged by Earth (proposed by Augustin-Jean Fresnel). b) That the aether is completely dragged by Earth and thus shares its motion at Earth's surface (proposed by George Gabriel Stokes). Fresnel's hypothesis of an (almost) stationary aether was preferred because it was confirmed by the Fizeau experiment and the aberration of light.[6] According to this hypothesis, Earth and the aether are in relative motion, thus a so called "aether wind" (Fig. 2) should exist. Although it would be possible, in theory, for the Earth's motion to match that of the aether at one moment in time, it was not possible for the Earth to remain at rest with respect to the aether at all times, because of the variation in both the direction and the speed of the motion. At any given point on the Earth's surface, the magnitude and direction of the wind would vary with time of day and season. By analysing the return speed of light in different directions at various different times, it was thought to be possible to measure the motion of the Earth relative to the aether.
Figure 2. A depiction of the concept of the "aether wind"
The expected relative difference in the measured speed of light was quite small, given that the velocity of the Earth in its orbit around the Sun was about one hundredth of one percent of the speed of light. A number of physicists had attempted to make this measurement during the mid-19th century (see Negative aether-drift experiments), however the results were all negative. Those experiments were only capable of measuring anisotropy effects of first order in v/c (v being Earth's velocity, c the speed of light), and the negative result could be explained by using Fresnel's dragging coefficient, according to which the aether and thus light is partially dragged by moving matter. In order to avoid this problem, arrangements capable of measuring second order effects were necessary, though this accuracy was simply too great for existing experimental setups. For instance, the Fizeau–Foucault apparatus could measure the speed of light to perhaps 5% accuracy, not nearly enough to make second order aether wind measurements.
MichelsonMorley experiment
44
1881 and 1887 experiments Michelson experiment (1881) Michelson had a solution to the problem of how to construct a device sufficiently accurate to detect aether flow. While teaching at his alma mater in 1877, the U.S. Naval Academy in Annapolis, Michelson conducted his first known light speed experiments as a part of a classroom demonstration. He left active U.S. Naval service in 1881 while he was in Germany concluding studies. In that year, Michelson used a prototype experimental device to make several more measurements.
Figure 3. Michelson's 1881 interferometer. Although ultimately proving incapable of distinguishing between differing theories of aether-dragging, its construction provided important lessons for the design of Michelson and Morley's 1887 [7] instrument.
The device he designed, later known as a Michelson interferometer, sent yellow light from a sodium flame (for alignment), or white light (for the actual observations), through a half-silvered mirror that was used to split it into two beams travelling at right angles to one another. After leaving the splitter, the beams travelled out to the ends of long arms where they were reflected back into the middle on small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference based on the spent time to transit the arms. If the Earth is traveling through an aether medium, a beam reflecting back and forth parallel to the flow of aether would take longer than a beam reflecting perpendicular to the aether because the time gained from traveling downwind is less than that lost traveling upwind. Michelson expected that the Earth's motion would produce a fringe shift 4% the size of a single fringe. Michelson did not observe the expected 0.04 fringe shift; the greatest average deviation that he measured (in the northwest direction) was only 0.018 fringes, while most of his measurements were much less. His conclusion was to rule out Fresnel's hypothesis of a stationary aether with partial aether dragging, confirming Stokes' hypothesis of complete aether dragging.[8] Alfred Potier (and later Hendrik Lorentz) pointed out to Michelson, however, that he had made an error of calculation, and that the expected fringe shift should only have been 0.02 fringes. Thus, Michelson's apparatus had experimental errors far too large to say anything conclusive about the aether wind. For a definitive measurement of the aether wind, a much more accurate and tightly controlled experiment would have to be carried out. The prototype was, however, successful in demonstrating that the basic method was feasible.[6][9]
Potier's and Lorentz's corrections Michelson obtained for the beam travel time in longitudinal direction
where
is the travel time in direction of motion,
in the opposite direction, and
the length of the
interferometer arm. However, for the transverse direction, Michelson obtained the incorrect expression
because he overlooked that the aether wind also affects the transverse beam travel time. The result would be a delay in one of the light beams that could be detected when the beams were recombined through interference. Any slight change in the spent time would then be observed as a shift in the positions of the interference fringes. If the aether
MichelsonMorley experiment
45
were stationary relative to the Sun, Michelson expected (using his incorrect formula) that the Earth's motion would produce a fringe shift 4% the size of a single fringe of yellow light. Michelson did not observe the expected 0.04 fringe shift; the maximum possible shift was at most only about 0.02 fringes. He concluded that there is no measurable aether drift.[8] However, as was shown by Potier and Lorentz (1886), the correct value for the transverse travel time is
and the fringe shift calculated from the difference between
where
and
is given by
is the wavelength. Lorentz pointed out that when the correct transverse travel time is considered, the
expected result in Michelson's experiment is reduced by half to approximately 0.02 fringes, which is nearly equal to the estimated experimental errors.[6]
Michelson–Morley experiment (1887)
MichelsonMorley experiment
46
Starting in 1885, Michelson collaborated with Edward Morley, spending considerable time and money to repeat the Fizeau experiment on Fresnel's drag coefficient (finished in 1886),[11] and to repeat the Michelson experiment (finished in 1887).[1] At this time Michelson was professor of physics at the Case School of Applied Science, and Morley was professor of chemistry at Western Reserve University, which shared a campus with the Case School on the eastern edge of Cleveland. Michelson suffered a nervous breakdown in September 1885, from which he recovered in October 1885. Morley ascribed this breakdown to the intense work of Michelson during the preparation of the experiments. In 1886, Michelson and Morley successfully confirmed Fresnel's drag coefficient - this result was also considered as a confirmation of the stationary aether concept.[2] This strengthened the hope of finding the aether wind. Thus Michelson and Morley created an improved version of the Michelson experiment with more than enough accuracy to detect this hypothetical effect. The experiment was performed in several periods of concentrated observations between April and July 1887, in Adelbert Dormitory of WRU (later renamed Pierce Hall, demolished in 1962).[12][13]
Figure 4. This figure illustrates the folded light path used in the Michelson-Morley interferometer that enabled a path length of 11 m. a is the light source, an oil lamp. b is a beam splitter. c is a compensating plate so that both the reflected and transmitted beams travel through the same amount of glass (important since experiments were run with white light which has an extremely short coherence length requiring precise matching of optical path lengths for fringes to be visible; monochromatic sodium light was used only for initial [8][10] alignment ). d, d' and e are mirrors. e' is a fine adjustment mirror. f is a telescope.
As shown in Fig. 4, the light was repeatedly reflected back and forth along the arms of the interferometer, increasing the path length to 11 m. At this length, the drift would be about 0.4 fringes. To make that easily detectable, the apparatus was assembled in a closed room in the basement of the heavy stone dormitory, eliminating most thermal and vibrational effects. Vibrations were further reduced by building the apparatus on top of a large block of sandstone (Fig. 1), about a foot thick and five feet square, which was then floated in an annular trough of mercury. They calculated that effects of about 1/100th of a fringe would be detectable.
MichelsonMorley experiment
Michelson and Morley and other early experimentalists using interferometric techniques in an attempt to measure the properties of the luminiferous aether, used monochromatic light only for initially setting up their equipment, always switching to white light for the actual measurements. The reason is that measurements were recorded visually. Monochromatic light would result in a uniform fringe pattern. Lacking modern means of environmental temperature control, the fringes showed continual drift even though the interferometer might be set up in a basement. Since the fringes would occasionally disappear Figure 5. Fringe pattern produced with a due to vibrations by passing horse traffic, distant thunderstorms and the Michelson interferometer using white light. As like, it would be easy to "get lost" when the fringes returned to configured here, the central fringe is white rather visibility. The advantages of white light, which produced a distinctive than black. colored fringe pattern, far outweighed the difficulties of aligning the apparatus due to its low coherence length. As Dayton Miller wrote, "White light fringes were chosen for the observations because they consist of a small group of fringes having a central, sharply defined black fringe which forms a permanent zero reference mark for all readings."[14][15] The mercury pool allowed the device to be easily turned, so that given a single steady push it would slowly rotate through the entire range of possible angles to the "aether wind", while measurements were continuously observed by looking through the eyepiece. Even over a period of minutes, it was presumed that some sort of effect would be noticed, since one of the arms would inevitably turn into the direction of the wind and the other away. It was expected that the effect would be graphable as a sine wave with two peaks and two troughs per rotation of the device. This is because during each full rotation, each arm would be parallel to the wind twice (facing into and away from the wind giving identical readings) and perpendicular to the wind twice. Additionally, due to the Earth's rotation, the wind would be expected to show periodic changes in direction and magnitude during the course of a sidereal day. Because of the motion of the Earth around the Sun, it was expected that yearly cycles would also be detectable in the measured data. Imagine a helicopter flying forward. While hovering, a helicopter's blades would be measured as travelling around typically at 300 mph at the tips. However, if the helicopter is travelling forward at 150 mph, there are points where the tips of the blades are travelling through the air at 150 mph (downwind) and 450 mph (upwind). The same effect would cause the magnitude of an aether wind to decrease and increase on a yearly basis.
47
MichelsonMorley experiment
Most famous "failed" experiment After all this thought and preparation, the experiment became what has been called the most famous failed experiment in history.[16] Instead of providing insight into the properties of the aether, Michelson and Morley's article in the American Journal of Science reported the measurement to be as small as one-fortieth of the expected displacement (see Fig. 6), but "since the displacement is proportional to the square of Figure 6. Michelson and Morley's results. The upper solid line is the curve for their the velocity" they concluded that the observations at noon, and the lower solid line is that for their evening observations. measured velocity was "probably less than Note that the theoretical curves and the observed curves are not plotted at the same one-sixth" of the expected velocity of the scale: the dotted curves, in fact, represent only one-eighth of the theoretical displacements. Earth's motion in orbit and "certainly less than one-fourth." Although this small "velocity" was measured, it was considered far too small to be used as evidence of speed relative to the aether, and it was later said to be within the range of an experimental error that would allow the speed to actually be zero. From the standpoint of the then current aether models, the experimental results were conflicting. The Fizeau experiment and the repetition of Michelson and Morley (1886) apparently confirmed the stationary aether with partial aether dragging, and refuted complete aether dragging. On the other hand, the much more precise Michelson–Morley experiment (1887) apparently confirmed complete aether dragging and refuted the stationary aether.[6] In addition, the Michelson-Morley null result was further substantiated by the null results of other second-order experiments of different kind, namely the Trouton–Noble experiment (1903) and the Experiments of Rayleigh and Brace (1902–1904). These problems and their solution led to the development of the Lorentz transformation and special relativity (see Fallout).
48
MichelsonMorley experiment
Subsequent experiments Although Michelson and Morley went on to different experiments after their first publication in 1887, both remained active in the field. Other versions of the experiment were carried out with increasing [17][18] sophistication. Morley was not convinced of his own results, and went on to conduct additional experiments with Dayton Miller from 1902 to 1904. Again, the result was negative within the margins of error.[19][20] Miller worked on increasingly larger interferometers, culminating in one with a 32 m (effective) arm length that he tried at various sites including on top of a mountain at the Mount Wilson observatory. To avoid the possibility of the aether wind being Figure 7. Simulation of the Kennedy/Illingworth refinement of the blocked by solid walls, his mountain top Michelson-Morley experiment. (a) Michelson-Morley interference pattern in monochromatic mercury light, with a dark fringe precisely centered on the screen. observations used a special shed with thin (b) The fringes have been shifted to the left by 1/100 of the fringe spacing. It is walls, mainly of canvas. From noisy, extremely difficult to see any difference between this figure and the one above. (c) irregular data, he consistently extracted a A small step in one mirror causes two views of the same fringes to be spaced 1/20 small positive signal that varied with each of the fringe spacing to the left and to the right of the step. (d) A telescope has been set to view only the central dark band around the mirror step. Note the symmetrical rotation of the device, with the sidereal day, brightening about the center line. (e) The two sets of fringes have been shifted to and on a yearly basis. His measurements in the left by 1/100 of the fringe spacing. An abrupt discontinuity in luminosity is the 1920s amounted to approximately visible across the step. 10 km/s instead of the nearly 30 km/s expected from the Earth's orbital motion alone. He remained convinced this was due to partial entrainment or aether dragging, though he did not attempt a detailed explanation, and ignored critiques demonstrating the inconsistency of his results, and the refutation by the Hammar experiment.[21][21] Miller's findings were considered important at the time, and were discussed by Michelson, Lorentz and others at a meeting reported in 1928.[22] There was general agreement that more experimentation was needed to check Miller's results. Miller later built a non-magnetic device to eliminate magnetostriction, while Michelson built one of non-expanding Invar to eliminate any remaining thermal effects. Others from around the world increased accuracy, eliminated possible side effects, or both. To date, no-one has been able to replicate Miller's results, and modern experimental accuracies are considered to have ruled them out.[23] Roberts (2006) has pointed out that the primitive data reduction techniques used by Miller and other early experimentalists, including Michelson and Morley, were capable of creating apparent periodic signals even when none existed in the actual data. After reanalyzing Miller's original data using modern techniques of quantitative error analysis, Roberts found Miller's apparent signals to be statistically insignificant.[24] Using a special optical arrangement involving a 1/20 wave step in one mirror, Roy J. Kennedy (1926) and K. K. Illingworth (1927) (Fig. 7) converted the task of detecting fringe shifts from the relatively insensitive one of estimating their lateral displacements, to the considerably more sensitive task of adjusting the light intensity on both sides of a sharp boundary for equal luminance.[25][26] If they observed unequal illumination on either side of the step, such as in Fig. 6e, they would add or remove calibrated weights from the interferometer until both sides of the step were once again evenly illuminated, as in Fig. 6d. The number of weights added or removed provided a measure of
49
MichelsonMorley experiment
50
the fringe shift. Different observers could detect changes as little as 1/300th to 1/1500th of a fringe. Kennedy also carried out an experiment at Mount Wilson, finding only about 1/10 the drift measured by Miller and no seasonal effects.[22] In 1930, Georg Joos conducted an experiment using an automated interferometer with 21 m long arms forged from pressed quartz having extremely low thermal coefficient of expansion, that took continuous photographic strip recordings of the fringes through dozens of revolutions of the apparatus. Displacements of 1/1000th of a fringe could be measured on the photographic plates. No periodic fringe displacements were found, placing an upper limit to the aether wind of 1.5 km/s.[27] The expected values are related to the relative speed between Earth and Sun of 30 km/s. With respect to the speed of the solar system around the galactic center of ca. 220 km/s, or the speed of the solar system relative to the CMB rest frame of ca. 368 km/s, the zero results of those experiments are even more obvious. Name
Location
[8]
Michelson
Potsdam
Michelson and Cleveland [1] Morley
Year
Arm Fringe Fringe Ratio length shift shift (meters) expected measured
Upper Limit on Vaether
Experimental Resolution
Null result
1881
1.2
0.04
≤ 0.02
2
∼ 20 km/s
0.02
yes
1887
11.0
0.4
< 0.02 or ≤ 0.01
40
∼ 4–8 km/s
0.01
yes
Cleveland
1902–1904 32.2
1.13
≤ 0.015
80
∼ 3.5 km/s 0.015
yes
[28]
Mt. Wilson
1921
32.0
1.12
≤ 0.08
15
∼ unclear 8–10 km/s
unclear
Miller
[28]
Cleveland
1923–1924 32.0
1.12
≤ 0.03
40
∼ 5 km/s
0.03
yes
Miller [28] (sunlight)
Cleveland
1924
32.0
1.12
≤ 0.014
80
∼ 3 km/s
0.014
yes
Tomaschek [29] (star light)
Heidelberg
1924
8.6
0.3
≤ 0.02
15
∼ 7 km/s
0.02
yes
Mt. Wilson
1925–1926 32.0
1.12
≤ 0.088
13
∼ unclear 8–10 km/s
unclear
Morley and [19][20] Miller Miller
[28][14]
Miller
Pasadena/Mt. 1926 Wilson
2.0
0.07
≤ 0.002
35
∼ 5 km/s
0.002
yes
Illingworth
Pasadena
1927
2.0
0.07
≤ 0.0004
175
∼ 2 km/s
0.0004
yes
Piccard & [30] Stahel
with a Balloon
1926
2.8
0.13
≤ 0.006
20
∼ 7 km/s
0.006
yes
Piccard & [31] Stahel
Brussels
1927
2.8
0.13
≤ 0.0002
185
∼ 2.5 km/s 0.0007
yes
Piccard & [32] Stahel
Rigi
1927
2.8
0.13
≤ 0.0003
185
∼ 2.5 km/s 0.0007
yes
Michelson et [33] al.
Mt. Wilson
1929
25.9
0.9
≤ 0.01
90
∼ 3 km/s
yes
Jena
1930
21.0
0.75
≤ 0.002
375
∼ 1.5 km/s 0.002
[25]
Kennedy
[26]
[27]
Joos
0.01
yes
MichelsonMorley experiment
51
Recent experiments Further information: Modern searches for Lorentz violation In recent times experiments similar to the Michelson–Morley experiment have become commonplace. Lasers and masers amplify light by repeatedly bouncing it back and forth inside a carefully tuned cavity, thereby inducing high-energy atoms in the cavity to give off more light. The result is an effective path length of kilometers. The light emitted in one cavity can be used to start the same cascade in another set at right angles, thereby creating an interferometer of extreme accuracy.[35] The first such experiment was led by Charles H. Townes, one of the co-creators of the first maser. Their 1958 experiment put an upper limit on drift, including any possible experimental errors, of only 30 m/s. In 1974 a repeat with accurate lasers in the triangular Trimmer experiment reduced this to 0.025 m/s, and included tests of entrainment by placing one leg in glass. [36]
Figure 8. Michelson-Morley experiment with cryogenic optical resonators of a [34] form such as was used by Müller et al. (2003). Two optical resonators constructed from crystalline sapphire, controlling the frequencies of two lasers, are set at right angles within a helium cryostat. A frequency comparator measures the beat frequency of the combined outputs of the two resonators.
The most precise experiments of this kind (using laser, maser, cryogenic optical resonators, etc.) were made in recent years. In some of them, the devices were rotated or remained stationary, and some were combined with the Kennedy–Thorndike experiment. As of 2009, the precision by which anisotropy of the speed of light can be excluded in resonator experiments, is at the level. Different isotropy tests achieving an even higher precision are called Clock comparison or Hughes-Drever experiments, by which the isotropy in the energy levels of nucleons and electrons can be measured. Author
Year
[37]
Brillet & Hall
[38]
1979 2003
Wolf et al.
[34]
Müller et al.
2003
[39]
2004
[40]
2004
Wolf et al. Wolf et al.
[41]
2005
[42]
2005
Antonini et al. Stanwix et al.
[43] 2005
Herrmann et al.
[44]
Stanwix et al.
[45]
Müller et al.
2006 2007
Maximum anisotropy of c
MichelsonMorley experiment
52 [4]
2009
Eisele et al.
[5]
Herrmann et al.
2009
Fallout Length contraction and special relativity Further information: History of special relativity The correct path to the solution of this problem was found in the FitzGerald–Lorentz contraction hypothesis, now simply called length contraction or Lorentz contraction, first proposed by George Fitzgerald (1889) and Hendrik Lorentz (1892). According to this physical law all objects physically contract along the line of motion (originally thought to be relative to the aether), so while the light may indeed transit slower on that arm, it also ends up travelling a shorter distance that exactly cancels out the drift. This was extended by Joseph Larmor (1897), Lorentz (1904) and Henri Poincaré (1905), who developed the complete Lorentz transformation including time dilation, which makes the stationary aether undetectable. Albert Einstein created special relativity in 1905, deriving the Lorentz transformation and thus length contraction from the relativity postulate and the constancy of the speed of light, without using the aether.[46] This was motivated by Maxwell's theory of electromagnetism (in the form as it was given by Lorentz in 1895) and the lack of evidence for the luminiferous aether but not, contrary to widespread belief, by the null result of the Michelson–Morley experiment.[47] The null result of the Michelson–Morley experiment, however, helped the notion of the constancy of the speed of light gain widespread and rapid acceptance. In 1932, Roy Kennedy and Edward Thorndike modified the Michelson–Morley experiment by making the path lengths of the split beam unequal, with one arm being very short. The Michelson–Morley experiment showed that the speed of light is independent of the orientation of the apparatus; the Kennedy–Thorndike experiment, which took place for many months as the Earth moved around the sun, showed that the speed of light is independent of the velocity of the apparatus in different inertial frames. The Michelson-Morley results could be explained by length contraction alone; the Kennedy-Thorndike experiment required that time dilation also be correct. Since no fringe shifts were seen, both length contraction and time dilation were verified, the two key effects of relativity.[48] Today, special relativity is generally considered the solution to all negative aether drift (or isotropy) measurements, including the Michelson–Morley null result. In addition, a series of high precision measurements have been conducted as tests of special relativity and modern searches for Lorentz violation in the photon, electron, nucleon, or neutrino sector, all of them confirming relativity.
Aether dragging Further information: Aether drag hypothesis Initially, the experiment of 1881 was meant to distinguish between the theory of Augustin-Jean Fresnel (1818), who proposed an almost stationary aether, and in which the aether is only partially dragged with a certain coefficient by matter; and the theory of George Gabriel Stokes (1845), who stated that the aether was fully dragged in the vicinity of the earth. Michelson initially believed the negative outcome confirmed the theory of Stokes. However, complete aether drag contradicts the observed aberration of light. In addition, Hendrik Lorentz showed in 1886 that Stokes's attempt to explain aberration is contradictory as well.[6][49] Furthermore, the assumption that the aether is not carried in the vicinity, but only within matter, was very problematic as shown by the Hammar experiment (1935). Hammar placed one arm of the interferometer between two huge lead blocks. If aether were dragged by mass, it was theorized that the blocks would have been enough to cause a visible effect. Once again, no effect was seen, so any such theory is considered as disproved.
MichelsonMorley experiment
Emission theory Walter Ritz's emitter theory (or ballistic theory), was also consistent with the results of the experiment, not requiring aether. The theory postulates that light has always the same velocity in respect to the source.[50] However de Sitter noted that emitter theory predicted several optical effects that were not seen in observations of binary stars in which the light from the two stars could be measured in a spectrometer. If emission theory were correct, the light from the stars should experience unusual fringe shifting due to the velocity of the stars being added to the speed of the light, but no such effect could be seen.[51] The Sagnac experiment placed a modified Michelson apparatus on a constantly rotating turntable; the main modification was that the light trajectory encloses an area. With this modified apparatus, any ballistic theories such as Ritz's could be tested directly, as the light going one way around the device would have a different length to travel than light going the other way (the eyepiece and mirrors would be moving toward/away from the light). In Ritz's theory there would be no shift, because the net velocity between the light source and detector was zero (they were both mounted on the turntable). However in this case an effect was seen, thereby eliminating any simple ballistic theory. This fringe-shift effect is used today in laser gyroscopes.
References Experiments [1] Michelson, Albert Abraham & Morley, Edward Williams (1887). "On the Relative Motion of the Earth and the Luminiferous Ether". American Journal of Science 34: 333–345. [2] Staley, Richard (2009), "Albert Michelson, the Velocity of Light, and the Ether Drift", Einstein's generation. The origins of the relativity revolution, Chicago: University of Chicago Press, ISBN 0-226-77057-5 [3] Earl R. Hoover, Cradle of Greatness: National and World Achievements of Ohio's Western Reserve (Cleveland: Shaker Savings Association, 1977) [4] Eisele, Ch.; Nevsky, A. Yu.; Schiller, S. (2009). "Laboratory Test of the Isotropy of Light Propagation at the 10-17 level". Physical Review Letters 103 (9): 090401. Bibcode 2009PhRvL.103i0401E. doi:10.1103/PhysRevLett.103.090401. PMID 19792767. [5] Herrmann, S.; Senger, A.; Möhle, K.; Nagel, M.; Kovalchuk, E. V.; Peters, A. (2009). "Rotating optical cavity experiment testing Lorentz invariance at the 10-17 level". Physical Review D 80 (100): 105011. arXiv:1002.1284. Bibcode 2009PhRvD..80j5011H. doi:10.1103/PhysRevD.80.105011. [6] Janssen, Michel & Stachel, John (2010), "The Optics and Electrodynamics of Moving Bodies" (http:/ / www. mpiwg-berlin. mpg. de/ Preprints/ P265. PDF), in John Stachel, Going Critical, Springer, ISBN 1-4020-1308-6, [7] Among other lessons was the need to control for vibration. Michelson (1881) wrote: "... owing to the extreme sensitiveness of the instrument to vibrations, the work could not be carried on during the day. The experiment was next tried at night. When the mirrors were placed half-way on the arms the fringes were visible, but their position could not be measured till after twelve o'clock, and then only at intervals. When the mirrors were moved out to the ends of the arms, the fringes were only occasionally visible. It thus appeared that the experiments could not be performed in Berlin, and the apparatus was accordingly removed to the Astrophysicalisches Observatorium in Potsdam ... Here, the fringes under ordinary circumstances were sufficiently quiet to measure, but so extraordinarily sensitive was the instrument that the stamping of the pavement, about 100 meters from the observatory, made the fringes disappear entirely!" [8] Michelson, Albert Abraham (1881). "The Relative Motion of the Earth and the Luminiferous Ether". American Journal of Science 22: 120–129. [9] Miller, A.I. (1981). Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911). Reading: Addison–Wesley. pp. 24. ISBN 0-201-04679-2. [10] Michelson (1881) wrote: "... a sodium flame placed at a produced at once the interference bands. These could then be altered in width, position, or direction, by a slight movement of the plate b, and when they were of convenient width and of maximum sharpness, the sodium flame was removed and the lamp again substituted. The screw m was then slowly turned till the bands reappeared. They were then of course colored, except the central band, which was nearly black." [11] Michelson, A. A. and Morley, E.W. (1886). "Influence of Motion of the Medium on the Velocity of Light". Am. J. Science 31: 377–386. [12] William Fickinger, Physics at a Research University: Case Western Reserve, 1830–1990, Cleveland, 2005, pp. 18–22, 48. The Dormitory was located on a now largely unoccupied space between the Biology Building and the Adelbert Gymnasium, both of which still stand on the CWRU campus. [13] Ralph R. Hamerla, An American Scientist on the Research Frontier: Edward Morley, Community, and Radical Ideas in Nineteenth-Century Science, Dordrecht, Springer, 2006, pp. 123–52. [14] Miller, Dayton C. (1933). "The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth". Reviews of Modern Physics 5 (3): 203–242. Bibcode 1933RvMP....5..203M. doi:10.1103/RevModPhys.5.203.
53
MichelsonMorley experiment [15] If one uses a half-silvered mirror as the beam splitter, the reflected beam will undergo a different number of front-surface reflections than the transmitted beam. At each front-surface reflection, the light will undergo a phase inversion. Since the two beams undergo a different number of phase inversions, when the path lengths of the two beams match or differ by an integral number of wavelengths (e.g. 0, 1, 2 ...), there will be destructive interference and a weak signal at the detector. If the path lengths of the beams differ by a half-integral number of wavelengths (e.g., 0.5, 1.5, 2.5 ...), there will be constructive interference and a strong signal. The results are opposite if a cube beam-splitter is employed, since a cube beam-splitter makes no distinction between a front- and rear-surface reflection. [16] Blum, Sergey V. Lototsky, Edward K.; Lototsky, Sergey V. (2006). Mathematics of physics and engineering (http:/ / books. google. com/ ?id=nFRG2UizET0C). World Scientific. p. 98. ISBN 981-256-621-X. ., Chapter 2, p. 98 (http:/ / books. google. com/ books?id=nFRG2UizET0C& pg=PA98) [17] Swenson, Loyd S. (1970). "The Michelson-Morley-Miller Experiments before and after 1905" (http:/ / adsabs. harvard. edu/ / abs/ 1970JHA. . . . . 1. . . 56S). Journal for the History of Astronomy 1: 56–78. Bibcode 1970JHA.....1...56S. . [18] L. Swenson The ethereal Aether - a history of the Michelson Morley Aether Drift Experiment 1880–1930, University of Texas Press, Austin 1972 [19] Edward W. Morley and Dayton C. Miller (1904). "Extract from a Letter dated Cleveland, Ohio, August 5th, 1904, to Lord Kelvin from Profs. Edward W. Morley and Dayton C. Miller". Philosophical Magazine. 6 8 (48): 753–754. [20] Edward W. Morley and Dayton C. Miller (1905). "Report of an experiment to detect the Fitzgerald-Lorentz Effect". Proceedings of the American Academy of Arts and Sciences XLI (12): 321–8. [21] Thirring (1926) as well as Lorentz pointed out that Miller's results failed even the most basic criteria required to believe in their celestial origin, namely that the azimuth of supposed drift should exhibit daily variations consistent with the source rotating about the celestial pole. Instead, while Miller's observations showed daily variations, their oscillations in one set of experiments might center, say, around a northwest-southeast line. [22] Michelson, A. A. et al. (1928). "Conference on the Michelson–Morley Experiment Held at Mount Wilson, February, 1927". Astrophysical Journal 68: 341–390. Bibcode 1928ApJ....68..341M. doi:10.1086/143148. [23] Shankland, Robert S. et al. (1955). "New Analysis of the Interferometer Observations of Dayton C. Miller". Reviews of Modern Physics 27 (2): 167–178. Bibcode 1955RvMP...27..167S. doi:10.1103/RevModPhys.27.167. [24] Roberts, T.J. (2006). "An Explanation of Dayton Miller's Anomalous "Ether Drift" Result" (http:/ / arxiv. org/ abs/ physics/ 0608238). . Retrieved 7 May 2012. [25] Kennedy, Roy J. (1926). "A Refinement of the Michelson-Morley Experiment". Proceedings of the National Academy of Sciences 12 (11): 621–629. Bibcode 1926PNAS...12..621K. doi:10.1073/pnas.12.11.621. [26] Illingworth, K. K. (1927). "A Repetition of the Michelson-Morley Experiment Using Kennedy's Refinement". Physical Review 30 (5): 692–696. Bibcode 1927PhRv...30..692I. doi:10.1103/PhysRev.30.692. [27] Joos, G. (1930). "Die Jenaer Wiederholung des Michelsonversuchs". Annalen der Physik 399 (4): 385–407. Bibcode 1930AnP...399..385J. doi:10.1002/andp.19303990402. [28] Miller, Dayton C. (1925). "Ether-Drift Experiments at Mount Wilson". Proceedings of the National Academy of Sciences 11 (6): 306–314. Bibcode 1925PNAS...11..306M. doi:10.1073/pnas.11.6.306. [29] Tomaschek, R. (1924). "Über das Verhalten des Lichtes außerirdischer Lichtquellen" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k153753/ f115). Annalen der Physik 378 (1): 105–126. Bibcode 1924AnP...378..105T. doi:10.1002/andp.19243780107. . [30] Piccard, A.; Stahel, E. (1926). "L'expérience de Michelson, réalisée en ballon libre" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k3136h/ f420). Comptes Rendus 183 (7): 420–421. . [31] Piccard, A.; Stahel, E. (1927). "Nouveaux résultats obtenus par l'expérience de Michelson" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k3137t/ f152). Comptes Rendus 184: 152. . [32] Piccard, A.; Stahel, E. (1927). "L'absence du vent d'éther au Rigi" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k31384/ f1198). Comptes Rendus 184: 1198–1200. . [33] Michelson, A. A.; Pease, F. G.; Pearson, F.; Pease; Pearson (1929). "Results of repetition of the Michelson-Morley experiment". Journal of the Optical Society of America 18 (3): 181. Bibcode 1929JOSA...18..181M. [34] Müller, H.; Herrmann, S.; Braxmaier, C.; Schiller, S.; Peters, A. (2003). "Modern Michelson-Morley experiment using cryogenic optical resonators". Phys. Rev. Lett. 91 (2): 020401. arXiv:physics/0305117. Bibcode 2003PhRvL..91b0401M. doi:10.1103/PhysRevLett.91.020401. PMID 12906465. [35] Relativity FAQ (2007): What is the experimental basis of Special Relativity? (http:/ / math. ucr. edu/ home/ baez/ physics/ Relativity/ SR/ experiments. html) [36] Jaseja, T. S.; Javan, A.; Murray, J.; Townes, C. H. (1964). "Test of Special Relativity or of the Isotropy of Space by Use of Infrared Masers". Phys. Rev. 133 (5a): 1221–1225. Bibcode 1964PhRv..133.1221J. doi:10.1103/PhysRev.133.A1221. [37] Brillet, A.; Hall, J. L. (1979). "Improved laser test of the isotropy of space". Phys. Rev. Lett. 42 (9): 549–552. Bibcode 1979PhRvL..42..549B. doi:10.1103/PhysRevLett.42.549. [38] Wolf, P.; Bize, S.; Clairon, A.; Luiten, A. N.; Santarelli, G; Tobar, M. E. (2003). "New Limit on Signals of Lorentz Violation in Electrodynamics". Phys. Rev. Lett. 90 (6): 060402. arXiv:gr-qc/0210049. Bibcode 2003PhRvL..90f0402W. doi:10.1103/PhysRevLett.90.060402. PMID 12633279. [39] Wolf, P.; Tobar, M. E.; Bize, S.; Clairon, A.; Luiten, A. N.; Santarelli, G. (2004). "Whispering Gallery Resonators and Tests of Lorentz Invariance". General Relativity and Gravitation 36 (10): 2351–2372. arXiv:gr-qc/0401017. Bibcode 2004GReGr..36.2351W.
54
MichelsonMorley experiment doi:10.1023/B:GERG.0000046188.87741.51. [40] Wolf, P.; Bize, S.; Clairon, A.; Santarelli, G.; Tobar, M. E.; Luiten, A. N. (2004). "Improved test of Lorentz invariance in electrodynamics". Physical Review D 70 (5): 051902. arXiv:hep-ph/0407232. Bibcode 2004PhRvD..70e1902W. doi:10.1103/PhysRevD.70.051902. [41] Antonini, P.; Okhapkin, M.; Göklü, E.; Schiller, S. (2005). "Test of constancy of speed of light with rotating cryogenic optical resonators". Physical Review A 71 (5): 050101. arXiv:gr-qc/0504109. Bibcode 2005PhRvA..71e0101A. doi:10.1103/PhysRevA.71.050101. [42] Stanwix, P. L.; Tobar, M. E.; Wolf, P.; Susli, M.; Locke, C. R.; Ivanov, E. N.; Winterflood, J.; van Kann, F. (2005). "Test of Lorentz Invariance in Electrodynamics Using Rotating Cryogenic Sapphire Microwave Oscillators". Physical Review Letters 95 (4): 040404. arXiv:hep-ph/0506074. Bibcode 2005PhRvL..95d0404S. doi:10.1103/PhysRevLett.95.040404. PMID 16090785. [43] Herrmann, S.; Senger, A.; Kovalchuk, E.; Müller, H.; Peters, A. (2005). "Test of the Isotropy of the Speed of Light Using a Continuously Rotating Optical Resonator". Phys. Rev. Lett. 95 (15): 150401. arXiv:physics/0508097. Bibcode 2005PhRvL..95o0401H. doi:10.1103/PhysRevLett.95.150401. PMID 16241700. [44] Stanwix, P. L.; Tobar, M. E.; Wolf, P.; Locke, C. R.; Ivanov, E. N. (2006). "Improved test of Lorentz invariance in electrodynamics using rotating cryogenic sapphire oscillators". Physical Review D 74 (8): 081101. arXiv:gr-qc/0609072. Bibcode 2006PhRvD..74h1101S. doi:10.1103/PhysRevD.74.081101. [45] Müller, H.; Stanwix, Paul L.; Tobar, M. E.; Ivanov, E.; Wolf, P.; Herrmann, S.; Senger, A.; Kovalchuk, E.; Peters, A. (2007). "Relativity tests by complementary rotating Michelson-Morley experiments". Phys. Rev. Lett. 99 (5): 050401. arXiv:0706.2031. Bibcode 2007PhRvL..99e0401M. doi:10.1103/PhysRevLett.99.050401. PMID 17930733. [46] Einstein, A (June 30, 1905). "Zur Elektrodynamik bewegter Körper" (http:/ / www. pro-physik. de/ Phy/ pdfs/ ger_890_921. pdf) (in German) (PDF). Annalen der Physik 17: 890–921. . Retrieved 2009-11-27. English translation: Perrett, W and Jeffery, GB (tr.); Walker, J (ed.). "On the Electrodynamics of Moving Bodies" (http:/ / www. fourmilab. ch/ etexts/ einstein/ specrel/ www/ ). Fourmilab. . Retrieved 2009-11-27. [47] Michael Polanyi, Personal Knowledge: Towards a Post-Critical Philosophy, ISBN 0-226-67288-3, footnote page 10–11: Einstein reports, via Dr N Balzas in response to Polanyi's query, that "The Michelson-Morely experiment had no role in the foundation of the theory." and "..the theory of relativity was not founded to explain its outcome at all." (http:/ / books. google. com/ books?id=0Rtu8kCpvz4C& lpg=PP1& pg=PT19#v=onepage& q=& f=false) [48] Kennedy, R. J.; Thorndike, E. M. (1932). "Experimental Establishment of the Relativity of Time". Phys. Rev. 42: 400–408. doi:10.1103/PhysRev.42.400. [49] Whittaker, Edmund Taylor (1910). A History of the theories of aether and electricity (http:/ / www. archive. org/ details/ historyoftheorie00whitrich) (1. ed.). Dublin: Longman, Green and Co.. . [50] Norton, John D. (2004). "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905" (http:/ / philsci-archive. pitt. edu/ archive/ 00001743/ ). Archive for History of Exact Sciences 59: 45–105. Bibcode 2004AHES...59...45N. doi:10.1007/s00407-004-0085-6. . [51] De Sitter, Willem (1913), "On the constancy of the velocity of light", Proceedings of the Royal Netherlands Academy of Arts and Sciences 16 (1): 395–396
Notes Bibliography
External links • Early Experiments (http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#2.early experiments) • For gravitational waves: PostScript file (http://axion.physics.ubc.ca/hyperspace/mog21.ps.gz) of the newsletter of the Topical Group on Gravitation of the American Physical Society Number 21 Spring 2003; Google.com can be used to extract the text of the document. • "Test Light Speed in Mile Long Vacuum Tube." (http://books.google.com/books?id=UigDAAAAMBAJ& pg=PA17&dq=1930+plane+"Popular&hl=en&ei=bfiPTs-NGInE0AHC_4k_&sa=X&oi=book_result& ct=result&resnum=8&ved=0CEwQ6AEwBzgK#v=onepage&q=1930 plane "Popular&f=true) Popular Science Monthly, September 1930, p. 17–18.
55
Oil drop experiment
Oil drop experiment The oil drop experiment was an experiment performed by Robert Millikan and Harvey Fletcher in 1909 to measure the elementary electric charge (the charge of the electron). The experiment entailed balancing the downward gravitational force with the upward drag and electric forces on tiny charged droplets of oil suspended between two metal electrodes. Since the density of the oil was known, the droplets' masses, and therefore their gravitational and buoyant forces, could be determined from their observed radii. Using a known Millikan's setup for the oil drop experiment electric field, Millikan and Fletcher could determine even the charge on oil droplets in mechanical equilibrium. By repeating the experiment for many droplets, they confirmed that the charges were all multiples of some fundamental value, and calculated it to be 1.5924(17) × 10−19 C, within 1% of the currently accepted value of 1.602176487(40) × 10−19 C. They proposed that this was the charge of a single electron.
Background Starting in 1900, while a professor at the University of Chicago, Millikan, with the significant input of Fletcher,[1] and after improving his setup, published his seminal study in 1913.[2] Millikan's experiment involved measuring the force on oil droplets in a glass chamber sandwiched between two electrodes, one above and one below. With the electrical field calculated, he could measure the droplet's charge, the charge on a single electron being (1.592 × 10−19 C). At the time of Millikan and Fletcher's oil drop experiments, the existence of subatomic particles was not universally accepted. Experimenting with cathode rays in 1897, J. J. Thomson had discovered negatively charged "corpuscles", as Robert A. Millikan in 1891 he called them, with a mass about 1840 times smaller than that of a hydrogen atom. Similar results had been found by George FitzGerald and Walter Kaufmann. Most of what was then known about electricity and magnetism, however, could be explained on the basis that charge is a continuous variable; in much the same way that many of the properties of light can be explained by treating it as a continuous wave rather than as a stream of photons. The so-called elementary charge e is one of the fundamental physical constants and its accurate value is of great importance. In 1923, Millikan won the Nobel Prize in physics in part because of this experiment. Aside from the measurement, the beauty of the oil drop experiment is that it is a simple, elegant hands-on demonstration that charge is actually quantized. Thomas Edison, who had previously thought of charge as a continuous variable, became convinced after working with Millikan and Fletcher's apparatus. This experiment has since been repeated by generations of physics students, although it is rather expensive and difficult to do properly.
56
Oil drop experiment
57
In the last two decades, several computer-automated experiments have been conducted to search for isolated fractionally charged particles. So far (2007), no evidence for fractional charge particles was found over more than 100 million drops measured.[3]
Experimental procedure Apparatus Millikan’s and Fletcher's apparatus incorporated a parallel pair of horizontal metal plates. By applying a potential difference across the plates, a uniform electric field was created in the space between them. A ring of insulating material was used to hold the plates apart. Four holes were cut into the ring, three for illumination by a bright light, and another to allow viewing through a microscope.
Simplified scheme of Millikan’s oil drop experiment
A fine mist of oil droplets was sprayed into a chamber above the plates. The oil was of a type usually used in vacuum apparatus and was chosen because it had an extremely low vapour pressure. Ordinary oil would evaporate under the heat of the light source causing the mass of the oil drop to change over the course of the experiment. Some oil drops became electrically charged through friction with the nozzle as they were sprayed. Alternatively, charging could be brought about by including an ionising radiation source (such as an X-ray Oil drop experiment apparatus tube). The droplets entered the space between the plates and, because they were charged, it could be made to rise and fall by changing the voltage across the plates.
Oil drop experiment
Method Initially the oil drops are allowed to fall between the plates with the electric field turned off. They very quickly reach a terminal velocity because of friction with the air in the chamber. The field is then turned on and, if it is large enough, some of the drops (the charged ones) will start to rise. (This is because the upwards electric force FE is greater for them than the downwards gravitational force g, in the same way bits of paper can be picked by a charged rubber rod). A likely looking drop is selected and kept in the middle of the field of view by alternately switching off the voltage until all the other drops have fallen. The experiment is then continued with this one drop. The drop is allowed to fall and its terminal velocity v1 in the absence of an electric field is calculated. The drag force acting on the drop can then be worked out using Stokes' law:
where v1 is the terminal velocity (i.e. velocity in the absence of an electric field) of the falling drop, η is the viscosity of the air, and r is the radius of the drop. The weight W is the volume V multiplied by the density ρ and the acceleration due to gravity g. However, what is needed is the apparent weight. The apparent weight in air is the true weight minus the upthrust (which equals the weight of air displaced by the oil drop). For a perfectly spherical droplet the apparent weight can be written as:
At terminal velocity the oil drop is not accelerating. Therefore the total force acting on it must be zero and the two forces F and W must cancel one another out (that is, F = W). This implies
Once r is calculated, W can easily be worked out. Now the field is turned back on, and the electric force on the drop is
where q is the charge on the oil drop and E is the electric field between the plates. For parallel plates
where V is the potential difference and d is the distance between the plates. One conceivable way to work out q would be to adjust V until the oil drop remained steady. Then we could equate FE with W. But in practice this is extremely difficult to do precisely. Also, determining FE proves difficult because the mass of the oil drop is difficult to determine without reverting back to the use of Stokes' Law. A more practical approach is to turn V up slightly so that the oil drop rises with a new terminal velocity v2. Then
58
Oil drop experiment
Fraud allegations There is some controversy over the use of selectivity in Millikan's results of his second experiment measuring the electron charge raised by the historian Gerald Holton. Holton (1978) pointed out that Millikan disregarded a large set of the oil drops gained in his experiments without apparent reason. Allan Franklin, a former high energy experimentalist and current philosopher of science at the University of Colorado has tried to rebut this point by Holton.[4] Franklin contends that Millikan's exclusions of data did not affect the final value of e that Millikan obtained but concedes that there was substantial "cosmetic surgery" that Millikan performed which had the effect of reducing the statistical error on e. This enabled Millikan to quote the figure that he had calculated e to better than one half of one percent; in fact, if Millikan had included all of the data he threw out, it would have been to within 2%. While this would still have resulted in Millikan having measured e better than anyone else at the time, the slightly larger uncertainty might have allowed more disagreement with his results within the physics community. David Goodstein counters that Millikan plainly states that he only included drops which had undergone a "complete series of observations" and excluded no drops from this group.[5]
Millikan's experiment as an example of psychological effects in scientific methodology In a commencement address given at the California Institute of Technology (Caltech) in 1974 (and reprinted in Surely You're Joking, Mr. Feynman!), physicist Richard Feynman noted: We have learned a lot from experience about how to handle some of the ways we fool ourselves. One example: Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right. It's a little bit off because he had the incorrect value for the viscosity of air. It's interesting to look at the history of measurements of the charge of an electron, after Millikan. If you plot them as a function of time, you find that one is a little bit bigger than Millikan's, and the next one's a little bit bigger than that, and the next one's a little bit bigger than that, until finally they settle down to a number which is higher. Why didn't they discover the new number was higher right away? It's a thing that scientists are ashamed of - this history - because it's apparent that people did things like this: When they got a number that was too high above Millikan's, they thought something must be wrong - and they would look for and find a reason why something might be wrong. When they got a number close to Millikan's value they didn't look so hard. And so they eliminated the numbers that were too far off, and did other things like that...[6][7] As of 2008, the accepted value for the elementary charge is 1.602176487(40) × 10−19 C,[8] where the 40 indicates the uncertainty of the last two decimal places. In his Nobel lecture, Millikan gave his measurement as 4.774(5) × 10−10 statC,[9] which equals 1.5924(17) × 10−19 C. The difference is less than one percent, but it is more than five times greater than Millikan's standard error, so the disagreement is significant.
59
Oil drop experiment
References [1] Elektrizitätsmengen, Phys. Zeit., 10(1910), p. 308 [2] Millikan, R. A. (1913). "On the Elementary Electric charge and the Avogadro Constant". Phys. Rev. 2 (2): 109–143. Bibcode 1913PhRv....2..109M. doi:10.1103/PhysRev.2.109. [3] SLAC - Fractional Charge Search - Results (http:/ / www. slac. stanford. edu/ exp/ mps/ FCS/ FCS_rslt. htm) [4] Franklin, A. (1997). "Millikan's Oil-Drop Experiments". The Chemical Educator 2 (1): 1–14. doi:10.1007/s00897970102a. [5] Goodstein, D. (2000). "In defense of Robert Andrews Millikan" (http:/ / eands. caltech. edu/ articles/ Millikan Feature. pdf). Engineering and Science (Pasadena, California: Caltech Office of Public Relations) 63 (4): 30–38. . Retrieved December 2009. [6] Feynman, Richard, "Cargo Cult Science" (http:/ / www. lhup. edu/ ~DSIMANEK/ cargocul. htm) (adapted from 1974 California Institute of Technology (http:/ / www. caltech. edu/ ) commencement address), Donald Simanek's Pages (http:/ / www. lhup. edu/ ~DSIMANEK/ home. htm), Lock Haven University (http:/ / www. lhup. edu/ ), rev. August 2008. [7] Feynman, Richard Phillips; Leighton, Ralph; Hutchings, Edward (1997-04-01). "Surely you're joking, Mr. Feynman!": adventures of a curious character (http:/ / books. google. com/ books?id=7papZR4oVssC& pg=PA342). New York: W. W. Norton & Company. p. 342. ISBN 978-0-393-31604-9. . Retrieved 10 July 2010. [8] NIST Reference on Constants, Units and Uncertainty (http:/ / physics. nist. gov/ cgi-bin/ cuu/ Value?e) [9] Millikan, Robert A. (May 23, 1924). The electron and the light-quant from the experimental point of view (http:/ / nobelprize. org/ nobel_prizes/ physics/ laureates/ 1923/ millikan-lecture. html) (Speech). Stockholm. . Retrieved 2006-11-12.
Further reading • Serway, Raymond A.; Faughn, Jerry S. (2006). Holt: Physics. Holt, Rinehart and Winston. ISBN 0-03-073548-3. • Thornton, Stephen T.; Rex, Andrew (2006). Modern Physics for Scientists and Engineers (3rd ed.). Brooks/Cole. ISBN 0-495-12514-8. • Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN 0-534-40842-7.
External links • Thomsen, Marshall, " Good to the Last Drop (http://www.physics.emich.edu/mthomsen/sege.htm)". Millikan Stories as "Canned" Pedagogy. Eastern Michigan University. • CSR/TSGC Team, " Quark search experiment (http://www.tsgc.utexas.edu/floatn/1997/teams/UT-austin. html)". The University of Texas at Austin. • The oil drop experiment appears in a list of Science's 10 Most Beautiful Experiments (http://physics.nad.ru/ Physics/English/top10.htm) originally published in the New York Times. • Engeness, T.E., " The Millikan Oil Drop Experiment (http://people.ccmr.cornell.edu/~muchomas/8.04/Lecs/ lec_Millikan/Mill.html)". 25 April 2005 • Millikan R. A. (1913). "On the elementary electrical charge and the Avogadro constant" (http://www.aip.org/ history/gap/PDF/millikan.pdf). The Physical Review, Series II 2: 109–143., Paper by Millikan discussing modifications to his original experiment to improve its accuracy. • Millikan Oil Drop Experiment in space (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal& id=APCPCS000504000001000715000001&idtype=cvips&gifs=yes). A variation of this experiment has been suggested for the International Space Station. from mona malik
60
Oxford Electric Bell
61
Oxford Electric Bell The Oxford Electric Bell or Clarendon Dry Pile is an experimental electric bell that was set up in 1840 and which has rung almost continuously ever since. It was "one of the first pieces" purchased for a collection of apparatus by clergyman and physicist Robert Walker.[1][2] It is located in the foyer of the Clarendon Laboratory at the University of Oxford, England. As of December 2009 it has been moved into an adjacent corridor due to building works but is still ringing, though inaudibly due to being behind two layers of glass.
Design The experiment consists of two brass bells, each positioned beneath a dry pile (a form of battery), the pair of piles connected in series. A metal sphere approximately 4 mm in diameter is suspended between the piles, and rings the bells by means of electrostatic force. As the clapper touches one bell, it is charged by one pile, and then electrostatically repelled, being attracted to the other bell. On hitting the other bell, the process repeats. The use of electrostatic forces means that while high voltage is required to create motion, only a tiny amount of charge is carried from one bell to the other, which is why the piles have been able to last since the apparatus was set up. Its oscillation frequency is 2 hertz.[3]
The Oxford Electric Bell in December 2009
Probably the most interesting part of the bell is the pair of dry piles. Nobody is certain of what they are composed, but it is known that they have been coated with molten sulphur to prevent effects from atmospheric moisture and it is thought that they may be Zamboni piles. At one point this sort of device played an important role in distinguishing between two different theories of electrical action: the theory of contact tension (an obsolete scientific theory based on then-prevailing electrostatic principles) and the theory of chemical action. The Oxford Electric Bell does not demonstrate perpetual motion. The bell will eventually stop when the dry piles are depleted of charge — that is, if the clapper does not wear out first.[4][5]
Charged by the two piles, the clapper moves back and forth between the two bells.
References [1] "Walker, Robert" (http:/ / dx. doi. org/ 10. 1093/ ref:odnb/ 38098), on the website of the Oxford Dictionary of National Biography (subscription or UK public library membership (http:/ / www. oup. com/ oxforddnb/ info/ freeodnb/ libraries/ ) required), [2] "Exhibit 1 - The Clarendon Dry Pile" (http:/ / www. physics. ox. ac. uk/ history. asp?page=exhibit1). Department of Physics. Oxford University. . Retrieved 8 January 2012. [3] Oxford Electric Bell (http:/ / atlasobscura. com/ place/ oxford-electric-bell), Atlas Obscura (http:/ / atlasobscura. com/ ). [4] The World's Longest Experiment (http:/ / thelongestlistofthelongeststuffatthelongestdomainnameatlonglast. com/ long203. html), The Longest List of the Longest Stuff at the Longest Domain Name at Long Last (http:/ / thelongestlistofthelongeststuffatthelongestdomainnameatlonglast. com/ ). [5] The Latest on Long-Running Experiments (http:/ / improbable. com/ airchives/ paperair/ volume7/ v7i3/ long-run-7-3. html), Improbable Research (http:/ / improbable. com/ ).
Oxford Electric Bell
62
Further reading • Willem Hackmann, " The Enigma of Volta's "Contact Tension" and the Development of the "Dry Pile" (http:// ppp.unipv.it/Collana/Pages/Libri/Saggi/Nuova Voltiana3_PDF/cap5/5new.pdf)", appearing in Nuova Voltiana: Studies on Volta and His Times (http://ppp.unipv.it/PagesIT/NuovaVoltFrame.htm), nb Volume 3 (Fabio Bevilacqua; Lucio Frenonese (Editors)), 2000, pp. 103–119. • "Exhibit 1 - The Clarendon Dry Pile" (http://www.physics.ox.ac.uk/history.asp?page=Exhibit1). Oxford Physics Teaching, History Archive. Retrieved 2008-01-18. • Croft, A J (1984). "The Oxford electric bell". European Journal of Physics 5 (4): 193. Bibcode 1984EJPh....5..193C. doi:10.1088/0143-0807/5/4/001. • Croft, A J (1985). "The Oxford electric bell". European Journal of Physics 6 (2): 128. Bibcode 1985EJPh....6..128C. doi:10.1088/0143-0807/6/2/511.
Rømer's determination of the speed of light Rømer's determination of the speed of light was the demonstration in 1676 that light has a finite speed, and so doesn't travel instantaneously. The discovery is usually attributed to Danish astronomer Ole Rømer (1644–1710),[1] who was working at the Royal Observatory in Paris at the time. Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter of Earth's orbit around the Sun: this is equivalent to about 220,000 kilometres per second in modern units, about 26% lower than the true value. While the exact details of Rømer's calculations have been lost, the error is probably due to an error in the orbital elements of Jupiter, leading Rømer to believe that Jupiter was closer to the Sun than is actually the case. Rømer's theory was controversial at the time he announced it, and he never convinced the director of the Royal Observatory, Giovanni Domenico Cassini, to fully accept it. However, it quickly gained support among other natural philosophers of the period, such as Christiaan Huygens and Isaac Newton. It was finally confirmed nearly two decades after Rømer's death, with the explanation in 1729 of stellar aberration by the English astronomer James Bradley.
Ole Rømer (1644–1710), depicted here some time after his discovery of the speed of light (1676), at a time when he was already a statesman in his native Denmark. The engraving is probably posthumous.
Background The determination of longitude was a significant practical problem in cartography and navigation. Philip III of Spain had offered a prize for a method to determine the longitude of a ship out of sight of land, and Galileo proposed a method of establishing the time of day, and thus longitude, based on the times of the eclipses of the moons of Jupiter, in essence using the Jovian system as a cosmic clock; this method was not significantly improved until accurate mechanical clocks were developed in the eighteenth century. Galileo proposed this method to the Spanish crown (1616–17) but it proved to be impractical, not least because of the difficulty of observing the eclipses on a ship. However, with refinements the method could be made to work on land. The Italian astronomer Giovanni Domenico Cassini had pioneered the use of the eclipses of the Galilean moons for longitude measurements, and published tables predicting when eclipses would be visible from a given location. He
Rømer's determination of the speed of light was invited to France by Louis XIV to set up the Royal Observatory, which opened in 1671 with Cassini as director, a post he would hold for the rest of his life. One of Cassini's first projects in his new post in Paris was to send Frenchman Jean Picard to the site of Tycho Brahe's old observatory at Uraniborg, on the island of Hven near Copenhagen. Picard was to observe and time the eclipses of Jupiter's moons from Uraniborg while Cassini recorded the times they were seen in Paris. If Picard recorded the end of an eclipse at 9 hours 43 minutes 54 seconds after midday in Uraniborg, while Cassini recorded the end of the same eclipse at 9 hours 1 minute 44 seconds after midday in Paris – a difference of 42 minutes 10 seconds – the difference in longitude could be calculated to be 10° 32' 30".[2] Picard was helped in his observations by a young Dane who had recently completed his studies at the University of Copenhagen – Ole Rømer – and he must have been impressed by his assistant's skills, as he arranged for the young man to come to Paris to work at the Royal Observatory there.
Eclipses of Io Io is the innermost of the four moons of Jupiter discovered by Galileo in January 1610. Rømer and Cassini refer to it as the "first satellite of Jupiter". It orbits Jupiter once every 42½ hours, and the plane of its orbit is very close to the plane of Jupiter's orbit around the sun. This means that it passes much of each orbit in the shadow of Jupiter – an eclipse. Viewed from the Earth, an eclipse of Io is seen in one of two ways. • Io suddenly disappears, as it moves into the shadow of Jupiter. This is termed an immersion. • Io suddenly reappears, as it moves out of the shadow of Jupiter. This is called an emergence. From the Earth, it is not possible to view both the immersion and the emergence for the same eclipse of Io, because one or the other will be hidden (occulted) by Jupiter itself. At the point of opposition (point H in the diagram below), both the immersion and the emergence would be hidden by Jupiter. For about four months after the opposition of Jupiter (from L to K in the diagram below), it is possible to view emergences of Io from its eclipses, while for about four months before the opposition (from F to G), it is possible to view immersions of Io into Jupiter's shadow. For about five or six months of the year, around the point of conjunction, it is impossible to observe the eclipses of Io at all because Jupiter is too close (in the sky) to the sun. Even during the periods before and after opposition, not all of the eclipses of Io can be observed from a given location on the Earth's surface: some eclipses will occur during the daytime for a given location, while other eclipses will occur while Jupiter is below the horizon (hidden by the Earth itself).
63
Rømer's determination of the speed of light
64
Observations Most of Rømer's papers were destroyed in the Copenhagen Fire of 1728, but one manuscript that survived contains a listing of about sixty observations of eclipses of Io from 1668 to 1678.[3] In particular, it details two series of observations on either side of the oppositions of 2 March 1672 and 2 April 1673. Rømer comments in a letter to Christiaan Huygens dated 30 September 1677 that these observations from 1671–73 form the basis for his calculations.[4] The surviving manuscript was written some time after January 1678, the date of the last recorded astronomical observation (an emergence of Io on 6 January), and so is posterior to Rømer's letter to Huygens. Rømer appears to be collecting data on eclipses of the Galilean moons in the form of an aide-mémoire, possibly as he was preparing to return to Denmark in 1681. The document also records the observations around the opposition of 8 July 1676 that formed the basis for the announcement of Rømer's results.
Rømer's aide-mémoire, written at some point after January 1678 and rediscovered in 1913. The timings of eclipses of Io appear on the right-hand side of this image, which would have been "page one" of the folded sheet. Click on image for an enlarged view.
Initial announcement On 22 August 1676,[5] Cassini made an announcement to the Royal Academy of Sciences in Paris that he would be changing the basis of calculation for his tables of eclipses of Io. He may also have stated the reason:[6] This second inequality appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit.[7] Most importantly, Cassini announced the prediction that the emergence of Io on 16 November 1676 would be observed about ten minutes later than would have been calculated by the previous method. There is no record of any observation of an emergence of Io on 16 November, but an emergence was observed on 9 November. With this experimental evidence in hand, Rømer explained his new method of calculation to the Royal Academy of Sciences on 22 November.[8] The original record of the meeting of the Royal Academy of Sciences has been lost, but Rømer's presentation was recorded as a news report in the Journal des sçavans on 7 December.[9] This anonymous report was translated into English and published in Philosophical Transactions of the Royal Society in London on 25 July 1677.[10][11]
A redrawn version of the illustration from the 1676 news report. Rømer compared the apparent duration of Io's orbits as Earth moved towards Jupiter (F to G) and as Earth moved away from Jupiter (L to K).
Rømer's determination of the speed of light
Rømer's reasoning Order of magnitude Rømer starts with an order of magnitude demonstration that the speed of light must be so great that it takes much less than one second to travel a distance equal to Earth's diameter. The point L on the diagram represents the second quadrature of Jupiter, when the angle between Jupiter and the Sun (as seen from Earth) is 90°.[12] Rømer assumes that an observer could see an emergence of Io at the second quadrature (L), and also the emergence which occurs after one orbit of Io around Jupiter (when the Earth is taken to be at point K, the diagram not being to scale), that is 42½ hours later. During those 42½ hours, the Earth has moved further away from Jupiter by the distance LK: this, according to Rømer, is 210 times the Earth's diameter.[13] If light travelled at a speed of one Earth-diameter per second, it would take 3½ minutes to travel the distance LK. And if the period of Io's orbit around Jupiter were taken as the time difference between the emergence at L and the emergence at K, the value would be 3½ minutes longer than the true value. Rømer then applies the same logic to observations around the first quadrature (point G), when Earth is moving towards Jupiter. The time difference between an immersion seen from point F and the next immersion seen from point G should be 3½ minutes shorter than the true orbital period of Io. Hence, there should be a difference of about 7 minutes between the periods of Io measured at the first quadrature and those measured at the second quadrature. In practice, no difference is observed at all, from which Rømer concludes that the speed of light must be very much greater than one Earth-diameter per second.[9]
Cumulative effect However Rømer also realised that any effect of the finite speed of light would add up over a long series of observations, and it is this cumulative effect that he announced to the Royal Academy of Sciences in Paris. The effect can be illustrated with Rømer's observations from spring 1672. Jupiter was in opposition on 2 March 1672: the first observations of emergences were on 7 March (at 07:58:25) and 14 March (at 09:52:30). Between the two observations, Io had completed four orbits of Jupiter, giving an orbital period of 42 hours 28 minutes 31¼ seconds. The last emergence observed in the series was on 29 April (at 10:30:06). By this time, Io had completed thirty orbits around Jupiter since 7 March: the apparent orbital period is 42 hours 29 minutes 3 seconds. The difference seems minute – 32 seconds – but it meant that the emergence on 29 April was occurring a quarter-hour after it would have been predicted. The only alternative explanation was that the observations on 7 and 14 March were wrong by two minutes.
Prediction Rømer never published the formal description of his method, possibly because of the opposition of Cassini and Picard to his ideas (see below).[14] However, the general nature of his calculation can be inferred from the news report in the Journal de sçavans and from Cassini's announcement on 22 August 1676. Cassini announced that the new tables would contain the inequality of the days or the true motion of the Sun [i.e. the inequality due to the eccentricity of the Earth’s orbit], the eccentric motion of Jupiter [i.e. the inequality due to the eccentricity of the orbit of Jupiter] and this new, not previously detected, inequality [i.e. due to the finite speed of light].[7] Hence Cassini and Rømer appear to have been calculating the times of each eclipse based on the approximation of circular orbits, and then applying three successive corrections to estimate the time that the eclipse would be observed in Paris.
65
Rømer's determination of the speed of light The three "inequalities" (or irregularities) listed by Cassini were not the only ones known, but they were the ones that could be corrected for by calculation. The orbit of Io is also slightly irregular because of orbital resonance with Europa and Ganymede, two of the other Galilean moons of Jupiter, but this would not be fully explained for another century. The only solution available to Cassini and to other astronomers of his time was to issue periodic corrections to the tables of eclipses of Io to take account of its irregular orbital motion: periodically resetting the clock, as it were. The obvious time to reset the clock was just after the opposition of Jupiter to the Sun, when Jupiter is at its closest to Earth and so most easily observable. The opposition of Jupiter to the Sun occurred on or around 8 July 1676. Rømer's aide-mémoire lists two observation of emergences of Io after this opposition but before Cassini's announcement: on 7 August at 09:44:50 and on 14 August at 11:45:55.[15] With these data, and knowing the orbital period of Io, Cassini could calculate the times of each of the eclipses over the next four to five months. The next step in applying Rømer's correction would be to calculate the position of Earth and Jupiter in their orbits for each of the eclipses. This sort of coordinate transformation was commonplace in preparing tables of positions of the planets for both astronomy and astrology: it is equivalent to finding each of the positions L (or K) for the various eclipses which might be observable. Finally, the distance between Earth and Jupiter can be calculated using standard trigonometry, in particular the law of cosines, knowing two sides (distance between the Sun and Earth; distance between the Sun and Jupiter) and one angle (the angle between Jupiter and Earth as formed at the Sun) of a triangle. The distance from the Sun to Earth was not well known at the time, but taking it as a fixed value a, the distance from the Sun to Jupiter can be calculated as some multiple of a from Kepler's third law. This model left just one adjustable parameter – the time taken for light to travel a distance equal to a, the radius of Earth's orbit. Rømer had about thirty observations of eclipses of Io from 1671–73 that he used to find the value which fitted best: eleven minutes. With that value, he could calculate the extra time it would take light to reach Earth from Jupiter in November 1676 compared to August 1676: about ten minutes.
Initial reactions Rømer's explanation of the difference between predicted and observed timings of Io's eclipses was widely, but far from universally, accepted. Huygens was an early supporter, especially as it supported his ideas about refraction,[7] and wrote to the French Controller-General of Finances Jean-Baptiste Colbert in Rømer's defence.[16] However Cassini, Rømer's superior at the Royal Observatory, was an early and tenacious opponent of Rømer's ideas,[7] and it seems that Picard, Rømer's mentor, shared many of Cassini's doubts.[17] Cassini's practical objections took up many debates at the Royal Academy of Sciences (with Huygens participating by letter from London).[18] Cassini noted that the other three Galilean moons did not seem to show the same effect as seen for Io, and that there were other irregularities which could not be explained by Rømer's theory. Rømer replied that it was much more difficult to accurately observe the eclipses of the other moons, and that the unexplained effects were much smaller (for Io) than the effect of the speed of light: however, he admitted to Huygens[4] that the unexplained "irregularities" in the other satellites were larger than the effect of the speed of light. The dispute had something of a philosophical note: Rømer claimed that he had discovered a simple solution to an important practical problem, while Cassini rejected the theory as flawed as it could not explain all the observations.[19] Cassini was forced to include "empirical corrections" in his 1693 tables of eclipses, but never accepted the theoretical basis: indeed, he chose different correction values for the different moons of Jupiter, in direct contradiction with Rømer's theory.[7] Rømer's ideas received a much warmer reception in England. Although Robert Hooke (1635–1703) dismissed the supposed speed of light as so large as to be virtually instantaneous,[20] the Astronomer Royal John Flamsteed (1646–1719) accepted Rømer's hypothesis in his ephemerides of eclipses of Io.[21] Edmond Halley (1656–1742), a future Astronomer Royal, was also an early and enthusiastic supporter.[7] Isaac Newton (1643–1727) also appears to
66
Rømer's determination of the speed of light have accepted Rømer's ideas, and gives a value of "seven or eight minutes" for light to travel from the Sun to Earth in his 1704 book Opticks.[22] Newton also notes that Rømer's observations had been confirmed by others,[22] presumably by Flamsteed and Halley in Greenwich at the very least: the value of 7–8 minutes is closer to the true value (8 minutes 19 seconds) than Rømer's initial estimate of 11 minutes. While it was obviously difficult for many (such as Hooke) to conceive of the enormous speed of light, Rømer's idea suffered a second handicap in that they were based on Kepler's model of the planets orbiting the Sun in elliptical orbits. While Kepler's model had widespread acceptance by the late seventeenth century, it was still considered sufficiently controversial for Newton to spend several pages discussing the observational evidence in favour in his Philosophiæ Naturalis Principia Mathematica (1687). Rømer's view that the velocity of light was finite was not fully accepted until measurements of stellar aberration were made in 1727 by James Bradley (1693–1762).[23] Bradley, who would be Halley's successor as Astronomer Royal, calculated a value of 8 minutes 13 seconds for light to travel from the Sun to Earth.[23] Ironically, stellar aberration had first been observed by Cassini and (independently) by Picard in 1671, but neither astronomer was able to give an explanation for the phenomenon.[7] Bradley's work also laid to rest any remaining serious objections to the Keplerian model of the Solar System.
Later measurements Swedish astronomer Pehr Wilhelm Wargentin (1717–83) used Rømer's method in the preparation of his ephemerides of Jupiter's moons (1746), as did Giovanni Domenico Maraldi working in Paris.[7] The remaining irregularities in the orbits of the Galilean moons would not be satisfactorily explained until the work of Joseph Louis Lagrange (1736–1813) and Pierre-Simon Laplace (1749–1827) on orbital resonance. In 1809, again making use of observations of Io, but this time with the benefit of more than a century of increasingly precise observations, the astronomer Jean Baptiste Joseph Delambre (1749–1822) reported the time for light to travel from the Sun to the Earth as 8 minutes 12 seconds. Depending on the value assumed for the astronomical unit, this yields the speed of light as just a little more than 300,000 kilometres per second. The first measurements of the speed of light using completely terrestrial apparatus were published in 1849 by Hippolyte Fizeau (1819–96). Compared to modern values, Fizeau's result (about 313,000 kilometres per second) was too high, and less accurate than those obtained by Rømer's method. It would be another thirty years before A. A. Michelson in the United States published his more precise results (299,910±50 km/s) and Simon Newcomb confirmed the agreement with astronomical measurements, almost exactly two centuries after Rømer's announcement.
Modern discussion Did Rømer measure the speed of light? Several modern discussions have suggested that Rømer should not be credited with the measurement of the speed of light, as he never gave a value in Earth-based units.[24] These authors credit Huygens with the first calculation of the speed of light.[25] Huygens' estimate was a value of 110,000,000 toises per second: as the toise was later determined to be just under two metres,[26] this gives the value in modern units. However, Huygens' estimate was not a precise calculation but rather an illustration at an order of magnitude level. The relevant passage from Treatise sur la lumière reads: If one considers the vast size of the diameter KL, which according to me is some 24 thousand diameters of the Earth, one will acknowledge the extreme velocity of Light. For, supposing that KL is no more than 22 thousand of these diameters, it appears that being traversed in 22 minutes this makes the speed a
67
Rømer's determination of the speed of light thousand diameters in one minute, that is 16-2/3 diameters in one second or in one beat of the pulse, which makes more than 11 hundred times a hundred thousand toises;[27] Huygens was obviously not concerned about the 9% difference between his preferred value for the distance from the Sun to Earth and the one he uses in his calculation. Nor was there any doubt in Huygens' mind as to Rømer's achievement, as he wrote to Colbert (emphasis added): I have seen recently, with much pleasure, the beautiful discovery of Mr. Romer, to demonstrate that light takes time in propagating, and even to measure this time;[16] Neither Newton nor Bradley bothered to calculate the speed of light in Earth-based units. The next recorded calculation was probably made by Fontenelle: claiming to work from Rømer's results, the historical account of Rømer's work written some time after 1707 gives a value of 48203 leagues per second.[28] This is 16.826 Earth-diameters (214,636 km) per second.
Doppler method It has also been suggested that Rømer was measuring a Doppler effect, and this 166 years before Christian Doppler's 1842 discovery.[29] The Doppler effect is the change in observed frequency of an oscillator (in this case, Io orbiting around Jupiter) when the observer (in this case, on Earth's surface) is moving: the frequency is higher when the observer is moving towards the oscillator and lower when the observer is moving away from the oscillator. This apparently anachronistic analysis implies that Rømer was measuring the ratio c⁄v, where c is the speed of light and v is the Earth's orbital velocity (strictly, the component of the Earth's orbital velocity parallel to the Earth–Jupiter vector), and indicates that the major inaccuracy of Rømer's calculations was his poor knowledge of the orbit of Jupiter.[29][13] There is no evidence that Rømer thought that he was measuring c⁄v: he gives his result as the time of 22 minutes for light to travel a distance equal to the diameter of Earth's orbit or, equivalently, 11 minutes for light to travel from the Sun to Earth.[4][9] It can be readily shown that the two measurements are equivalent: if we give τ as the time taken for light to cross the radius of an orbit (e.g. from the Sun to Earth) and P as the orbital period (the time for one complete rotation), then[30]
Bradley, who was measuring c⁄v in his studies of aberration in 1729, was well aware of this relation as he converts his results for c⁄v into a value for τ without any comment.[23]
Bibliography • Bobis, Laurence; Lequeux, James (2008), "Cassini, Rømer and the velocity of light" [31], J. Astron. Hist. Heritage 11 (2): 97–105. • Bradley, James (1729), "Account of a new discovered Motion of the Fix'd Stars" [32], Philosophical Transactions of the Royal Society of London 35: 637–60. • Cohen, I. B. (1940), "Roemer and the first determination of the velocity of light (1676)", Isis 31 (2): 327–79, doi:10.1086/347594; reprinted in book form by the Burndy Library, 1942. • Daukantas, Patricia (July 2009), "Ole Rømer and the Speed of Light" [33], Optics & Photonics News: 42–47. • French, A. P. (1990), "Roemer: a cautionary tale" [34], in Roche, John, Physicists look back: studies in the history of physics, CRC Press, pp. 120–23, ISBN 0-85274-001-8. • Godin, Louis; Fontenelle, Bernard de, eds. (1729–34), Mémoires de l'Académie royale des sciences depuis 1666 jusqu'en 1699 [35], Paris: Compagnie des libraires, pp. 112–15, 140–41. (French) • Huygens, Christiaan (16 September 1677), "Lettre Nº 2103" [36], in Bosscha, J., Œuvres complètes de Christiaan Huygens (1888–1950). Tome VIII: Correspondance 1676–1684, The Hague: Martinus Nijhoff, 1899, pp. 30–31. (Latin)
68
Rømer's determination of the speed of light • Huygens, Christiaan (14 October 1677), "Lettre Nº 2105" [37], in Bosscha, J., Œuvres complètes de Christiaan Huygens (1888–1950). Tome VIII: Correspondance 1676–1684, The Hague: Martinus Nijhoff, 1899, pp. 36–37. (French)
• Huygens, Christiaan (1690), Traitée de la Lumière [38], Leiden: Pierre van der Aa. (French) • Meyer, Kirstine (1915), "Om Ole Rømers Opdagelse af Lysets Tøven", Det Kongelige Danske Videnskabernes Selskabs Skrifter, 7. Række, naturvidenskabelig og mathematisk Afdeling XII: 3. (Danish) • Newton, Isaac (1704), "Book II, Prop. XI" [39], Opticks, London: Sam. Smith. and Benj. Walford. • Rømer, Ole (30 September 1677), "Lettre Nº 2104" [40], in Bosscha, J., Œuvres complètes de Christiaan Huygens (1888–1950). Tome VIII: Correspondance 1676–1684, The Hague: Martinus Nijhoff, 1899, pp. 32–35. (Latin) • Saito, Yoshio (2005), "A Discussion of Roemer's Discovery concerning the Speed of Light", AAPPS Bulletin 15 (3): 9–17. • Shea, James H. (1998), "Ole Rømer, the speed of light, the apparent period of Io, the Doppler effect, and the dynamics of Earth and Jupiter", Am. J. Phys. 66 (7): 561–69, Bibcode 1998AmJPh..66..561S, doi:10.1119/1.19020. • Teuber, Jan (2004), "Ole Rømer og den bevægede Jord - en dansk førsteplads?", in Friedrichsen, Per; Henningsen, Ole; Olsen, Olaf et al., Ole Rømer - videnskabsmand og samfundstjener, Copenhagen: Gads Forlag, pp. 218, ISBN 87-12-04139-4. (Danish) • Wróblewski, Andrzej (1985), "de Mora Luminis: A spectacle in two acts with a prologue and an epilogue", Am. J. Phys. 53 (7): 620–30, Bibcode 1985AmJPh..53..620W, doi:10.1119/1.14270.
Notes [1] There are several alternative spellings of Rømer's surname: Roemer, Rœmer, Römer etc. The Danish Ole is sometimes latinized to Olaus. [2] The timing of the emergence comes from one of the few surviving manuscripts of Rømer, in which he records the date as 19 March 1671: see Meyer (1915). By consistency with the other timings recorded in the manuscript (written several years after the event), it has been assumed that Rømer noted the Paris time of the emergence. The time difference of 42 minutes and 10 seconds between Paris and Uraniborg comes from the same manuscript: the modern value is 41 minutes 26 seconds. [3] Meyer (1915). [4] Rømer (1677). [5] Several texts erroneously place the date of the announcement in 1685 or even in 1684. Bobis and Lequeux (2008) have convincingly demonstrated that the announcement was made on 22 August 1676, and that it was made by Cassini and not Rømer. [6] The original record of the meeting of the Royal Academy of Sciences has been lost. The quotation comes from an unpublished manuscript in Latin preserved in the library of the Paris Observatory, probably written by Joseph-Nicolas Delisle (1688–1768) at some point before 1738. See Bobis and Lequeux (2008), which contains a facsimile of the manuscript. [7] Bobis and Lequeux (2008). [8] Teuber (2004). [9] "Démonstration touchant le mouvement de la lumière trouvé par M. Römer de l’Académie Royale des Sciences" (http:/ / www-obs. univ-lyon1. fr/ labo/ fc/ ama09/ pages_jdsc/ pages/ jdsc_1676_lumiere. pdf), Journal des Sçavans: 233–36, 1676, . (French) [10] "A demonstration concerning the motion of light, communicated from Paris, in the Journal des Scavans, and here made English" (http:/ / www. archive. org/ stream/ philosophicaltra02royarich#page/ 397/ mode/ 1up), Philosophical Transactions of the Royal Society of London 12: 893–94, 1677, Bibcode 1677RSPT...12..893., . [11] Bobis and Lequeux (2008) tentatively attribute the translation to Edmond Halley (1656–1742), who would become English Astronomer Royal and who is best known for his calculations concerning Halley's comet. However, other sources – not least his own Catalogus Stellarum Australium (http:/ / books. google. es/ books?id=QVg4AAAAMAAJ& pg=PA11& dq=Catalogus+ Stellarum+ Australium& ei=VrvtSs35AZWayASfgfmLCg& hl=ca#v=onepage& q=& f=false) published in 1679 – suggest that Halley was on the island of St. Helena in the South Atlantic Ocean at the time. [12] Although the news report doesn't make it explicit, the choice of a point of quadrature for the example is unlikely to be fortuitous. At the second quadrature, the motion of the Earth in its orbit is taking it directly away from Jupiter. As such, it is the point at which the greatest effect is expected over a single orbit of Io. [13] The figure of 210 Earth-diameters per orbit of Io for the orbital speed of the Earth relative to Jupiter is far lower than the real figure, which averages around 322 Earth-diameters per orbit of Io taking into account the orbital motion of Jupiter. Rømer appears to have believed that Jupiter is closer to the Sun (and hence moving faster along its orbit) than is really the case. [14] The Royal Academy of Sciences had instructed Rømer to publish a joint paper with his colleagues. [15] Saito (2005).
69
Rømer's determination of the speed of light [16] Huygens (14 October 1677). "J'ay veu depuis peu avec bien de la joye la belle invention qu'a trouvé le Sr. Romer, pour demonstrer que la lumiere en se repandant emploie du temps, et mesme pour mesurer ce temps, qui est une decouverte fort importante et a la confirmation de la quelle l'observatoire Royal s'emploiera dignement. Pour moy cette demonstration m'a agrée d'autant plus, que dans ce que j'escris de la Dioptrique j'ay supposé la mesme chose…" [17] Rømer (1677). "Dominos Cassinum et Picardum quod attinet, quorum judicium de illa re cognoscere desideras, hic quidem plane mecum sentit." [18] See note 2 at Huygens (16 September 1677). [19] This last point is put quite clearly as late as 1707 by Cassini's nephew, Giacomo Filippo Maraldi (1665–1729), who also worked at the Royal Observatory: "In order for an hypothesis to be accepted, it is not enough that it agrees with some observations, it must also be consistent with the other phenomena." Quoted in Bobis and Lequeux (2008). [20] In his 1680 Lectures on Light: "so exceedingly swift that 'tis beyond Imagination […] and if so, why it may not be as well instantaneous I know no reason." Quoted in Daukantas (2009). [21] Daukantas (2009). [22] Newton (1704): "Light is propagated from luminous Bodies in time and spends about seven or eight minutes of an hour in passing from the Sun to the Earth. This was observed first by Romer, and then by others, by means of the Eclipses of the Satellites of Jupiter." [23] Bradley (1729). [24] Cohen (1940). Wróblewski (1985). [25] French (1990), pp. 120–21. (http:/ / books. google. com/ books?id=5H3Oo0iicrkC& pg=PA120) [26] The exact ratio is 1 toise = 54000⁄27706 metres, or approximately 1.949 m: French law of 19 frimaire An VIII (10 December 1799). Huygens was using Picard's value (1669) of the circumference of the Earth as 360×25×2282 toises, while the 1799 legal conversion uses the more precise results of Delambre and Méchain. [27] Huygens (1690), pp. 8–9. (http:/ / books. google. com. au/ books?id=No8PAAAAQAAJ& pg=PA8) Translation by Silvanus P. Thompson. (http:/ / www. gutenberg. org/ catalog/ world/ readfile?fk_files=164378& pageno=11) [28] Godin and Fonetenelle (1729–34). "Il suit des Observations de Mr. Roëmer, que la lumiére dans une seconde de tems fait 48203 lieuës communes de France, & 377⁄1141 parties d'une de ces lieuës, fraction qui doit bien être négligée." [29] Shea (1998). [30] The expression is given for the approximation to a circular orbit. The derivation is as follows: (1) express the orbital velocity in terms of the orbital radius r and the orbital period P: v = 2πr⁄P (2) substitute τ = r⁄c → v = 2πτc⁄P (3) rearrange to find c⁄v. [31] http:/ / www. bibli. obspm. fr/ Bobis%20and%20Lequeux. pdf [32] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k55840n. image. f375. langEN [33] http:/ / www. opnmagazine-digital. com/ opn/ 200907/ ?pg=45#pg44 [34] http:/ / books. google. com/ books?id=5H3Oo0iicrkC& pg=PA120 [35] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k56063967 [36] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k77856x. image. f37. langEN [37] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k77856x. image. f43. langEN [38] http:/ / books. google. com. au/ books?id=No8PAAAAQAAJ& printsec=frontcover [39] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k3362k. image. f235. vignettesnaviguer [40] http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k77856x. image. f39. langEN#
References External links • Short, uncluttered explanation by Ethan Siegel (http://scienceblogs.com/startswithabang/2011/09/ how_we_found_the_speed_of_ligh.php) • Visualize Solar System at a given Epoch (http://math-ed.com/Resources/GIS/Geometry_In_Space/java1/ Temp/TLVisPOrbit.html) • The history of a velocity (http://www.rundetaarn.dk/engelsk/observatorium/light1.html) • Rømer and the Doppler principle (http://www.rundetaarn.dk/engelsk/observatorium/light.htm) • Proceeding of a Rømer Experiment for Schools (http://eaae-astronomy.org/WG3-SS/WorkShops/Romer. html) from EAAE Summer Schools
70
Sagnac effect
71
Sagnac effect The Sagnac effect (also called Sagnac interference), named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in opposite directions. To act as a ring the trajectory must enclose an area. On return to the point of entry the light is allowed to exit the apparatus in such a way that an interference pattern is obtained. The position of the interference fringes is dependent on the angular velocity of the setup. This arrangement is also called a Sagnac interferometer. The Sagnac effect is the electromagnetic counterpart of the mechanics of rotation. A gimbal mounted gyroscope remains pointing in the same direction after spinning up, and thus can be used as the reference for an inertial guidance system. A Sagnac interferometer measures its own angular velocity with respect to the local inertial frame; hence just as a gyroscope it can provide the reference for an inertial guidance system. The principles behind the two devices are different, however. A gyroscope uses the principle of conservation of angular momentum whereas the interferometer does not.
Description and operation Usually several mirrors are used, so that the light beams follow a triangular or square trajectory. Fiber optics can also be employed to guide the light. The ring interferometer is located on a platform that can rotate. When the platform is rotating the lines of the interference pattern are displaced as compared to the position of the interference pattern when the platform is not rotating. The amount of displacement is proportional to the angular velocity of the rotating platform. The axis of rotation does not have to be inside the enclosed area. When the platform is rotating, the point of entry/exit moves during the transit time of the light. So one beam has covered less distance than the other beam. This creates the shift in the interference pattern. Therefore, the interference pattern obtained at each angular velocity of the platform features a different phase-shift particular to that angular velocity.
Schematic representation of a Sagnac interferometer.
In the above discussion, the rotation mentioned is rotation with respect to an inertial reference frame.
History In theory, the first suggestion to undertake such an interferometry experiment was given by Oliver Lodge in 1897, and then by Albert Abraham Michelson in 1904. They hoped that if someone can carry out such an experiment, which was aimed to measure the rotation of the Earth by optical means, it would be possible to decide between the idea of a stationary aether, and an aether which is completely dragged by the Earth. That is, if the aether is carried along by the Earth (or by the interferometer) the result would be negative, while a stationary aether would give a positive result. [1] [2] [3] Max von Laue in 1911 continued the theoretical work of Michelson, and also incorporated special relativity in his calculations. He predicted a positive result (to first order in v/c) for both special relativity and for the stationary aether, because in those theories the speed of light is independent of the velocity of the source, and thus the propagation time for the counter-propagating rays is not the same when viewed from inertial frames of reference; only complete-aether-drag models would give a negative result.[4][5] While Laue confined his investigations on inertial frames, Paul Langevin (1921/35) and many others described the effect when viewed from rotating reference frames (in both special and general relativity, see Born coordinates).[6][7]
Sagnac effect
72
In practice, the first interferometry experiment aimed at observing the correlation of angular velocity and phase-shift was performed by the Frenchman Georges Sagnac in 1913, which is why the effect is named for him. Its purpose was to detect "the effect of the relative motion of the ether".[8][9] Sagnac only mentioned the consistency with a stationary aether. However, as explained above, two years earlier Max von Laue already predicted this effect on the basis of special relativity, so this effect is consistent with special relativity as well.[4] An experiment conducted in 1911 by Franz Harress, aimed at making measurements of Fresnel drag of light propagating through moving glass, was in 1920 recognized by Laue as actually constituting a Sagnac experiment. Harress had ascribed the "unexpected bias" to something else.[10] In 1926 a very ambitious ring interferometry experiment was set up by Albert Michelson and Henry Gale. The aim was to find out whether the rotation of the Earth has an effect on the propagation of light in the vicinity of the Earth. The Michelson–Gale–Pearson experiment was a very large ring interferometer, (a perimeter of 1.9 kilometer), large enough to detect the angular velocity of the Earth. The outcome of the experiment was that the angular velocity of the Earth as measured by astronomy was confirmed to within measuring accuracy. The ring interferometer of the Michelson-Gale experiment was not calibrated by comparison with an outside reference (which was not possible, because the setup was fixed to the Earth). From its design it could be deduced where the central interference fringe ought to be if there would be zero shift. The measured shift was 230 parts in 1000, with an accuracy of 5 parts in 1000. The predicted shift was 237 parts in 1000.[11]
Theory The shift in interference fringes can be viewed simply as a consequence of different distances light travels due to the rotation of the observer. The simplest derivation is for a circular ring rotating at an angular velocity of , but the result is general for loop geometries with other shapes. If a light source emits in both directions from one point on the rotating ring, light traveling with the rotation direction will travel more than one circumference around the ring and hit the light source from behind after a time
is the distance (0 to 0' in the figure) the mirror has moved in that same time:
Eliminating
from the two equations above we get:
Likewise, the light traveling against the rotation will travel less than one circumference before hitting the light source on the front side. So the time for this direction of light to reach the moving source again is:
Since
Light traveling opposite directions go different distances before reaching the moving source again.
one can use the binomial approximation: the time difference traveled by the light to the
screen for an interference pattern is
where A is the area of the ring. This result happens to be general for any shape of loop with area A.
Sagnac effect
73
We imagine a screen for viewing fringes placed at the light source (or we use a beamsplitter to send light from the source point to the screen). If the light were pulses shorter than , there would be no interference. But applications use steady light, and shifting interference fringes are seen due to the presence of the two beams of light on the screen that left the source at different times and hence have different phases at the screen. The phase shift is , which causes fringes to shift in proportion to
and
.
In the case of light propagating in vacuum pre-relativistic theories and relativistic physics predict the same. In other words, in the case of propagation in vacuum a Sagnac experiment does not distinguish between pre-relativistic physics and relativistic physics. Both predict the same. When the Sagnac setup has the light propagating in fibre optics then the setup is effectively a combination of a Sagnac experiment and the Fizeau experiment. In glass the speed of light is slower than in vacuum, and the fibre optics itself is a moving medium. In that case the relativistic velocity addition rule applies. Pre-relativistic theories of light propagation cannot account for the Fizeau effect. (By 1900 Lorentz could account for the Fizeau effect, but by that time his theory had evolved to a form where in effect it was mathematically equivalent to special relativity. Hence only relativistic physics can account for the physics of fibre optic Sagnac interferometers.) A clock attached to the ring would run slower due to its velocity than an inertial observer's, the light frequency of the moving source would increase to cancel that. Also, Doppler effects cancel out, so the Sagnac effect does not involve Doppler effect. In the case of ring laser interferometry it is important to be aware of this. When the ring laser setup is rotating the counterpropagating beams undergo frequency shifts in opposite directions. This frequency shift is not related to Doppler shift.
Reference frames The Sagnac effect is not an artifact of the choice of reference frame. It is independent of the choice of reference frame, as is shown by a calculation that invokes the metric tensor for an observer at the axis of rotation of the ring interferometer and rotating with it yielding the same outcome. If one starts with the Minkowski metric and does the coordinate conversions and (see Born coordinates), the line element of the resultant metric is where • • • • •
is proper time for the central observer, is distance from the center, is the angular distance along the ring from the direction the central observer is facing, is the direction perpendicular to the plane of the ring, and is the rate of rotation of the ring and the observer.
Under this metric, the speed of light tangent to the ring is
depending on whether the light is moving against
or with the rotation of the ring. Note that only the case of
is inertial. For
non-inertial, which is why the speed of light at positions distant from the observer (at
this frame of reference is ) can vary from
.
Sagnac effect
74
Synchronization procedures The procedures for synchronizing clocks all over the globe must take the rotation of the Earth into account. The signals used for the synchronizing procedure can be in the form of electric pulses conducted in electric wires, they can be light pulses conducted in fiber optic cables, or they can be radio signals. If a number of stations situated on the equator relay pulses to one another, will the time-keeping still match after the relay has circumnavigated the globe? One condition for handling the relay correctly is that the time it takes the signal to travel from one station to the next is taken into account each time. On a non-rotating planet that ensures fidelity: two time-disseminating relays, going full circle in opposite directions around the globe, will arrive at the originating station simultaneously. However, on a rotating planet, it must also be taken into account that the receiver moves during the transit time of the signal, shortening or lengthening the transit time compared to what it would be in the situation of a non-rotating planet. It is recognized that the synchronization of clocks and ring interferometry are related in a fundamental way. Therefore the necessity to take the rotation of the Earth into account in synchronization procedures is also called the Sagnac effect.
Practical uses The Sagnac effect is employed in current technology. One use is in inertial guidance systems. Ring laser gyroscopes are extremely sensitive to rotations, which need to be accounted for if an inertial guidance system is to return correct results. The ring laser also can detect the sidereal day, which can also be termed "mode 1". Global navigation systems, such as GPS, GLONASS, COMPASS or Galileo, need to take the rotation of the Earth into account in the procedures of using radio signals to synchronize clocks.
Ring lasers The type of ring interferometer described in the opening section is sometimes called a 'passive ring interferometer'. A passive ring interferometer uses light entering the setup from outside. The interference pattern that is obtained is a fringe pattern, and what is measured is a phase shift. It is also possible to construct a ring interferometer that is self-contained, based on a completely different arrangement. This is called a "ring laser". The light is generated and sustained by incorporating laser excitation in the path of the light. To understand what happens in a ring laser cavity, it is helpful to discuss the physics of the laser process in a laser setup with continuous generation of light. As the laser excitation is started, the molecules inside the cavity emit photons, but since the molecules have a thermal velocity, the light inside the laser cavity is at first a range of frequencies, corresponding to the statistical distribution of velocities. The process of stimulated emission makes one frequency quickly outcompete other frequencies, and after that the light is very close to monochromatic.
Schematic representation of a ring laser setup.
Sagnac effect
75 For the sake of simplicity, assume that all emitted photons are emitted in a direction parallel to the ring. (That is, in fact, a huge simplification, but serves this explanation well.) The image 'frequency shift' illustrates the effect of the ring laser's rotation.
Image: frequency shift. Schematic representation of the frequency shift when a ring laser interferometer is rotating. Both the counterpropagating light and the co-propagating light go through 12 cycles of their frequency.
Animation: propagating photons. The red and blue dots represent counter-propagating photons, the grey dots represent molecules in the laser cavity.
In a linear laser the laser light that is generated fits the length of the laser cavity exactly; an integer multiple of the wavelength fits the length of the laser cavity. This means that in traveling back and forth the laserlight goes through an integer number of cycles of its frequency. In the case of a ring laser the same applies: the number of cycles of the laser light's frequency is the same in both directions. This quality of the same number of cycles in both directions is preserved when the ring laser setup is rotating. The image illustrates that there is wavelength shift (hence a frequency shift) in such a way that the number of cycles is the same in both directions of propagation. By bringing the two frequencies of laserlight to interference a beat frequency can be obtained; the beat frequency is the difference between the two frequencies. This beat frequency can be thought of as an interference pattern in time. (The more familiar interference fringes of interferometry are a spatial pattern). The period of this beat frequency is linearly proportional to the angular velocity of the ring laser with respect to inertial space.
No calibration
In contrast with the case of passive ring interferometry, in the case of ring laser interferometry there is no need for calibration. With passive ring interferometry there is no way of establishing which position of the interference fringes corresponds to zero angular velocity of the ring interferometer setup. Ring laser interferometry, on the other hand, is self-calibrating. The beat frequency will be zero if and only if the ring laser setup is non-rotating with respect to inertial space. The animation 'propagating photons' illustrates the physical property that makes the ring laser interferometer process a self-calibrating process. The grey dots represent molecules in the laser cavity that act as resonators. Along every section of the ring cavity the speed of light is the same in both directions. When the ring laser device is rotating then it rotates with respect to that background. In other words: the invariance of the speed of light is the reference for the self-calibrating property of the ring laser interferometer.
Lock-in Because of the way the laser light is generated, light in laser cavities has a strong tendency to be monochromatic (and usually that is precisely what laser apparatus designers want). This tendency to not split in two frequencies is called 'lock-in'. The ring laser devices incorporated in navigational instruments (to serve as a ring laser gyroscope) are generally too small to avoid spontaneously falling into lock at low rates of rotation. By "dithering" the gyro through a small angle at high frequency, staying out of lock, while not ensured, becomes more likely.
Sagnac effect
76
Sagnac Effect in translational motion In all configurations shown in above, all segments of light propagation paths move in a rotational way. Recent experiments demonstrated that there is a travel-time difference between two counterpropagating light beams in a fiber segment of length ΔL moving at a speed v (with respect to the inertial frame where the interferometer is momentarily at rest at their arrival), whether the motion is uniformly translational or rotational in a loop.[12] The finding includes the Sagnac effect of rotation, , as a special case of generalized Sagnac effect,
where L is the total light propagation length projected on the motion direction, and
the travel time difference is independent of the refractive index of the medium that light propagates. A new fiber optic sensor based on the generalized Sagnac effect for measuring translational motion with a high sensitivity is suggested.[13]
References [1] Anderson, R., Bilger, H.R., Stedman, G.E. (1994). "Sagnac effect: A century of Earth-rotated interferometers". Am. J. Phys. 62 (11): 975–985. Bibcode 1994AmJPh..62..975A. doi:10.1119/1.17656. [2] Lodge, Oliver (1897). "Experiments on the Absence of Mechanical Connexion between Ether and Matter". Phil. Trans. Roy. Soc. 189: 149–166. [3] Michelson, A.A. (1904). "Relative Motion of Earth and Aether". Philosophical Magazine 8 (48): 716–719. [4] Pauli, Wolfgang (1981). Theory of Relativity. New York: Dover. ISBN 0-486-64152-X. [5] Laue, Max von (1911). "On an Experiment on the Optics of Moving Bodies". Münchener Sitzungsberichte: 405–412. [6] Guido Rizzi, Matteo Luca Ruggiero (1981). "The relativistic Sagnac Effect: two derivations". In G. Rizzi and M.L. Ruggiero. Relativity in Rotating Frames. Dordrecht: Kluwer Academic Publishers. arXiv:gr-qc/0305084. ISBN 0-486-64152-X. [7] L.D. Landau, E.M. Lifshitz, (1962). “The Classical Theory of Fields”. 2nd edition, Pergamon Press, pp. 296 - 297. [8] Sagnac, Georges (1913). "The demonstration of the luminiferous aether by an interferometer in uniform rotation". Comptes Rendus 157: 708–710. [9] Sagnac, Georges (1913). "On the proof of the reality of the luminiferous aether by the experiment with a rotating interferometer". Comptes Rendus 157: 1410–1413. [10] Laue, Max von (1920). "Zum Versuch von F. Harreß" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k15364f. image. f452). Annalen der Physik 367 (13): 448–463. Bibcode 1920AnP...367..448L. doi:10.1002/andp.19203671303. . [11] Albert Abraham Michelson, Henry G. Gale: The Effect of the Earth's Rotation on the Velocity of Light (http:/ / adsabs. harvard. edu/ abs/ 1925ApJ. . . . 61. . 140M), in: The Astrophysical Journal 61 (1925), S. 140–145 [12] Ruyong Wang, Yi Zheng, Aiping Yao, Dean Langley (2003). "Modified Sagnac Experiment for Measuring Travel-time Difference between Counter-propagating Light Beams in a Uniformly Moving Fiber". Physics Letters A 312: 7–10. arXiv:physics/0609222. Bibcode 2003PhLA..312....7W. doi:10.1016/S0375-9601(03)00575-9. [13] Ruyong Wang, Yi Zheng, Aiping Yao (2004). "Generalized Sagnac Effect". Physical Review Letters 93 (14): 143901. arXiv:physics/0609235. Bibcode 2004PhRvL..93n3901W. doi:10.1103/PhysRevLett.93.143901.
External links • Large Laser Gyroscopes for Monitoring Earth Rotation (http://www.wettzell.ifag.de/LKREISEL/G/ LaserGyros.html) • Mathpages article on the Sagnac Effect (http://www.mathpages.com/rr/s2-07/2-07.htm) • Ring-laser tests of fundamental physics and geophysics (http://www.physics.berkeley.edu/research/packard/ related/Gyros/LaserRingGyro/Steadman/StedmanReview1997.pdf) (Extensive review by G E Stedman. PDF-file, 1.5 MB) • The Sagnac Effect and its Application for GPS (http://relativity.livingreviews.org/open?pubNo=lrr-2003-1& page=node1.html) GPS-related article by Neil Ashby • Live data from New Zealand 21 m x 40 m ring laser gyro (http://www.ringlaser.org.nz/content/live_data. php)
Terrella
77
Terrella A terrella (meaning "little earth") is a small magnetised model ball representing the Earth, that is thought to have been invented by the English physician William Gilbert while investigating magnetism, and further developed 300 years later by the Norwegian scientist and explorer Kristian Birkeland, while investigating the aurora. Terrellas had been used up until the late 20th century to attempt to simulate the Earth's magnetosphere, but have now been replaced by computer simulations.
Kristian Birkeland's magnetised terrella. In this experiment, he noted two spirals which he considered may be similar to that of spiral [1][2] nebulae.
William Gilbert's terrella William Gilbert, the royal physician to Queen Elizabeth I, devoted much of his time, energy and resources to the study of the Earth's magnetism. It had been known for centuries that a freely suspended compass needle pointed north. Later investigators (including Christopher Columbus) found that direction deviated somewhat from true north, and Robert Norman showed the force on the needle was not horizontal but slanted into the Earth. William Gilbert's explanation was that the Earth itself was a giant magnet, and he demonstrated this by creating a scale model of the magnetic Earth, a "terrella", a sphere formed out of a lodestone. Passing a small compass over the terrella, Gilbert demonstrated that a horizontal William Gilbert's terrella compass would point towards the magnetic pole, while a dip needle, balanced on a horizontal axis perpendicular to the magnetic one, indicated the proper "magnetic inclination" between the magnetic force and the horizontal direction. Gilbert later reported his findings in De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure, published in 1600.
Terrella
78
Kristian Birkeland's terrella Kristian Birkeland was a Norwegian physicist who, around 1895, tried to explain why the lights of the polar aurora appeared only in regions centered at the magnetic poles. He simulated the effect using a "terrella," a sphere in a vacuum tank to which he directed beams of cathode rays, later identified as electrons, and found they indeed produced a glow in regions around the poles of the terrella. Because of residual gas in the chamber, the glow also outlined the path of the particles. Neither he nor his associate Carl Størmer (who calculated such paths) could understand why the actual aurora avoided the area around the poles themselves. We now know this relates to the origin of the auroral electrons, which is actually inside the Earth's magnetosphere, the region of space controlled by the Earth's magnetism. Birkeland believed the electrons came from the Sun, since large auroral outbursts were associated with sunspot activity.
Kristian Birkeland and his magnetized terrella experiment, which led him to surmise that charged particles interacting with the Earth's [1] magnetic field were the cause of the aurora.
Birkeland constructed several terrellas. One large terrella experiment was reconstructed in Tromsø, Norway.[3]
Other terrellas Baron Karl von Reichenbach, February 12, 1788, Stuttgart - January 1869. The Baron used an electromagnet, placed within a large hollow iron sphere, and this was examined in the darkroom under varying degrees of electrification. The Baron referred to the iron globe as his "terrella", or "little earth". Brunberg and Dattner in Sweden, around 1950, used a terrella to simulate trajectories of particles in the Earth's field. Podgorny in the Soviet Union, around 1972, built terrellas at which a flow of plasma was directed, simulating the solar wind. Hafiz-Ur Rahman at the University of California, Riverside conducted more realistic experiments around 1990. All such experiments are difficult to interpret, and are never able to scale all the parameters needed to properly simulate the Earth's magnetosphere, which is why such experiments have now been completely replaced by computer simulations.
Notes [1] Birkeland, Kristian (1908 (section 1), 1913 (section 2)). The Norwegian Aurora Polaris Expedition 1902-1903 (http:/ / www. archive. org/ details/ norwegianaurorap01chririch). New York and Christiania (now Oslo): H. Aschehoug & Co. . out-of-print, full text online [2] Section 2, Chapter VI, page 678 [3] Terje Brundtland. "The Birkeland Terrella" (http:/ / www. mhs. ox. ac. uk/ sphaera/ index. htm?issue7/ articl6). . Retrieved 24 May 2012.
References External links • NASA Educational Website on the Terrella (http://www-istp.gsfc.nasa.gov/Education/wterrell.html)
TroutonNoble experiment
79
Trouton–Noble experiment The Trouton–Noble experiment (also connected to thought experiments such as the "Trouton-Noble paradox", "Right-angle lever paradox", or "Lewis-Tolman paradox") attempted to detect motion of the Earth through the luminiferous aether, and was conducted in 1901–1903 by Frederick Thomas Trouton (who also developed the Trouton's ratio) and H. R. Noble. It was based on a suggestion by George FitzGerald that a charged parallel-plate capacitor moving through the aether should orient itself perpendicular to the motion. Like the earlier Michelson–Morley experiment, Trouton and Noble obtained a null result: no motion relative to the aether could be detected.[1] [2] This null result was reproduced, with increasing sensitivity, by Rudolf Tomaschek (1925, 1926), Chase (1926, 1927) and Hayden in 1994. [3] [4] [5] [6] [7] [8] Such experimental results are now seen, consistent with special relativity, to reflect the validity of the principle of relativity and the absence of any absolute rest frame (or aether). See also Tests of special relativity.
Trouton–Noble Experiment In the experiment, a suspended parallel-plate capacitor is held by a fine torsion fiber and is charged. If the aether theory were correct, the change in Maxwell's equations due to the Earth's motion through the aether would lead to a torque causing the plates to align perpendicular to the motion. This is given by:
where
is the torque,
the energy of the condenser,
the angle between the normal of the plate and the
velocity. On the other hand, the assertion of special relativity that Maxwell's equations are invariant for all frames of reference moving at constant velocities would predict no torque (a null result). Thus, unless the aether were somehow fixed relative to the Earth, the experiment is a test of which of these two descriptions is more accurate. Its null result thus confirms Lorentz invariance of special relativity. However, while the negative experimental outcome can easily be explained in the rest frame of the device, the explanation from the viewpoint of a non-co-moving frame (concerning the question, whether the same torque should arise as in the "aether frame" described above, or whether no torque arises at all) is much more difficult and is called "Trouton-Noble paradox".
TroutonNoble experiment
80
Right-angle lever paradox. The Trouton–Noble paradox is essentially equivalent to a thought experiment called "right angle lever paradox", first discussed by Gilbert Newton Lewis and Richard Chase Tolman in 1909.[9] Suppose a right-angle lever with endpoints abc. In its rest frame, the forces towards ba and towards bc must be equal to obtain equilibrium, thus no torque is given by the law of the lever:
where
is the torque, and
the rest length of one lever arm.
However, due to length contraction, ba is longer than bc in a non-co-moving system, thus the law of the lever gives:
It can be seen that the torque is not zero, which apparently would cause the lever to rotate in the non-co-moving frame. Since no rotation is observed, Lewis and Tolman thus concluded that no torque exists, therefore:
However, as shown by Max von Laue (1911),[10] this is in contradiction with the relativistic expressions of force,
which gives
When applied to the law of the lever, the following torque is produced:
Which is principally the same problem as in the Trouton-Noble paradox.
Solutions The detailed relativistic analysis of both the Trouton-Noble paradox and the Right-angle lever paradox requires care to correctly reconcile, for example, the effects seen by observers in different frames of reference, but ultimately all such theoretical descriptions are shown to give the same result. In both cases an apparent net torque on an object (when viewed from a certain frame of reference) does not result in any rotation of the object, and in both cases this is explained by correctly accounting, in the relativistic way, for the transformation of all the relevant forces, momenta and the accelerations produced by them. The early history of descriptions of this experiment is reviewed by Janssen (1995).[11]
TroutonNoble experiment
Laue current The first solution of the Trouton-Noble paradox was given by Hendrik Lorentz (1904). His result is based on the assumption, that the torque and momentum due to electrostatic forces, is compensated by the torque and momentum due to molecular forces.[12] This was further elaborated by Max von Laue (1911), who gave the standard solution for these kind of paradoxes. It was based on the so called "inertia of energy" in its general formulation by Max Planck. According to Laue, an energy current connected with a certain momentum ("Laue current") is produced in moving bodies by elastic stresses. The resulting mechanical torque in the case of the Trouton-Noble experiment amounts to:
and in the right-angle lever:
which exactly compensates the electromagnetic torque mentioned above, thus no rotation occurs on both cases. Or in other words: The electromagnetic torque is actually necessary for the uniform motion of a body, i.e., to hinder the body to rotate due to the mechanical torque caused by elastic stresses.[13] [10] [14] [15] Since then, many papers appeared which elaborated on Laue's current, providing some modifications or re-interpretations, and included different variants of "hidden" momentum.[16]
Reformulations of force and momentum Other authors were unsatisfied with the idea that torques and counter-torques arise only because different inertial frames are chosen. Their aim was to replace the standard expressions for momentum and force and thus equilibrium by manifestly Lorentz covariant ones from the outset. So when there is no torque in the rest frame of the considered object, then there are no torques in other frames as well.[17] This is in analogy to the 4/3 problem of the electromagnetic mass of electrons, where similar methods were employed by Enrico Fermi (1921) and Fritz Rohrlich (1960): In the standard formulation of relativistic dynamics the hyperplanes of simultaneity of any observer can be used, while in the Fermi/Rohrlich definition the hyperplane of simultaneity of the object's rest frame should be used.[11] According to Janssen, deciding between Laue's standard model and such alternatives is merely a matter of convention.[11] Following this line of reasoning, Rohrlich (1966) distinguished between "apparent" and "true" Lorentz transformations. For example, a "true" transformation of length would be the result of a direct application of the Lorentz transformation, which gives the non-simultaneous positions of the endpoints in another frame. On the other hand, length contraction would be an example of an apparent transformation, since the simultaneous positions of the endpoints in the moving frame must be calculated in addition to the initial Lorentz transformation. Furthermore, Cavalleri/Salgarelli (1969) distinguished between "synchronous" and "asynchronous" equilibrium conditions. In their view, synchronous consideration of forces should only be used for the object's rest frame, while in moving frames the same forces should be considered asynchronously.[18]
Force and Acceleration A solution without using compensating forces, and without the need of redefining the relativistic concepts of force, equilibrium etc., was published by Paul Sophus Epstein (1911).[19][20] A similar solution was re-discovered by Franklin (2006)[21]. They alluded to the fact that force and acceleration not always have the same direction, that is, the relation of mass, force and acceleration has tensor character in relativity. So the role played by the concept of force in relativity is very different from that of Newtonian mechanics.
81
TroutonNoble experiment
82
Epstein imagined a massless rod with endpoints OM, which is mounted at point O, and a particle with rest mass m is mounted at M. The rod encloses the angle with O. Now a force towards OM is applied at M, and equilibrium in its rest frame is achieved when
. As already shown above, these forces have the form in a
non-co-moving frame:
Thus
.
So the resultant force does not directly point from O to M. Does this lead to a rotation of the rod? No, because Epstein now considered the accelerations caused by the two forces. The relativistic expressions in the case, where a mass m is accelerated by these two forces in the longitudinal and transverse direction, are: , where Thus
.
.
Thus no rotation occurs in this system as well. Similar considerations are also to be applied to the right-angle lever and Trouton-Noble paradox. So the paradoxes are resolved, because the two accelerations (as vectors) point to the center of gravity of the system (condenser), although the two forces do not. Epstein added, that if one finds it more satisfying to re-establish the parallelism between force and acceleration with which we are accustomed in Newtonian mechanics, one has to include a compensating force, which formally corresponds to Laue's current. Epstein developed such a formalism in the subsequent sections of his 1911 paper.
References [1] F. T. Trouton and H. R. Noble, "The mechanical forces acting on a charged electric condenser moving through space," Phil. Trans. Royal Soc. A 202, 165–181 (1903). [2] F. T. Trouton and H. R. Noble, "The Forces Acting on a Charged Condenser moving through Space. Proc. Royal Soc. 74 (479): 132-133 (1903). [3] R. Tomaschek (1925). "Über Versuche zur Auffindung elektrodynamischer Wirkungen der Erdbewegung in großen Höhen I" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k15380p/ f765. image). Annalen der Physik 78: 743–756. . [4] R. Tomaschek (1926). "Über Versuche zur Auffindung elektrodynamischer Wirkungen der Erdbewegung in großen Höhen II" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k15382c/ f533. image). Annalen der Physik 80: 509–514. . [5] Carl T. Chase (1926). "A Repetition of the Trouton-Noble Ether Drift Experiment". Physical Review 28 (2): 378–383. Bibcode 1926PhRv...28..378C. doi:10.1103/PhysRev.28.378. [6] Carl T. Chase (1927). "The Trouton–Noble Ether Drift Experiment". Physical Review 30 (4): 516–519. Bibcode 1927PhRv...30..516C. doi:10.1103/PhysRev.30.516. [7] R. Tomaschek (1927). "Bemerkung zu meinen Versuchen zur Auffindung elektrodynamischer Wirkungen in großen Höhen" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k15386r/ f170. image). Annalen der Physik 84: 161–162. . [8] H. C. Hayden (1994). "High sensitivity Trouton–Noble experiment". Rev. Scientific Instruments 65 (4): 788–792. Bibcode 1994RScI...65..788H. doi:10.1063/1.1144955. [9] Lewis, Gilbert N. & Tolman, Richard C. (1909), "The Principle of Relativity, and Non-Newtonian Mechanics", Proceedings of the American Academy of Arts and Sciences 44: 709–726 [10] Laue, Max von (1911). "Ein Beispiel zur Dynamik der Relativitätstheorie". Verhandlungen der Deutschen Physikalischen Gesellschaft 13: 513–518. • English Wikisource translation: An Example Concerning the Dynamics of the Theory of Relativity [11] Janssen (1995), see "Further reading" [12] Lorentz, Hendrik Antoon (1904), "Electromagnetic phenomena in a system moving with any velocity smaller than that of light", Proceedings of the Royal Netherlands Academy of Arts and Sciences 6: 809–831 [13] Laue, Max von (1911). "Zur Dynamik der Relativitätstheorie". Annalen der Physik 340 (8): 524–542. Bibcode 1911AnP...340..524L. doi:10.1002/andp.19113400808. •
English Wikisource translation: On the Dynamics of the Theory of Relativity
TroutonNoble experiment [14] Laue, Max von (1911). "Bemerkungen zum Hebelgesetz in der Relativitätstheorie". Physikalische Zeitschrift 12: 1008–1010. • English Wikisource translation: Remarks on the Law of the Lever in the Theory of Relativity [15] Laue, Max von (1912). "Zur Theorie des Versuches von Trouton und Noble". Annalen der Physik 343 (7): 370–384. Bibcode 1912AnP...343..370L. doi:10.1002/andp.19123430705. • English Wikisource translation: On the Theory of the Experiment of Trouton and Noble [16] See "further reading", especially Nickerson/McAdory (1975), Singal (1993), Teukolsky (1996), Jefimenko (1999), Jackson (2004). [17] See "further reading", for instance Butler (1968), Aranoff (1969, 1972), Grøn (1975), Janssen (1995, 2008), Ivezić (2006). [18] Rohrlich (1967), Cavalleri/Salgarelli (1969) [19] Epstein, P. S. (1911). "Über relativistische Statik". Annalen der Physik 341 (14): 779–795. Bibcode 1911AnP...341..779E. doi:10.1002/andp.19113411404. • English Wikisource translation: Concerning Relativistic Statics [20] Epstein, P. S. (1927). "Conference on the Michelson-Morley experiment" (http:/ / articles. adsabs. harvard. edu/ / full/ 1928CMWCI. 373. . . 43E/ 0000045. 000. html). Contributions from the Mount Wilson Observatory 373: 45–49. Bibcode 1928CMWCI.373...43E. . [21] Franklin (2006, 2008), see "Further reading".
Further reading History • Michel Janssen, "A comparison between Lorentz's ether theory and special relativity in the light of the experiments of Trouton and Noble, Ph.D. thesis (1995). Online: TOC (http://www.mpiwg-berlin.mpg.de/ litserv/diss/janssen_diss/TitleTOC.pdf), pref. (http://www.mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/ intro.pdf), intro-I (http://www.mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/introI.pdf), 1 (http://www. mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/Chapter1.pdf), 2 (http://www.mpiwg-berlin.mpg.de/litserv/ diss/janssen_diss/Chapter2.pdf), intro-II (http://www.mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/ introII.pdf), 3 (http://www.mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/Chapter3.pdf), 4 (http://www. mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/Chapter4.pdf), refs (http://www.mpiwg-berlin.mpg.de/ litserv/diss/janssen_diss/References.pdf). • Janssen, Michel H. P. (2008), "Drawing the line between kinematics and dynamics in special relativity" (http:// philsci-archive.pitt.edu/3895/), Symposium on Time and Relativity: 1–76 Textbooks • Tolman, R.C. (1917), "The Right-Angled Lever" (http://www.archive.org/details/theoryrelativmot00tolmrich), The theory of relativity of motion, Berkeley: University of California press, pp. 152-153 • Pauli, Wolfgang (1921/1981). "Applications to special cases. Trouton's and Noble's experiment". Theory of Relativity. New York: Dover. pp. 127–130. ISBN 0-486-64152-X. • Panofsky, Wolfgang; Phillips, Melba (1962/2005). Classical electricity and magnetism. Dover. pp. 274, 349. ISBN 0-486-43924-0. • Jackson, John D. (1998). Classical Electrodynamics (3rd ed.). Wiley. ISBN 0-471-30932-X. American Journal of Physics • Gamba, A. (1967). "Physical Quantities in Different Reference Systems According to Relativity". American Journal of Physics 35 (2): 83–89. Bibcode 1967AmJPh..35...83G. doi:10.1119/1.1973974. • Butler, J. W. (1968). "On the Trouton-Noble Experiment". American Journal of Physics 36 (11): 936–941. Bibcode 1968AmJPh..36..936B. doi:10.1119/1.1974358. • Aranoff, S. (1969). "Torques and Angular Momentum on a System at Equilibrium in Special Relativity". American Journal of Physics 37 (4): 453–454. Bibcode 1969AmJPh..37..453A. doi:10.1119/1.1975612. • Furry, W. H. (1969). "Examples of Momentum Distributions in the Electromagnetic Field and in Matter". American Journal of Physics 37 (6): 621–636. Bibcode 1969AmJPh..37..621F. doi:10.1119/1.1975729.
83
TroutonNoble experiment • Butler, J. W. (1969). "A Proposed Electromagnetic Momentum-Energy 4-Vector for Charged Bodies". American Journal of Physics 37 (12): 1258–1272. Bibcode 1969AmJPh..37.1258B. doi:10.1119/1.1975297. • Butler, J. W. (1970). "The Lewis-Tolman Lever Paradox". American Journal of Physics 38 (3): 360–368. Bibcode 1970AmJPh..38..360B. doi:10.1119/1.1976326. • Rohrlich, F. (1970). "Electromagnetic Momentum, Energy, and Mass". American Journal of Physics 38 (11): 1310–1316. Bibcode 1970AmJPh..38.1310R. doi:10.1119/1.1976082. • Sears, Francis W. (1972). "Another Relativistic Paradox". American Journal of Physics 40 (5): 771–773. Bibcode 1972AmJPh..40..771S. doi:10.1119/1.1986643. • Aranoff, S. (1973). "More on the Right-Angled Lever at Equilibrium in Special Relativity". American Journal of Physics 41 (9): 1108–1109. Bibcode 1973AmJPh..41.1108A. doi:10.1119/1.1987485. • Nickerson, J. Charles; McAdory, Robert T. (1975). "The Trouton-Noble paradox". American Journal of Physics 43 (7): 615–621. Bibcode 1975AmJPh..43..615N. doi:10.1119/1.9761. • Cavalleri, G.; Grøn, Ø.; Spavieri, G.; Spinelli, G. (1978). "Comment on the article "Right-angle lever paradox" by J. C. Nickerson and R. T. McAdory". American Journal of Physics 46 (1): 108–109. Bibcode 1978AmJPh..46..108C. doi:10.1119/1.11106. • Grøn, Ø. (1978). "Relativistics statics and F. W. Sears". American Journal of Physics 46 (3): 249–250. Bibcode 1978AmJPh..46..249G. doi:10.1119/1.11164. • Holstein, Barry R.; Swift, Arthur R. (1982). "Flexible string in special relativity". American Journal of Physics 50 (10): 887–889. Bibcode 1982AmJPh..50..887H. doi:10.1119/1.13002. • Singal, Ashok K. (1993). "On the "explanation" of the null results of Trouton-Noble experiment". American Journal of Physics 61 (5): 428–433. Bibcode 1993AmJPh..61..428S. doi:10.1119/1.17236. • Teukolsky, Saul A. (1996). "The explanation of the Trouton-Noble experiment revisited". American Journal of Physics 64 (9): 1104–1109. Bibcode 1996AmJPh..64.1104T. doi:10.1119/1.18329. • Jackson, J. D. (2004). "Torque or no torque? Simple charged particle motion observed in different inertial frames". American Journal of Physics 72 (12): 1484–1487. Bibcode 2004AmJPh..72.1484J. doi:10.1119/1.1783902. European Journal of Physics • Aguirregabiria, J. M.; Hernandez, A.; Rivas, M. (1982). "A Lewis-Tolman-like paradox". European Journal of Physics 3 (1): 30–33. Bibcode 1982EJPh....3...30A. doi:10.1088/0143-0807/3/1/008. • Franklin, Jerrold (2006). "The lack of rotation in the Trouton Noble experiment". European Journal of Physics 27 (5): 1251–1256. arXiv:physics/0603110. Bibcode 2006EJPh...27.1251F. doi:10.1088/0143-0807/27/5/024. • Franklin, Jerrold (2008). "The lack of rotation in a moving right angle lever". European Journal of Physics 29 (6): N55-N58. arXiv:0805.1196. Bibcode 2008EJPh...29...55F. doi:10.1088/0143-0807/29/6/N01. Journal of Physics A • Jefimenko, Oleg D. (1999). "The Trouton-Noble paradox". Journal of Physics A 32 (20): 3755–3762. Bibcode 1999JPhA...32.3755J. doi:10.1088/0305-4470/32/20/308. Nuovo Cimento • Arzeliès, H. (1965). "Sur le problème relativiste du levier coudé". Il Nuovo Cimento 35 (3): 783–791. doi:10.1007/BF02739341. • Rohrlich, F. (1966). "True and apparent transformations, classical electrons, and relativistic thermodynamics". Il Nuovo Cimento B 45 (1): 76–83. Bibcode 1966NCimB..45...76R. doi:10.1007/BF02710587. • Newburgh, R. G. (1969). "The relativistic problem of the right-angled lever: The correctness of the Laue solution". Il Nuovo Cimento B 61 (2): 201–209. Bibcode 1969NCimB..61..201N. doi:10.1007/BF02710928.
84
TroutonNoble experiment • Cavalleri, G.; Salgarelli, G. (1969). "Revision of the relativistic dynamics with variable rest mass and application to relativistic thermodynamics". Il Nuovo Cimento A 62 (3): 722–754. Bibcode 1969NCimA..62..722C. doi:10.1007/BF02819595. • Aranoff, S. (1972). "Equilibrium in special relativity" (http://www.analysis-knowledge.com/Physics/ Equilibrium in Special Relativity.pdf). Il Nuovo Cimento B 10 (1): 155–171. Bibcode 1972NCimB..10..155A. doi:10.1007/BF02911417. • Grøn, Ø. (1973). "The asynchronous formulation of relativistic statics and thermodynamics". Il Nuovo Cimento B 17 (1): 141–165. Bibcode 1973NCimB..17..141G. doi:10.1007/BF02906436. • Pahor, S.; Strnad, J. (1974). "Statics in special relativity". Il Nuovo Cimento B 20 (1): 105–112. Bibcode 1974NCimB..20..105P. doi:10.1007/BF02721111. • Cavalleri, G.; Spavieri, G.; Spinelli, G. (1975). "Ropes and pulleys in special relativity (relativistic statics of threads)". Il Nuovo Cimento B 25 (1): 348–356. Bibcode 1975NCimB..25..348C. doi:10.1007/BF02737685. • Chamorro, A.; Hernández, A. (1978). "A synchronous formulation of relativistic statics". Il Nuovo Cimento B 41 (1): 236–244. Bibcode 1977NCimB..41..236C. doi:10.1007/BF02726555. • Hernández, A.; Rivas, M.; Aguirregabiria, J. M. (1982). "A quantitative analysis of the trouton-noble experiment". Il Nuovo Cimento B 72 (1): 1–12. Bibcode 1982NCimB..72....1H. doi:10.1007/BF02894929. • Ai, Hsiao-Bai (1993). "The historical misconception in relativistic statics". Il Nuovo Cimento B 108 (1): 7–15. Bibcode 1993NCimB.108....7A. doi:10.1007/BF02874335. • Nieves, L.; Rodriguez, M.; Spavieri, G.; Tonni, E. (2001). "An experiment of the Trouton-Noble type as a test of the differential form of Faraday's law". Il Nuovo Cimento B 116 (5): 585. Bibcode 2001NCimB.116..585N. • Spavieri, G.; Gillies, G. T. (2003). "Fundamental tests of electrodynamic theories: Conceptual investigations of the Trouton-Noble and hidden momentum effects". Il Nuovo Cimento B 118 (3): 205. Bibcode 2003NCimB.118..205S. Foundations of Physics • Prokhovnik, S. J.; Kovács, K. P. (1985). "The application of special relativity to the right-angled lever". Foundations of Physics 15 (2): 167–173. Bibcode 1985FoPh...15..167P. doi:10.1007/BF00735288. • Spavieri, Gianfranco (1990). "Proposal for experiments to detect the missing torque in special relativity". Foundations of Physics Letters 3 (3): 291–302. Bibcode 1990FoPhL...3..291S. doi:10.1007/BF00666019. • Ivezić, Tomislav (2005). "Axiomatic Geometric Formulation of Electromagnetism with Only One Axiom: The Field Equation for the Bivector Field F with an Explanation of the Trouton-Noble Experiment". Foundations of Physics Letters 18 (5): 401–429. arXiv:physics/0412167. Bibcode 2005FoPhL..18..401I. doi:10.1007/s10702-005-7533-7. • Ivezić, Tomislav (2006). "Four-Dimensional Geometric Quantities versus the Usual Three-Dimensional Quantities: The Resolution of Jackson's Paradox". Foundations of Physics 36 (10): 1511–1534. arXiv:physics/0602105. Bibcode 2006FoPh...36.1511I. doi:10.1007/s10701-006-9071-y. • Ivezić, Tomislav (2006). "Trouton Noble Paradox Revisited". Foundations of Physics 37 (4–5): 747–760. arXiv:physics/0606176. Bibcode 2007FoPh...37..747I. doi:10.1007/s10701-007-9116-x.
85
TroutonNoble experiment
External links • Kevin Brown, " Trouton-Noble and The Right-Angle Lever (http://www.mathpages.com/home/kmath651/ kmath651.htm) at MathPages. • Michel Janssen, " The Trouton Experiment and E = mc2 (http://www.tc.umn.edu/~janss011/pdf files/ troutonshort.pdf)," Einstein for Everyone course at UMN (2002).
Trouton–Rankine experiment The Trouton–Rankine experiment was an experiment designed to measure if the Lorentz–FitzGerald contraction of an object according to one frame (as defined by the luminiferous aether) produced a measurable effect in the rest frame of the object, so that the ether would act as a "preferred frame". The experiment was first performed by Frederick Thomas Trouton and Alexander Oliver Rankine in 1908. The outcome of the experiment was negative, which is in agreement with the principle of relativity (and thus special relativity as well), according to which observers at rest in a certain inertial reference frame, cannot measure their own translational motion by instruments at rest in the same frame. Consequently, also length contraction cannot be measured by co-moving observers. See also Tests of special relativity.
Description The famous Michelson–Morley experiment of 1887 showed that the then-accepted aether theory needed to be modified. FitzGerald and Lorentz, independently of each other, proposed a length contraction of the experimental apparatus in the direction of motion (with respect to the Luminiferous aether) that would explain the almost null result of the Michelson Morley experiment. The first attempts to measure some consequences of this contraction in the lab frame (the inertial frame of reference of an observer co-moving with the experimental apparatus) were made in the Experiments of Rayleigh and Brace (1902, 1904), though the result was negative. By 1908, however, the then-current theories of electrodynamics, Lorentz ether theory (now superseded) and Special Relativity (now generally accepted, and doesn't include an aether at all), predicted that the Lorentz–FitzGerald contraction is not measurable in a co-moving frame, because these theories were based on the Lorentz transformation. Frederick Thomas Trouton, (after conducting the Trouton–Noble experiment in 1903), instead did the calculations using his own interpretation of electrodynamics, calculating the length contraction according to the velocity of the experimental apparatus in the aether frame, but calculating the electrodynamics by applying Maxwell's equations and Ohm's law in the lab frame. According to Trouton's view of electrodynamics, the calculations then predicted a measurable effect of the length contraction in the lab frame. Together with Alexander Oliver Rankine, he set out to verify this in 1908 by attempting to measure the change of the resistance of a coil as they changed its orientation to the "aether velocity" (the velocity of the lab through the luminiferous aether). This was done by putting four identical such coils in a Wheatstone bridge configuration which allowed them to precisely measure any change in resistance. The circuit was then rotated through 90 degrees about its axis as the resistance was measured. Because the Lorentz–FitzGerald contraction is only in the direction of motion, from the point of view of the "Aether frame" the length of the coils depended on their angle with respect to their Aether velocity. Trouton and Rankine therefore believed that the resistance as measured in the rest frame of the experiment should change as the device was rotated. However their careful measurements showed no detectable change in resistance.[1][2] This showed that if the Lorentz–FitzGerald contraction existed, it was not measurable in the rest frame of the object – only theories containing the complete Lorentz transformation, like special relativity, are still valid.
86
TroutonRankine experiment
References [1] Trouton F. T., Rankine A. (1908). "On the electrical resistance of moving matter". Proc. Roy. Soc. 80 (420): 420. Bibcode 1908RSPSA..80..420T. doi:10.1098/rspa.1908.0037. JSTOR 19080525. [2] Laub, Jakob (1910). "Über die experimentellen Grundlagen des Relativitätsprinzips". Jahrbuch der Radioaktivität und Elektronik 7: 460–461.
External links • On the Electrodynamics of Moving Bodies (http://www.fourmilab.ch/etexts/einstein/specrel/www/) Einstein's 1905 paper • Electromagnetic phenomena in a system moving with any velocity smaller than that of light Lorentz's 1904 paper • Sfarty, A., The Trouton Rankine Experiment and the End of the FitzGerald Contraction, http://www.mrelativity. net/Papers/29/Trouton_Rankine.pdf.
87
88
Gravity & General Relativity Cavendish experiment The Cavendish experiment, performed in 1797–98 by British scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory,[1] and the first to yield accurate values for the gravitational constant.[2][3] Because of the unit conventions then in use, the gravitational constant does not appear explicitly in Cavendish's work. Instead, the result was originally expressed as the specific gravity of the Earth,[4] or equivalently the mass of the Earth; and were the first accurate values for these geophysical constants. The experiment was devised sometime before 1783[5] by geologist John Michell,[6] who constructed a torsion balance apparatus for it. However, Michell died in 1793 without completing the work, and after his death the apparatus passed to Francis John Hyde Wollaston and then to Henry Cavendish, who rebuilt the apparatus but kept close to Michell's original plan. Cavendish then carried out a series of measurements with the equipment, and reported his results in the Philosophical Transactions of the Royal Society in 1798.[7]
The experiment The apparatus constructed by Cavendish was a torsion balance made of a six-foot (1.8 m) wooden rod suspended from a wire, with a 2-inch (unknown operator: u'strong' mm) diameter 1.61-pound (unknown operator: u'strong' kg) lead sphere attached to each end. Two 12-inch (unknown operator: u'strong' mm) 348-pound (unknown operator: u'strong' kg) lead balls were located near the smaller balls, about 9 inches (unknown operator: u'strong' mm) away, and held in place with a separate suspension system.[8] The experiment measured the faint gravitational attraction between the small balls and the larger ones.
Vertical section drawing of Cavendish's torsion balance instrument including the building in which it was housed. The large balls were hung from a frame so they could be rotated into position next to the small balls by a pulley from outside. Figure 1 of Cavendish's paper.
The two large balls were positioned on alternate sides of the horizontal wooden arm of the balance. Their mutual attraction to the small balls caused the arm to rotate, twisting the wire supporting the arm. The arm stopped rotating when it reached an angle where the twisting force of the wire balanced the combined gravitational force of attraction between the large and small lead spheres. By measuring the angle of the rod, and knowing the twisting force (torque) of the wire for a given angle, Cavendish was able to determine the force between the pairs of masses. Since the gravitational force of the Earth on the small ball could be measured directly by weighing it, the ratio of the two forces allowed the density of the earth to be calculated, using Newton's law of gravitation.
Cavendish found that the Earth's density was 5.448 ± 0.033 times that of water (due to a simple arithmetic error, found in 1821 by F. Baily, the erroneous value 5.48 ± 0.038 appears in his paper).[9]
Cavendish experiment
Detail showing torsion balance arm (m), large ball (W), small ball (x), and isolating box (ABCDE).
89 To find the wire's torsion coefficient, the torque exerted by the wire for a given angle of twist, Cavendish timed the natural oscillation period of the balance rod as it rotated slowly clockwise and counterclockwise against the twisting of the wire. The period was about 20 minutes. The torsion coefficient could be calculated from this and the mass and dimensions of the balance. Actually, the rod was never at rest; Cavendish had to measure the deflection angle of the rod while it was oscillating.[10]
Cavendish's equipment was remarkably sensitive for its time.[9] The force involved in twisting the torsion –7 [11] balance was very small, 1.74 x 10 N, about 1/50,000,000 of the weight of the small balls[12] or roughly the weight of a large grain of sand.[13] To prevent air currents and temperature changes from interfering with the measurements, Cavendish placed the entire apparatus in a wooden box about 2 feet (unknown operator: u'strong' m) thick, 10 feet (unknown operator: u'strong' m) tall, and 10 feet (unknown operator: u'strong' m) wide, all in a closed shed on his estate. Through two holes in the walls of the shed, Cavendish used telescopes to observe the movement of the torsion balance's horizontal rod. The motion of the rod was only about 0.16 inches (unknown operator: u'strong' mm).[14] Cavendish was able to measure this small deflection to an accuracy of better than one hundredth of an inch using vernier scales on the ends of the rod.[15] Cavendish's experiment was repeated by Reich (1838), Baily (1843), Cornu & Baille (1878), and many others. Its accuracy was not exceeded for 97 years, until C. V. Boys' 1895 experiment. In time, Michell's torsion balance became the dominant technique for measuring the gravitational constant (G), and most contemporary measurements still use variations of it. This is why Cavendish's experiment became the Cavendish experiment.[16]
Did Cavendish determine G? The formulation of Newtonian gravity in terms of a gravitational constant did not become standard until long after Cavendish's time. Indeed, one of the first references to G is in 1873, 75 years after Cavendish's work.[17] Cavendish expressed his result in terms of the density of the Earth, and he referred to his experiment in correspondence as 'weighing the world'. Later authors reformulated his results in modern terms.[18][19][20] thus:
After converting to SI units, Cavendish's value for the Earth's density, 5.448 g cm−3, gives G = 6.74 × 10−11 m3 kg−1 s−2, which differs by only 1% from the currently accepted value: 6.67428 × 10−11 m3 kg−1 s−2. For this reason, historians of science have argued that Cavendish did not measure the gravitational constant.[21][22][23][24] Physicists, however, often use units where the gravitational constant takes a different form. The Gaussian gravitational constant used in space dynamics is a defined constant, and the Cavendish experiment can be considered as a measurement of the astronomical unit. In Cavendish's time, physicists used the same units for mass and weight, in effect taking as a standard acceleration. Then, since was known, played the role of an inverse gravitational constant. The density of the Earth was hence a much sought-after quantity at the time, and there had been earlier attempts to measure it, such as the Schiehallion experiment in 1774.
Cavendish experiment
90
For these reasons, physicists generally do credit Cavendish with the first measurement of the gravitational constant.[25][26][27][28][29]
Derivation of G and the Earth's mass For the definitions of terms, see the drawing below and the table at the end of this section. The following is not the method Cavendish used, but shows how modern physicists would use his results.[30][31][32] From Hooke's law, the torque on the torsion wire is proportional to the deflection angle of the balance. The torque is
where
is the torsion coefficient of the wire. However, the torque can also be written as a product of the
attractive forces between the balls and the distance to the suspension wire. Since there are two pairs of balls, each experiencing force F at a distance L / 2 from the axis of the balance, the torque is LF. Equating the two formulas for torque gives the following:
For F, Newton's law of universal gravitation is used to express the attractive force between the large and small balls:
Substituting F into the first equation above gives
To find the torsion coefficient ( ) of the wire, Cavendish measured the natural resonant oscillation period T of the torsion balance:
Assuming the mass of the torsion beam itself is negligible, the moment of inertia of the balance is just due to the small balls: , and so: Diagram of torsion balance
Solving this for
, substituting into (1), and rearranging for G, the result is:
Once G has been found, the attraction of an object at the Earth's surface to the Earth itself can be used to calculate the Earth's mass and density:
Cavendish experiment
91
Definition of terms
SYMBOL UNITS
DEFINITION Deflection of torsion balance beam from its rest position Gravitational force between masses M and m Gravitational constant Mass of small lead ball Mass of large lead ball Distance between centers of large and small balls when balance is deflected Length of torsion balance beam between centers of small balls Torsion coefficient of suspending wire Moment of inertia of torsion balance beam Period of oscillation of torsion balance Acceleration of gravity at the surface of the Earth Mass of the Earth Radius of the Earth Density of the Earth
References • Boys, C. Vernon (1894). "On the Newtonian constant of gravitation" [33]. Nature 50 (1292): 330–4. Bibcode 1894Natur..50..330.. doi:10.1038/050330a0. • Cavendish, Henry (1798). "Experiments to Determine the Density of the Earth" [34]. In MacKenzie, A. S.. Scientific Memoirs Vol.9: The Laws of Gravitation. American Book Co.. 1900. pp. 59–105 Online copy of Cavendish's 1798 paper, and other early measurements of gravitational constant. • Clotfelter, B. E. (1987). "The Cavendish experiment as Cavendish knew it". American Journal of Physics 55 (3): 210–213. Bibcode 1987AmJPh..55..210C. doi:10.1119/1.15214. Establishes that Cavendish didn't determine G. • Falconer, Isobel (1999). "Henry Cavendish: the man and the measurement". Measurement Science and Technology 10 (6): 470–477. Bibcode 1999MeScT..10..470F. doi:10.1088/0957-0233/10/6/310. • "Gravitation Constant and Mean Density of the Earth" [35]. Encyclopædia Britannica, 11th Ed.. 12. The Encyclopædia Britannica Co.. 1910. pp. 385–389. • Hodges, Laurent (1999). "The Michell-Cavendish Experiment, faculty website, Iowa State Univ." [36]. Retrieved 2007-08-28. Discusses Michell's contributions, and whether Cavendish determined G. • Lally, Sean P. (1999). "Henry Cavendish and the Density of the Earth". The Physics Teacher 37 (1): 34–37. Bibcode 1999PhTea..37...34L. doi:10.1119/1.880145. • McCormmach, Russell; Jungnickel, Christa (1996). Cavendish [37]. Philadelphia, Pennsylvania: American Philosophical Society. ISBN 0-87169-220-1. • Poynting, John H. (1894). The Mean Density of the Earth: An essay to which the Adams prize was adjudged in 1893 [38]. London: C. Griffin & Co.. Review of gravity measurements since 1740. • This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). Encyclopædia Britannica (11th ed.). Cambridge University Press.
Cavendish experiment
Notes [1] Boys 1894 (http:/ / books. google. com/ books?id=ZrloHemOmUEC& pg=PA355) p. 355 [2] Encyclopædia Britannica 1910 (http:/ / books. google. com/ books?id=DgTALFa3sa4C& pg=PA385) p. 385 'The aim [of experiments like Cavendish's] may be regarded either as the determination of the mass of the Earth,...conveniently expressed...as its "mean density", or as the determination of the "gravitation constant", G'. Cavendish's experiment is generally described today as a measurement of G (Clotfelter 1987 p. 210). [3] Many sources state erroneously that this was the first measurement of G (or the Earth's density), such as Feynman, Richard P. (1963) ( – Scholar search (http:/ / scholar. google. co. uk/ scholar?hl=en& lr=& q=author:Feynman+ intitle:Lectures+ on+ Physics,+ Vol. 1& as_publication=& as_ylo=& as_yhi=& btnG=Search)). Lectures on Physics, Vol.1 (http:/ / books. google. com/ ?id=k6MQrphL-NIC& pg=PA28). Addison-Wesley. pp. 6–7. ISBN 0-201-02116-1. . There were previous measurements, chiefly Bouguer (1740) and Maskelyne (1774), but they were very inaccurate ( Poynting 1894 (http:/ / books. google. com/ books?id=dg0RAAAAIAAJ))( Encyclopædia Britannica 1910 (http:/ / books. google. com/ books?id=DgTALFa3sa4C& pg=PA385)). [4] Clotfelter 1987, p. 210 [5] McCormmach & Jungnickel 1996 (http:/ / books. google. com/ books?id=EUoLAAAAIAAJ& pg=PA336& sig=--1AlZ9rl_0AEL7h73LZvtK01S4), p.336: A 1783 letter from Cavendish to Michell contains '...the earliest mention of weighing the world'. Not clear whether 'earliest mention' refers to Cavendish or Michell. [6] Cavendish 1798 (http:/ / books. google. com/ books?id=O58mAAAAMAAJ& pg=PA59), p. 59 Cavendish gives full credit to Michell for devising the experiment [7] Cavendish, H. 'Experiments to determine the Density of the Earth', Philosophical Transactions of the Royal Society of London, (part II) 88 p.469-526 (21 June 1798), reprinted in Cavendish 1798 (http:/ / books. google. com/ books?id=O58mAAAAMAAJ& pg=PA59) [8] Cavendish 1798 (http:/ / books. google. com/ books?id=O58mAAAAMAAJ& pg=PA59), p.59 [9] Poynting 1894 (http:/ / books. google. com/ books?id=dg0RAAAAIAAJ& pg=PA45), p.45 [10] Cavendish 1798 (http:/ / books. google. com/ books?id=O58mAAAAMAAJ& pg=PA64), p.64 [11] Boys 1894 (http:/ / books. google. com/ books?id=ZrloHemOmUEC& pg=PA357) p.357 [12] Cavendish 1798 (http:/ / books. google. com/ books?id=O58mAAAAMAAJ& pg=PA60) p. 60 [13] A 2 mm sand grain weighs ~13 mg. Theodoris, Marina (2003). "Mass of a Grain of Sand" (http:/ / hypertextbook. com/ facts/ 2003/ MarinaTheodoris. shtml). The Physics Factbook. . [14] Cavendish 1798 (http:/ / books. google. com/ books?id=O58mAAAAMAAJ& pg=PA99), p. 99, Result table, (scale graduations = 1/20 in ≈ 1.3 mm) The total deflection shown in most trials was twice this since he compared the deflection with large balls on opposite sides of the balance beam. [15] Cavendish 1798 (http:/ / books. google. com/ books?id=O58mAAAAMAAJ& pg=PA63), p.63 [16] McCormmach & Jungnickel 1996 (http:/ / books. google. com/ books?id=EUoLAAAAIAAJ& pg=PA341& sig=--1AlZ9rl_0AEL7h73LZvtK01S4), p.341 [17] Cornu, A. and Baille, J. B. (1873), Mutual determination of the constant of attraction and the mean density of the earth, C. R. Acad. Sci., Paris Vol. 76, 954-958. [18] Boys 1894 (http:/ / books. google. com/ books?id=ZrloHemOmUEC& pg=PA353), p.330 In this lecture before the Royal Society, Boys introduces G and argues for its acceptance [19] Poynting 1894 (http:/ / books. google. com/ books?id=dg0RAAAAIAAJ& pg=PA4), p.4 [20] MacKenzie 1900 (http:/ / books. google. com/ books?id=O58mAAAAMAAJ& pg=PA1), p.vi [21] Clotfelter 1987 [22] McCormmach & Jungnickel 1996 (http:/ / books. google. com/ books?id=EUoLAAAAIAAJ& pg=PA336& sig=--1AlZ9rl_0AEL7h73LZvtK01S4), p.337 [23] Hodges 1999 (http:/ / www. public. iastate. edu/ ~lhodges/ Michell. htm) [24] Lally 1999 [25] Halliday, David; Resnick, Robert (1993). Fundamentals of Physics (http:/ / books. google. com/ ?id=-AjnmJHPiKMC& pg=PA418). John Wiley & Sons. pp. 418. ISBN 978-0-471-14731-2. 'The apparatus used in 1798 by Henry Cavendish to measure the gravitational constant' [26] Feynman, Richard P. (1963) ( – Scholar search (http:/ / scholar. google. co. uk/ scholar?hl=en& lr=& q=author:Feynman+ intitle:Lectures+ on+ Physics,+ Vol. 1& as_publication=& as_ylo=& as_yhi=& btnG=Search)). Lectures on Physics, Vol.1 (http:/ / books. google. com/ ?id=k6MQrphL-NIC& pg=PA28). Addison-Wesley. pp. 6–7. ISBN 0-201-02116-1. 'Cavendish claimed he was weighing the Earth, but what he was measuring was the coefficient G...' [27] Feynman, Richard P. (1967) ( – Scholar search (http:/ / scholar. google. co. uk/ scholar?hl=en& lr=& q=author:Feynman+ intitle:The+ Character+ of+ Physical+ Law& as_publication=& as_ylo=& as_yhi=& btnG=Search)). The Character of Physical Law (http:/ / books. google. com/ ?id=k6MQrphL-NIC& pg=PA28). MIT Press. pp. 28. ISBN 0-262-56003-8. 'Cavendish was able to measure the force, the two masses, and the distance, and thus determine the gravitational constant G' [28] "Cavendish Experiment, Harvard Lecture Demonstrations, Harvard Univ" (http:/ / www. fas. harvard. edu/ ~scdiroff/ lds/ NewtonianMechanics/ CavendishExperiment/ CavendishExperiment. html). . Retrieved 2007-08-26. '[the torsion balance was]...modified by Cavendish to measure G.'
92
Cavendish experiment [29] Shectman, Jonathan (2003). Groundbreaking Experiments, Inventions, and Discoveries of the 18th Century (http:/ / books. google. com/ ?id=SsbChdIiflsC& pg=PAxlvii). Greenwood. pp. xlvii. ISBN 978-0-313-32015-6. 'Cavendish calculates the gravitational constant, which in turn gives him the mass of the earth...' [30] Cavendish Experiment, Harvard Lecture Demonstrations, Harvard Univ. (http:/ / www. fas. harvard. edu/ ~scdiroff/ lds/ NewtonianMechanics/ CavendishExperiment/ CavendishExperiment. html) [31] Poynting 1894 (http:/ / books. google. com/ books?id=dg0RAAAAIAAJ& pg=PA41), p.41 [32] Clotfelter 1987 p.212 explains Cavendish's original method of calculation [33] http:/ / books. google. com/ ?id=ZrloHemOmUEC& pg=PA353 [34] http:/ / books. google. com/ ?id=O58mAAAAMAAJ& pg=PA59 [35] http:/ / books. google. com/ books?id=DgTALFa3sa4C& pg=PA385 [36] http:/ / www. public. iastate. edu/ ~lhodges/ Michell. htm [37] http:/ / books. google. com/ ?id=EUoLAAAAIAAJ [38] http:/ / books. google. com/ ?id=dg0RAAAAIAAJ
External links • Sideways Gravity in the Basement, The Citizen Scientist, July 1, 2005 (http://www.sas.org/tcs/ weeklyIssues_2005/2005-07-01/feature1/index.html), retrieved Aug. 9, 2007. Homebrew Cavendish experiment, showing calculation of results and precautions necessary to eliminate wind and electrostatic errors. • Measuring Big G, Physics Central (http://www.physicscentral.com/explore/action/bigg-research.cfm), retrieved Aug. 9, 2007. Recent experiment at Univ. of Washington to measure the gravitational constant using variation of Cavendish method. • The Controversy over Newton's Gravitational Constant, Eöt-Wash Group, Univ. of Washington (http://www. npl.washington.edu/eotwash/experiments/bigG/bigG.html), retrieved Aug. 9, 2007. Discusses current state of measurements of G. • Model of Cavendish's torsion balance (http://www.scienceandsociety.co.uk/results.asp?image=10314095), retrieved Aug. 28, 2007, at Science Museum, London. • Weighing the Earth (http://www.juliantrubin.com/bigten/cavendishg.html) - background and experiment
93
De Sitter double star experiment
94
De Sitter double star experiment The de Sitter effect was described by de Sitter in 1913 and used to support the special theory of relativity against a competing 1908 emission theory by Walter Ritz that postulated a variable speed of light. De Sitter showed that Ritz's theory predicted that the orbits of binary stars would appear more eccentric than consistent with experiment and with the laws of mechanics.[1][2][3][4] A similar effect was already described by Daniel Frost Comstock in 1910.[5] See also Tests of special relativity. de Sitter's double star argument
The effect According to simple emission theory, light thrown off by an object should move at a speed of emitting object.
with respect to the
If there are no complicating dragging effects, the light would then be expected to move at this same speed until it eventually reached an observer. For an object moving directly towards (or away from) the observer at metres per second, this light would then be expected to still be travelling at ( or ) metres per second at the time it reached us. Willem de Sitter argued that if this was true, a star in a double-star system would usually have an orbit that caused it to have alternating approach and recession velocities, and light emitted from different parts of the orbital path would then travel towards us at different speeds. For a nearby star with a small orbital velocity (or whose orbital plane was almost perpendicular to our line of view) this might merely make the star's orbit seem erratic, but for a sufficient combination of orbital speed and distance (and inclination), the "fast" light given off during approach would be able to catch up with and even overtake "slow" light emitted earlier during a recessional part of the star's orbit, and the star would present an image that was scrambled and out of sequence. De Sitter made a study of double stars (1913) and found no cases where the stars' images appeared scrambled. Since the total flight-time difference between "fast" and "slow" lightsignals would be expected to scale linearly with distance in simple emission theory, and the study would (statistically) have included stars with a reasonable spread of distances and orbital speeds and orientations, deSitter concluded that the effect should have been seen if the model was correct, and its absence meant that the emission theory was almost certainly wrong.
Notes • De Sitter experiments refute the idea that light might travel at a speed that was partially dependent on the velocity of the emitter ( ), where the emitter's velocity v can be positive or negative, and k is a factor between 0 and 1, denoting the extent to which the speed of light depends on the source velocity. De Sitter established an upper limit of .[4] • De Sitter's argument was criticized because of possible extinction effects. That is, during their flight to Earth, the light rays should have been absorbed and re-emitted by interstellar matter nearly at rest relative to Earth, so that the speed of light should become constant with respect to Earth. However, Kenneth Brecher published the results of a similar double-survey in 1977, and reached a similar conclusion - that any apparent irregularities in double-star orbits were too small to support the emission theory. Contrary to De Sitter, he observed the x-ray spectrum, thereby eliminating possible influences of the extinction effect. He established an upper limit of .[6]
De Sitter double star experiment
References [1] W. de Sitter, Ein astronomischer Beweis für die Konstanz der Lichgeshwindigkeit (http:/ / www. datasync. com/ ~rsf1/ desit-1g. htm) Physik. Zeitschr, 14, 429 (1913). [2] W. de Sitter, Über die Genauigkeit, innerhalb welcher die Unabhängigkeit der Lichtgeschwindigkeit von der Bewegung der Quelle behauptet werden kann (http:/ / www. datasync. com/ ~rsf1/ desit-2g. htm) Physik. Zeitschr, 14, 1267 (1913). [3] De Sitter, Willem (1913), "A proof of the constancy of the velocity of light", Proceedings of the Royal Netherlands Academy of Arts and Sciences 15 (2): 1297–1298 [4] De Sitter, Willem (1913), "On the constancy of the velocity of light", Proceedings of the Royal Netherlands Academy of Arts and Sciences 16 (1): 395–396 [5] Comstock, Daniel Frost (1910), "A Neglected Type of Relativity", Physical Review 30 (2): 267 [6] Kenneth Brecher, Is the Speed of Light Independent of the Velocity of the Source?, (http:/ / adsabs. harvard. edu/ abs/ 1977PhRvL. . 39. 1051B) Phys. Rev. Letters 39 (17) 1051-1054 (1977).
Gravity Probe A Gravity Probe A (GP-A) was a space-based experiment to test the theory of general relativity, performed jointly by the Smithsonian Astrophysical Observatory and the National Aeronautics and Space Administration. It sent a hydrogen maser, a highly accurate frequency standard, into space to measure the rate change of a clock in lower gravity with high precision. The probe was launched on June 18, 1976 on top of a Scout rocket and remained in space for 1 hour and 55 minutes, as intended. It then crashed into the Atlantic Ocean.
Experimental setup The 100 kg Gravity Probe A spacecraft housed the hydrogen maser system that ran throughout the mission, and a microwave repeater to measure the Doppler shift of the maser signal. The satellite was launched nearly vertically upward to cause a large change in the local gravity seen by the maser, reaching a height of unknown operator: u','unknown operator: u','unknown operator: u',' (unknown operator: u'strong'unknown operator: u','mi). At this height, general relativity predicted a clock should run 4.5 parts in 1010 faster than one on the Earth.
Results The clock rate was measured from the ground by comparing the microwave signal from the clock to a maser on the ground and subtracting a signal from the spacecraft that measured the Doppler shift. The clock rate was measured for most of the duration of the flight and compared to theoretical predictions. The stability of the maser permitted measurement of changes in the rate of the maser of 1 part in 1014 for a 100-sec measurement. The experiment was thus able to test the equivalence principle. Gravity Probe A confirmed the prediction that gravity slows the flow of time, and the observed effects matched the predicted effects to an accuracy of about 70 parts per million.
References • R.F.C. Vessot et al. (1980). "Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser". Physical Review Letters 45 (26): 2081–2084. Bibcode 1980PhRvL..45.2081V. doi:10.1103/PhysRevLett.45.2081.
95
Gravity Probe B
96
Gravity Probe B Gravity Probe B
Operator
NASA and Stanford University
Major contractors Lockheed Martin Mission type
Test of General relativity
Satellite of
Earth
Orbits
Polar orbit at 642 km
Launch date
16:57:25, 20 April 2004 (UTC)
Launch vehicle
Delta II rocket
Launch site
Vandenberg Air Force Base, CA
Mission duration
17.5 months
COSPAR ID
2004-014A
Homepage
einstein.stanford.edu
Mass
3,100 kg
Dimensions
Length: 6.4 meters [1] Diameter: 2.6 meters
Power
Total power: 606 watts (Spacecraft: 293 W, payload: 313 W)
Batteries
35 Amp hour
[1]
[1]
[2]
[1]
[1]
[1]
Orbital elements [1]
Semimajor axis
7,027.4 km (4,366.6 mi)
Eccentricity
0.0014
Inclination
90.007°
Apoapsis
659.1 km from surface
Periapsis
639.5 km from surface
Orbital period
97.65 minutes
[1] [1] [1] [1]
[3]
Gravity Probe B (GP-B) is a satellite-based mission which launched on 20 April 2004 on a Delta II rocket.[4] The spaceflight phase lasted until 2005;[5] its aim was to measure spacetime curvature near Earth, and thereby the stress–energy tensor (which is related to the distribution and the motion of matter in space) in and near Earth. This
Gravity Probe B
97
provided a test of general relativity, gravitomagnetism and related models. The principal investigator was Francis Everitt. Initial results confirmed the expected geodetic effect to an accuracy of about 1%. The expected frame-dragging effect was similar in magnitude to the current noise level (the noise being dominated by initially unmodeled effects). Work is continuing to model and account for these sources of unintended signal, thus permitting extraction of the frame-dragging signal if it exists at the expected level. By August 2008 the uncertainty in the frame-dragging signal had been reduced to 15%,[6] and the December 2008 NASA report indicated that the geodetic effect was confirmed to better than 0.5%.[7] In an article published in the journal Physical Review Letters in 2011, the authors reported analysis of the data from all four gyroscopes results in a geodetic drift rate of −6,601.8±18.3 milliarcsecond/year (mas/yr) and a frame-dragging drift rate of −37.2±7.2 mas/yr, to be compared with the GR predictions of −6,606.1 mas/yr and −39.2 mas/yr, respectively.[8]
Overview Gravity Probe B was a relativity gyroscope experiment funded by NASA. Efforts were led by Stanford University physics department with Lockheed Martin as the primary subcontractor. Mission scientists view it as the second gravity experiment in space, following the successful launch of Gravity Probe A (GP-A) in 1976. Some preliminary results were presented at a special session during the American Physical Society meeting, 14–17 April 2007. NASA initially requested a proposal for extending the GP-B data analysis phase through December 2007. The data analysis phase was further extended to September 2008, and possibly later, when definitive science results on the frame-dragging effect are expected. The mission plans were to test two unverified predictions of general relativity: frame-dragging and the geodetic effect. The experiment planned to check, very precisely, tiny changes in the direction of spin of four gyroscopes contained in an Earth satellite orbiting at 650 km (400 mi) altitude, crossing directly over the poles. The gyroscopes were so free from disturbance that they provided a near-perfect space-time reference system. They were intended to measure how space and time are "warped" by the presence of the Earth, and by how much the Earth's rotation "drags" space-time around with it. This is the so-called frame-dragging effect, an example of gravitomagnetism. It is an analog of magnetism in classical electrodynamics, but caused by rotating masses rather than rotating electric charges.
Gravity Probe B with solar panels folded.
Previously, only two analyses of the laser-ranging data obtained by the two LAGEOS satellites, published in 1997 and 2004, claimed to have found the frame-dragging effect with an accuracy of about 20% and 10% respectively,[9][10][11] whereas Gravity Probe B aims to measure the effect to a precision of 1%. However, Lorenzo Iorio claimed that the level of total uncertainty of the tests conducted with the two LAGEOS satellites has likely been greatly underestimated.[12][13][14][15][16][17] A recent analysis of Mars Global Surveyor data has claimed to have confirmed the effect to a precision of 0.5%,[18] although the accuracy of this claim is disputed.[19][20] Also the Lense–Thirring effect of the Sun has been recently investigated in view of a possible
Gravity Probe B
98
detection with the inner planets in the near future.[21][22] The probe has also detected the so-called geodetic effect, a much larger effect caused by space-time being 'curved' by the mass of the Earth. A gyroscope's axis when parallel transported around the Earth in one complete revolution does not end up pointing in exactly the same direction as before. The angle 'missing' may be thought of as the amount the gyroscope 'leans over' into the slope of the space-time curvature. A more precise explanation for the space curvature part of the geodetic precession is obtained by using a nearly flat cone to model the space curvature of the Earth's gravitational field. Such a cone is made by cutting out a thin 'pie-slice' from a circle and gluing the cut edges together. The spatial geodetic precession is a measure of the missing 'pie-slice' angle. Gravity Probe B should measure this effect to an accuracy of one part in 10,000, the most stringent check on general relativistic predictions to date. The launch was planned for 19 April 2004 at Vandenberg Air Force Base but was scrubbed within 5 minutes of the scheduled launch window due to changing winds in the upper atmosphere. An unusual feature of the mission is that it only had a one-second launch window due to the precise orbit required by the experiment. On 20 April, at 9:57:23 AM PDT (16:57:23 UTC) the spacecraft was launched successfully. The satellite was placed in orbit at 11:12:33 AM (18:12:33 UTC) after a cruise period over the south pole and a short second burn. The mission lasted 16 months.
Experimental setup The Gravity Probe B experiment comprises four London moment gyroscopes and a reference telescope sighted on HR8703 (also known as IM Pegasi), a binary star in the constellation Pegasus. In polar orbit, with the gyro spin directions also pointing toward HR8703, the frame-dragging and geodetic effects came out at right angles, each gyroscope measuring both. The gyroscopes are housed in a dewar of superfluid helium, maintaining a temperature of under 2 kelvins (−271 °C, −456 °F). Near-absolute zero temperatures are required in order to minimize molecular interference, and enable the lead and niobium components of the gyroscope mechanisms to become superconductive.
At the time, the fused quartz gyroscopes created for Gravity Probe B were the most nearly perfect [23] spheres ever created by humans. The gyroscopes differ from a perfect sphere by no more than 40 atoms of thickness, refracting the image of Einstein in background.
At the time, the gyroscopes were the most nearly spherical objects ever made. Approximately the size of ping pong balls, they are perfectly round to within forty atoms (less than 10 nm). If one of these spheres were scaled to the size of the earth, the tallest mountains and deepest ocean trench would measure only 2.4 m (8 ft) high.[24] They are composed of fused quartz and coated with an extremely thin layer of niobium. A primary concern is minimizing any influence on their spin, so the gyroscopes must never touch their containing compartment. They are held suspended with electric fields, spun up using a flow of helium gas, and their spin axes are sensed by monitoring the magnetic field of the superconductive niobium layer with SQUIDs. (A spinning superconductor generates a magnetic field precisely aligned with the rotation axis – see London moment.)
IM Pegasi was chosen as the guide star for multiple reasons. First, it needed to be bright enough to be usable for sightings. Then it was close to the ideal positions near at the celestial equator of the sky coordinates. Also important was its well understood motion in the sky, which was helped by the fact that this star emits relatively strong radio signals. As a preparation for the setup of this mission, astronomers analyzed the radio-based position measurements with respect to far distant quasars taken over the last few years to understand its motion as precisely as needed.
Gravity Probe B
History The conceptual design for this mission was first proposed by an MIT professor, George Pugh, who was working with the U.S. Department of Defense in 1959 and later discussed by Leonard Schiff (Stanford) in 1960 at Pugh's suggestion, based partly on a theoretical paper about detecting frame dragging that Schiff had written in 1957. It was proposed to NASA in 1961, and they supported the project with funds in 1964. This grant ended in 1977 after a long phase of engineering research into the basic requirements and tools for the satellite. In 1986 NASA changed plans for the shuttle, which forced the mission A representation of the geodetic effect. team to switch from a shuttle-based launch design to one that is based on the Delta 2, and in 1995 tests planned of a prototype on a shuttle flight were cancelled as well. Gravity Probe B marks the first time in history that a university has been in control of the development and operations of a space satellite funded by NASA. Total cost of this project is about $750 million.[25]
Mission timeline This is a list of major events for the GP-B experiment. • 20 April 2004: Launch of GP-B from Vandenberg AFB and successful insertion into polar orbit. • 27 August 2004: GP-B entered its science phase. On mission day 129 all systems were configured to be ready for data collection, with the only exception being gyro 4, which needed further spin axis alignment. • 15 August 2005: The science phase of the mission ended and the spacecraft instruments transitioned to the final calibration mode. • 26 September 2005: The calibration phase ended with liquid helium still in the dewar. The spacecraft was returned to science mode pending the depletion of the last of the liquid helium. • February 2006: Phase I of data analysis complete • September 2006: Analysis team realised that more error analysis, particularly around the polhode motion of the gyros, was necessary than could be done in the time to April 2007, and applied to NASA for an extension of funding to the end of 2007. • December 2006: Completion of Phase III of data analysis • 14 April 2007: Announcement of best results obtained to date. Francis Everitt gave a plenary talk at the meeting of the American Physical Society announcing initial results:[26] "The data from the GP-B gyroscopes clearly confirm Einstein's predicted geodetic effect to a precision of better than 1 percent. However, the frame-dragging effect is 170 times smaller than the geodetic effect, and Stanford scientists are still extracting its signature from the spacecraft data." — Gravity Probe B website[27] • 8 December 2010: GP-B spacecraft decommissioned, left in its 642 km (400 mi) polar orbit.[28] • 4 May 2011: GP-B Final experimental results were announced. In a public press and media event at NASA Headquarters, GP-B Principal Investigator, Francis Everitt announced the final results of Gravity Probe B.[29] On 9 February 2007, it was announced that a number of unexpected signals had been received and that these would need to be separated out before final results could be released. In April it was announced that the spin axes of the gyroscopes were affected by torque, in a manner that varied over time, requiring further analysis to allow the results to be corrected for this source of error. Consequently, the date for the final release of data has been pushed back several times. In the data for the frame-dragging results presented at the April 2007 meeting of the American Physical Society, the random errors were much larger than the theoretical expected value and scattered on both the positive and negative sides of a null result, therefore causing skepticism on whether any useful data could be
99
Gravity Probe B extracted in the future to test this effect. In June 2007, a detailed update was released explaining the cause of the problem, and the solution that was being worked on. Although electrostatic patches caused by non-uniform coating of the spheres was anticipated, and was thought to have been controlled for before the experiment, it is now known that the final layer of the coating on the spheres defined two halves of slightly different potential, which gave the sphere an electrostatic axis. This created a classical dipole torque on each rotor, of a magnitude similar to the expected frame dragging effect. In addition, it dissipated energy from the polhode motion by inducing currents in the housing electrodes, causing the motion to change with time. This meant that a simple time-average polhode model was insufficient, and a detailed orbit by orbit model was needed to remove the effect. As it was anticipated that "anything could go wrong", the final part of the flight mission was calibration, where amongst other activities, data was gathered with the spacecraft axis deliberately mis-aligned for 24 hours, to exacerbate any potential problems. This data proved invaluable for identifying the effects. With the electrostatic torque modelled as a function of axis misalignment, and the polhode motion modelled at a sufficiently fine level, it is hoped to isolate the relativity torques to the originally expected resolution. Stanford has agreed to release the raw data to the public at an unspecified date in the future. It is likely that this data will be examined by independent scientists and independently reported to the public well after the September 2008 release. Because future interpretations of the data by scientists outside of GP-B may differ from the official results, it may take several more years for all of the data received by GP-B to be completely understood.
NASA review A review by a panel of 15 experts commissioned by NASA has recommended against extending the data analysis phase beyond 2008. They warn that the required reduction in noise level (due to classical torques and breaks in data collection due to solar flares) "is so large that any effect ultimately detected by this experiment will have to overcome considerable (and in our opinion, well justified) skepticism in the scientific community".[30]
Data analysis after NASA NASA funding and sponsorship of the program ended on 30 September 2008, but GP-B has secured alternative funding from King Abdulaziz City of Science and Technology KACST in Saudi Arabia, that will enable the science team to continue working at least through December 2009. On 29 August 2008, the 18th meeting of the external GP-B Science Advisory Committee was held at Stanford to report progress. The ensuing SAC report to NASA states: The progress reported at SAC-18 was truly extraordinary and we commend the GPB team for this achievement. This has been a heroic effort, and has brought the experiment from what seemed like a state of potential failure, to a position where the SAC now believes that they will obtain a credible test of relativity, even if the accuracy does not meet the original goal. In the opinion of the SAC Chair, this rescue warrants comparison with the mission to correct the flawed optics of the Hubble Space Telescope, only here at a minuscule fraction of the cost. —SAC #18 Report to NASA The Stanford-based analysis group and NASA announced on 4 May 2011 that the data from GP-B indeed confirms the two predictions of Albert Einstein's general theory of relativity.[31] The findings were accepted for publication in the journal Physical Review Letters.[8] The analysis has however drawn some criticism. Following the Physical Review Letters paper, a Nature editorial piece (subtitled "General relativity vindicated, but was the mission worth it?") quotes Ignazio Ciufolini as saying "It may be that people repeating this analysis with another working hypothesis on the nature of the systematic errors would get another result".[32] Science journals have expressed negative overviews, citing the $760,000,000 cost and that prior experiments had made 130-150 times more accurate measures over six years earlier.[33][34][35]
100
Gravity Probe B
References [1] "NASA GP-B Fact Sheet" (http:/ / einstein. stanford. edu/ content/ fact_sheet/ GPB_FactSheet-0405. pdf). . Retrieved 17 March 2011. [2] http:/ / einstein. stanford. edu/ [3] G. Hanuschak, H. Small, D. DeBra, K. Galal, A. Ndili, P. Shestople. "Gravity Probe B GPS Orbit Determination with Verification by Satellite Laser Ranging" (http:/ / einstein. stanford. edu/ content/ sci_papers/ papers/ Hanuschak_ION_Paper. pdf). . Retrieved 17 March 2011. [4] "Gravity Probe B: FAQ" (http:/ / einstein. stanford. edu/ content/ faqs/ faqs. html#launch). . Retrieved 14 May 2009. [5] "Gravity Probe B: FAQ" (http:/ / einstein. stanford. edu/ content/ faqs/ faqs. html#operations). . Retrieved 14 May 2009. [6] Gugliotta, G. (16 February 2009). "Perseverance Is Paying Off for a Test of Relativity in Space" (http:/ / www. nytimes. com/ 2009/ 02/ 17/ science/ 17gravity. html?_r=1). New York Times. . Retrieved 18 February 2009. [7] Everitt, C.W.F.; Parkinson, B.W. (2009). "Gravity Probe B Science Results—NASA Final Report" (http:/ / einstein. stanford. edu/ content/ final_report/ GPB_Final_NASA_Report-020509-web. pdf) (PDF). . Retrieved 2 May 2009. [8] Everitt et al. (2011). "Gravity Probe B: Final Results of a Space Experiment to Test General Relativity". Physical Review Letters 106 (22): 221101. arXiv:1105.3456. Bibcode 2011PhRvL.106v1101E. doi:10.1103/PhysRevLett.106.221101. PMID 21702590. [9] Ciufolini, I.; Lucchesi, D.; Vespe, F.; Chieppa, F. (1997). "Detection of Lense–Thirring Effect Due to Earth's Spin". arXiv:gr-qc/9704065 [gr-qc]. [10] "Einstein's warp effect measured" (http:/ / news. bbc. co. uk/ 2/ hi/ science/ nature/ 3762852. stm). BBC News. 21 October 2004. . Retrieved 14 May 2009. [11] Peplow, M. (2004). "Spinning Earth twists space". Nature News. doi:10.1038/news041018-11. [12] Iorio, L. (2005). "On the reliability of the so far performed tests for measuring the Lense–Thirring effect with the LAGEOS satellites". New Astronomy 10 (8): 603–615. arXiv:gr-qc/0411024. Bibcode 2005NewA...10..603I. doi:10.1016/j.newast.2005.01.001. [13] Iorio, L. (2006). "A critical analysis of a recent test of the Lense–Thirring effect with the LAGEOS satellites". Journal of Geodesy 80 (3): 123–136. arXiv:gr-qc/0412057. Bibcode 2006JGeod..80..128I. doi:10.1007/s00190-006-0058-4. [14] Iorio, L. (2007). "An assessment of the measurement of the Lense–Thirring effect in the Earth gravity field, in reply to: "On the measurement of the Lense–Thirring effect using the nodes of the LAGEOS satellites, in reply to "On the reliability of the so far performed tests for measuring the Lense–Thirring effect with the LAGEOS satellites" by L. Iorio," by I. Ciufolini and E. Pavlis". Planetary and Space Science 55 (4): 503. arXiv:gr-qc/0608119. Bibcode 2007P&SS...55..503I. doi:10.1016/j.pss.2006.08.001. [15] Iorio, L. (February 2010). "Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense–Thirring test". Central European Journal of Physics 8 (1): 25–32. Bibcode 2010CEJPh...8...25I. doi:10.2478/s11534-009-0060-6. [16] Iorio, L. (December 2009). "An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense–Thirring Effect with Satellite Laser Ranging". Space Science Reviews 148 (1–4): 363–381. Bibcode 2009SSRv..148..363I. doi:10.1007/s11214-008-9478-1. [17] Iorio, L. (2009). "Recent Attempts to Measure the General Relativistic Lense–Thirring Effect with Natural and Artificial Bodies in the Solar System". Proceedings of Science PoS (ISFTG). 017. arXiv:0905.0300. [18] Iorio, L. (August 2006). "A note on the evidence of the gravitomagnetic field of Mars". Classical and Quantum Gravity 23 (17): 5451–5454. arXiv:gr-qc/0606092. Bibcode 2006CQGra..23.5451I. doi:10.1088/0264-9381/23/17/N01. [19] Krogh, K. (November 2007). "Comment on 'Evidence of the gravitomagnetic field of Mars'". Classical and Quantum Gravity 24 (22): 5709–5715. Bibcode 2007CQGra..24.5709K. doi:10.1088/0264-9381/24/22/N01. [20] Iorio, L. (June 2010). "On the Lense-Thirring test with the Mars Global Surveyor in the gravitational field of Mars". Central European Journal of Physics 8 (3): 509–513. arXiv:gr-qc/0701146. Bibcode 2010CEJPh...8..509I. doi:10.2478/s11534-009-0117-6. [21] Iorio, L. (2005). "Is it possible to measure the Lense–Thirring effect on the orbits of the planets in the gravitational field of the Sun?". Astronomy and Astrophysics 431: 385. arXiv:gr-qc/0407047. Bibcode 2005A&A...431..385I. doi:10.1051/0004-6361:20041646. [22] Iorio, L. (2008). "Advances in the Measurement of the Lense–Thirring Effect with Planetary Motions in the Field of the Sun". Scholarly Research Exchange 2008: 1. Bibcode 2008ScReE2008.5235I. doi:10.3814/2008/105235. [23] Barry, P.L. (26 April 2004). "A Pocket of Near-Perfection" (http:/ / science. nasa. gov/ headlines/ y2004/ 26apr_gpbtech. htm). Science@NASA. . Retrieved 20 May 2009. [24] Hardwood, W. (20 April 2004). "Spacecraft launched to test Albert Einstein's theories" (http:/ / www. spaceflightnow. com/ delta/ d304/ ). Spaceflight Now. . Retrieved 14 May 2009. [25] Gravity Probe B finally pays off (http:/ / www. sciencenews. org/ view/ generic/ id/ 73870/ title/ Gravity_Probe_B_finally_pays_off_) [26] "Exciting April Plenary Talks – Saturday, 14 April" (http:/ / www. aps. org/ meetings/ april/ plenary. cfm). . Retrieved 16 November 2006. [27] Khan, B. (14 April 2007). "Was Einstein Right" (http:/ / einstein. stanford. edu/ content/ press_releases/ SU/ pr-aps-041807. pdf) (PDF). Stanford News. . Retrieved 14 May 2009. [28] "Gravity Probe-B Latest News" (http:/ / www. nasa. gov/ mission_pages/ gpb/ index. html). NASA. . Retrieved 20 February 2011. [29] "Public Announcement of GP-B Final Experimental Results" (http:/ / einstein. stanford. edu/ highlights/ status1. html). NASA and Stanford university. . Retrieved 6 May 2011. [30] Hecht, J. (20 May 2008). "Gravity Probe B scores 'F' in NASA review" (http:/ / space. newscientist. com/ article/ dn13938-gravity-probe-b-scores-f-in-nasa-review. html?feedId=online-news_rss20). New Scientist. . Retrieved 20 May 2008. [31] Stanford's Gravity Probe B confirms two Einstein theories (http:/ / news. stanford. edu/ news/ 2011/ may/ gravity-probe-mission-050411. html)
101
Gravity Probe B
102
[32] "Troubled probe upholds Einstein" (http:/ / www. nature. com/ news/ 2011/ 110510/ full/ 473131a. html). Nature 473 (7346): 131–132. 2011. Bibcode 2011Natur.473..131R. doi:10.1038/473131a. . [33] Cho, Adrian (4 May 2011). "At Long Last, Gravity Probe B Satellite Proves Einstein Right" (http:/ / news. sciencemag. org/ sciencenow/ 2011/ 05/ at-long-last-gravity-probe-b. html). Science Now. . [34] "Gravity Probe B: Relatively Important?" (http:/ / www. skyandtelescope. com/ community/ skyblog/ newsblog/ 121390204. html). Sky & Telescope 122 (August): 16. 2011. . [35] "Gravity Probe B Says Einstein was Right. Again." (http:/ / news. discovery. com/ space/ gravity-probe-b-110506. html). Discover (magazine). 2011. .
External links • Gravity Probe B web site at NASA (http://www.nasa.gov/mission_pages/gpb/index.html) • Gravity Probe B Web site at Stanford (http://einstein.stanford.edu) • Graphic explanation of how Gravity Probe B works (http://news.bbc.co.uk/2/hi/science/nature/3639193. stm#graphic) • NASA GP-B launch site (http://www.ksc.nasa.gov/elvnew/gpb) • NASA article on the technologies used in Gravity Probe B (http://science.nasa.gov/headlines/y2004/ 26apr_gpbtech.htm) • Frame Dragging (http://www.rdrop.com/users/green/school/framdrag.htm) • General Relativistic Frame Dragging (http://www.phy.duke.edu/~kolena/framedrag.html) • Layman's article on the project progress (http://www.washingtonpost.com/ac2/wp-dyn/ A43049-2004Jul11?language=printer)
Pound–Rebka experiment The Pound–Rebka experiment is a well known experiment to test Albert Einstein's theory of general relativity. It was proposed by Robert Pound and his graduate student Glen A. Rebka Jr. in 1959,[1] and was the last of the classical tests of general relativity to be verified (in the same year). It is a gravitational redshift experiment, which measures the redshift of light moving in a gravitational field, or, equivalently, a test of the general relativity prediction that clocks should run at different rates at different places in a non-uniform gravitational field. It is considered to be the experiment that ushered in an era of precision tests of general relativity.
Jefferson laboratory at Harvard University. The experiment occurred in the left "tower". The attic was later extended in 2004.
The test is based on the following principle: When an atom transits from an excited state to a base state, it emits a photon with a specific frequency and energy. When the same atom in its base state encounters a photon with that same frequency and energy, it will absorb that photon and transit to the excited state. If the photon's frequency and energy is different by even a little, the atom cannot absorb it (this is the basis of quantum theory). When the photon travels through a gravitational field, its frequency and therefore its energy will change due to the gravitational redshift. As a result the receiving atom can no longer absorb it. But if the emitting atom moves with just the right speed relative to the receiving atom the resulting doppler shift will cancel out the gravitational shift and the receiving atom will be able to absorb the photon. The "right" relative speed of the atoms is therefore a measure of the gravitational shift. The frequency of the photon "falling" towards the bottom of the tower is blueshifted. Pound and Rebka countered the gravitational blueshift by moving the emittor away from the receiver, thus generating a relativistic Doppler redshift: Special Relativity predicts a Doppler redshift of :
PoundRebka experiment
103
On the other hand, General Relativity predicts a gravitational blueshift of:
The detector at the bottom sees a superposition of the two effects. The Emitter was moved vertically and the speed was varied until the two effects cancelled each other, a phenomenon detected by reaching resonance. Mathematically:
In the case of the Pound–Rebka experiment
. Therefore:
= 7.5×10−7 m/s In the more general case when h ≈ R the above is no longer true. The energy associated with gravitational redshift over a distance of 22.5 meters is very small. The fractional change in energy is given by δE/E, is equal to gh/c2 = 2.5×10−15. Therefore short wavelength high energy photons are required to detect such minute differences. The 14 keV gamma rays emitted by iron-57 when it transitions to its base state proved to be sufficient for this experiment. Normally, when an atom emits or absorbs a photon, it also moves (recoils) a little, which takes away some energy from the photon due to the principle of conservation of momentum. The Doppler shift required to compensate for this recoil effect would be much larger (about 5 orders of magnitude) than the Doppler shift required to offset the gravitational redshift. But in 1958 Mössbauer reported that all atoms in a solid lattice absorb the recoil energy when a single atom in the lattice emits a gamma ray. Therefore the emitting atom will move very little (just as a cannon will not produce a large recoil when it is braced, e.g. with sandbags). This allowed Pound and Rebka to set up their experiment as a variation of Mössbauer spectroscopy. The test was carried out at Harvard University's Jefferson laboratory. A solid sample containing iron (57Fe) emitting gamma rays was placed in the center of a loudspeaker cone which was placed near the roof of the building. Another sample containing 57Fe was placed in the basement. The distance between this source and absorber was 22.5 meters (73.8 ft). The gamma rays traveled through a Mylar bag filled with helium to minimize scattering of the gamma rays. A scintillation counter was placed below the receiving 57Fe sample to detect the gamma rays that were not absorbed by the receiving sample. By vibrating the speaker cone the gamma ray source moved with varying speed, thus creating varying Doppler shifts. When the Doppler shift canceled out the gravitational blueshift, the receiving sample absorbed gamma rays and the number of gamma rays detected by the scintillation counter dropped accordingly. The variation in absorption could be correlated with the phase of the speaker vibration, hence with the speed of the emitting sample and therefore the doppler shift. To compensate for possible systematic errors, Pound and Rebka varied the speaker frequency between 10 Hz and 50 Hz, interchanged the source and absorber-detector, and used different speakers (ferroelectric and moving coil magnetic transducer).[2] The reason for exchanging the positions of the absorber and the detector is doubling the effect. Pound subtracted two experimental results: (1) the frequency shift with the source at the top of the tower (2) the frequency shift with the source at the bottom of the tower
PoundRebka experiment
104
The frequency shift for the two cases has the same magnitude but opposing signs. When subtracting the results, Pound and Rebka obtained a result twice as big as for the one-way experiment. The result confirmed that the predictions of general relativity were borne out at the 10% level.[3] This was later improved to better than the 1% level by Pound and Snider.[4] Another test involving a space-borne hydrogen maser increased the accuracy of the measurement to about 10−4 (0.01%).[5]
References [1] Pound, R. V.; Rebka Jr. G. A. (November 1, 1959). "Gravitational Red-Shift in Nuclear Resonance". Physical Review Letters 3 (9): 439–441. Bibcode 1959PhRvL...3..439P. doi:10.1103/PhysRevLett.3.439. [2] Mester, John (2006) (PDF). Experimental Tests of General Relativity (http:/ / luth2. obspm. fr/ IHP06/ lectures/ mester-vinet/ IHP-2GravRedshift. pdf). pp. 9–11. . Retrieved 2007-04-13. [3] Pound, R. V.; Rebka Jr. G. A. (April 1, 1960). "Apparent weight of photons". Physical Review Letters 4 (7): 337–341. Bibcode 1960PhRvL...4..337P. doi:10.1103/PhysRevLett.4.337. [4] Pound, R. V.; Snider J. L. (November 2, 1964). "Effect of Gravity on Nuclear Resonance". Physical Review Letters 13 (18): 539–540. Bibcode 1964PhRvL..13..539P. doi:10.1103/PhysRevLett.13.539. [5] Vessot, R. F. C.; M. W. Levine, E. M. Mattison, E. L. Blomberg, T. E. Hoffman, G. U. Nystrom, B. F. Farrel, R. Decher, P. B. Eby, C. R. Baugher, J. W. Watts, D. L. Teuber and F. D. Wills (December 29, 1980). "Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser". Physical Review Letters 45 (26): 2081–2084. Bibcode 1980PhRvL..45.2081V. doi:10.1103/PhysRevLett.45.2081.
External links • Physical Review focus story (http://focus.aps.org/story/v16/st1). • A detailed description of the experiment (http://www.lightandmatter.com/html_books/genrel/ch01/ch01. html#Section1.5).
Schiehallion experiment The Schiehallion experiment was an 18th-century experiment to determine the mean density of the Earth. Funded by a grant from the Royal Society, it was conducted in the summer of 1774 around the Scottish mountain of Schiehallion, Perthshire. The experiment involved measuring the tiny deflection of a pendulum due to the gravitational attraction of a nearby mountain. Schiehallion was considered the ideal location after a search for candidate mountains, thanks to its isolation and almost symmetrical shape. One of the triggers for the experiment were anomalies noted during the survey of the Mason–Dixon Line.
Schiehallion's isolated position and symmetrical shape lent well to the experiment
The experiment had previously been considered, but rejected, by Isaac Newton as a practical demonstration of his theory of gravitation. However, a team of scientists, notably Nevil Maskelyne, the Astronomer Royal, were convinced that the effect would be detectable and undertook to conduct the experiment. The deflection angle depended on the relative densities and volumes of the Earth and the mountain: if the density and volume of Schiehallion could be ascertained, then so could the density of the Earth. Once this was known, then this would in turn yield approximate values for those of the other planets, their moons, and the Sun, previously known only in terms of their relative ratios. As an additional benefit, the concept of contour
Schiehallion experiment lines, devised to simplify the process of surveying the mountain, later became a standard technique in cartography.
Background A pendulum hangs straight downwards in a symmetrical gravitational field. However, if a sufficiently large mass such as a mountain is nearby, its gravitational attraction should pull the pendulum's plumb-bob slightly out of true. The change in plumb-line angle against a known object—such as a star—could be carefully measured on opposite sides of the mountain. If the mass of the mountain could be independently established from a determination of its volume and an estimate of the mean density of its rocks, then these values could be extrapolated to provide the mean density of the Earth, and by extension, its mass. Isaac Newton had considered the effect in the Principia,[1] but pessimistically thought that any real mountain would produce too small a deflection to measure.[2] Gravitational effects, he wrote, were only discernible on the planetary scale.[2] Newton's pessimism was unfounded: although his calculations had suggested a deviation of less than 2 minutes of arc (for an idealised three-mile high mountain), this angle, though very slight, was within the theoretical capability of instruments of his day.[3] An experiment to test Newton's idea would both provide supporting evidence for his law of universal gravitation, and estimates of the mass and density of the Earth. Since the masses of astronomical objects were known only in terms of relative ratios, the mass of the Earth would provide reasonable values to the other planets, their moons, and the Sun. The data were also capable of determining the value of Newton's gravitational constant G, though this was not a goal of the experimenters; references to a value for G would not appear in the scientific literature until almost a hundred years later.[4]
Finding the mountain Chimborazo, 1738 A pair of French astronomers named Pierre Bouguer and Charles Marie de La Condamine were the first to attempt the experiment, conducting their measurements on the 6268-metre (unknown operator: u'strong' ft) volcano Chimborazo in Ecuador[a] in 1738.[5] Their expedition had left France for South America in 1735 to try to measure the meridian arc length of one degree of latitude near the equator, but they took advantage of the Chimborazo, the subject of the French 1738 experiment opportunity to attempt the deflection experiment. In December 1738, under very difficult conditions of terrain and climate, they conducted a pair of measurements at altitudes of 4,680 and 4,340 m.[6] Bouguer wrote in a 1749 paper that they had been able to detect a deflection of 8 seconds of arc, but he downplayed the significance of their results, suggesting that the experiment would be better carried out under easier conditions in France or England.[3][6] He added that the experiment had at least proved that the Earth could not be a hollow shell, as some thinkers of the day, including Edmond Halley, had suggested.[5]
105
Schiehallion experiment
106
Schiehallion, 1774 That a further attempt should be made on the experiment was proposed to the Royal Society in 1772 by Nevil Maskelyne, Astronomer Royal.[7] He suggested that the experiment would "do honour to the nation where it was made"[3] and proposed Whernside in Yorkshire, or the Blencathra-Skiddaw massif in Cumberland as suitable targets. The Royal Society formed the Committee of Attraction to consider the matter, appointing Maskelyne, Joseph Banks and Benjamin Franklin amongst its members.[8] The Committee despatched the astronomer and surveyor Charles Mason[b] to find a suitable mountain.[1]
The symmetrical ridge of Schiehallion viewed across Loch Rannoch
After a lengthy search over the summer of 1773, Mason reported that the best candidate was Schiehallion (then spelled Schehallien), a 1083-metre (unknown operator: u'strong' ft) peak lying between Loch Tay and Loch Rannoch in the central Scottish Highlands.[8] The mountain stood in isolation from any nearby hills, which would reduce their gravitational influence, and its symmetrical east–west ridge would simplify the calculations. Its steep northern and southern slopes would allow the experiment to be sited close to its centre of mass, maximising the deflection effect.
Mason however declined to conduct the work himself for the offered commission of one guinea per day.[8] The task therefore fell to Maskelyne, for which he was granted a temporary leave of his duties as Astronomer Royal. He was aided in the task by mathematician and surveyor Charles Hutton and Reuben Burrow, a mathematician of the Royal Greenwich Observatory. A workforce of labourers was engaged to construct observatories for the astronomers, and assist in the surveying. The science team was particularly well-equipped: its astronomical instruments included a 12-inch (unknown operator: u'strong' cm) brass quadrant from Cook's 1769 transit of Venus expedition, a 10-foot (unknown operator: u'strong' m) zenith sector, and a regulator (precision pendulum clock) for timing the astronomical observations.[9] They also acquired a theodolite and Gunter's chain for surveying the mountain, and a pair of barometers for measuring altitude.[9] Generous funding for the experiment was available due to underspend on the transit of Venus expedition, which had been turned over to the Society by the King.[1][3]
Schiehallion experiment
Measurements Astronomical Observatories were constructed to the north and south of the mountain, plus a bothy to accommodate equipment and the [6][c] scientists. Most of the workforce was however housed in rough canvas tents. Maskelyne's astronomical measurements were the first to be conducted. It was necessary for him to determine the zenith distances with respect to the plumb line for a set of stars at the precise time that each passed due south.[3][10][11] Weather conditions were frequently unfavourable due to mist and rain. However, from the south observatory, he was able to take 76 measurements on 34 stars in one direction, and then 93 observations on 39 stars in the The deflection is the difference between the true zenith Z as determined by other. From the north side, he then astrometry, and the apparent zenith Z′ as determined by a plumb-line conducted a set of 68 observations on 32 stars and a set of 100 on 37 stars.[6] By conducting sets of measurements with the plane of the zenith sector first facing east and then west, he successfully avoided any systematic errors arising from collimating the sector.[1] To determine the deflection due to the mountain, it was necessary to account for the curvature of the Earth: an observer will see the local zenith shift by the same angle as any change in latitude. After accounting for observational effects such as precession, aberration of light and nutation, Maskelyne showed that the difference between the locally-determined zenith for observers north and south of Schiehallion was 54.6 arc seconds.[6] Once the surveying team had provided a difference of 42.94″ latitude between the two stations, he was able to subtract this, and after rounding to the accuracy of his observations, announce that the sum of the north and south deflections was 11.6″.[3][6][12] Maskelyne published his initial results in the Philosophical Transactions of the Royal Society in 1775,[12] using preliminary data on the mountain's shape and hence the position of its center of gravity. This led him to expect a deflection of 20.9″ if the mean densities of Schiehallion and the Earth were equal.[3][13] Since the deflection was about half this, he was able to make a preliminary announcement that the mean density of the Earth was approximately double that of Schiehallion. A more accurate value would have to await completion of the surveying process.[12] Maskelyne took the opportunity to note that that Schiehallion exhibited a gravitational attraction, and thus all mountains did; and that Newton's inverse square law of gravitation had been confirmed.[12][14] An appreciative Royal Society presented Maskelyne with the 1775 Copley Medal; the biographer Chalmers later noting that "If any doubts yet remained with respect to the truth of the Newtonian system, they were now totally removed".[15]
107
Schiehallion experiment
108
Surveying The work of the surveying team was greatly hampered by the inclemency of the weather, and it took until 1776 to complete the task.[13] To find the volume of the mountain, it was necessary to divide it into a set of vertical prisms and compute the volume of each. The triangulation task falling to Charles Hutton was considerable: the surveyors had obtained thousands of bearings to more than a thousand points around the mountain.[16] Moreover, the vertices of his prisms did not always conveniently coincide with the surveyed heights. To make sense of all his data, he hit upon the idea of interpolating a series of lines at set intervals between his measure values, marking points of equal height. In doing so, not only could he easily determine the heights of his prisms, but from the swirl of the lines one could get an instant impression of the form of the terrain. Hutton had invented contour lines, in common use since for depicting cartographic relief.[6][16][d] Hutton's solar system density table Body
Density, kg·m−3 [17]
Hutton, 1778
[18]
Modern value
Sun
1,100
1,408
Mercury
9,200
5,427
Venus
5,800
5,204
Earth
4,500
5,515
Moon
3,100
3,340
Mars
3,300
3,934
Jupiter
1,100
1,326
Saturn
410
687
Hutton had to compute the individual attractions due to each of the many prisms that formed his grid, a process which was as laborious as the survey itself. The task occupied his time for a further two years before he could present his results, which he did in a hundred-page paper to the Royal Society in 1778.[17] He found that the attraction of the plumb-bob to the Earth would be 9,933 times that of the sum of its attractions to the mountain at the north and south stations, if the density of the Earth and Schiehallion had been the same.[16] Since the actual deflection of 11.6″ implied a ratio of 17,804:1 after accounting for the effect of latitude on gravity, he was able to state that the Earth had a mean density of , or about that of the mountain.[13][16][17] The lengthy process of surveying the mountain had not therefore greatly affected the outcome of Maskelyne's calculations. Hutton took a density of 2,500 kg·m−3 for Schiehallion, and announced that the density of the Earth was of this, or 4,500 kg·m−3.[16] In comparison with the modern accepted figure of 5,515 kg·m−3,[18] the density of the Earth had been computed with an error of less than 20%. That the mean density of the Earth should so greatly exceed that of its surface rocks naturally meant that there must be more dense material lying deeper. Hutton correctly surmised that the core material was likely metallic, and might have a density of 10,000 kg·m−3.[16] He estimated this metallic portion to occupy some 65% of the diameter of the Earth.[17] With a value for the mean density of the Earth, Hutton was able to set some values to Jérôme Lalande's planetary tables, which had previously only been able to express the densities of the major solar system objects in relative terms.[17]
Schiehallion experiment
109
Repeat experiments A more direct, and more accurate, measurement of the mean density of the Earth was made 24 years after Schiehallion, when in 1798 Henry Cavendish used an exquisitely sensitive torsion balance to measure the attraction between large masses of lead. Cavendish's figure of 5,448 ± 0.033 kg·m−3 was only 1.2% from the currently accepted value of 5,515 kg·m−3, and his result would not be significantly improved upon until 1895 by Charles Boys.[e] The care with which Cavendish conducted the experiment and the accuracy of his result has led his name to since be associated with it.[19] John Playfair carried out a second survey of Schiehallion in 1811; on the basis of a rethink of its rock strata, he suggested a density of 4,560 to 4,870 kg·m−3,[20] though the then elderly Hutton vigorously defended the original value in an 1821 paper to the Society.[3][21] Playfair's calculations had raised the density closer towards its modern value, but was still too low and significantly poorer than Cavendish's computation of some years earlier. The Schiehallion experiment was repeated in 1856 by Henry James, director-general of the Ordnance Survey, who instead used the hill Arthur's Seat in central Edinburgh.[6][11][22] With the resources of the Ordnance Survey at his disposal, James extended his topographical survey to a 21-kilometre radius, taking him as far as the borders of Midlothian. He obtained a density of about 5,300 kg·m−3.[3][13] An experiment in 2005 undertook a variation of the 1774 work: instead of computing local differences in the zenith, the experiment made a very accurate comparison Arthur's Seat, Edinburgh, the site of Henry James' 1856 of the period of a pendulum at the top and bottom of experiment Schiehallion. The period of a pendulum is a function of g, the local gravitational acceleration. The pendulum is expected to run more slowly at altitude, but the mass of the mountain will act to reduce this difference. This experiment has the advantage of being considerably easier to conduct than the 1774 one, but to achieve the desired accuracy, it is necessary to measure the period of the pendulum to within one part in one million.[10] This experiment yielded a value of the mass of the Earth of 8.1 ± 2.4 × 1024 kg,[23] corresponding to a mean density of 7,500 ± 1,900 kg·m−3.[f] A modern re-examination of the geophysical data was able to take account of factors the 1774 team could not. With the benefit of a 120-km radius digital elevation model, greatly improved knowledge of the geology of Schiehallion, and in particular a computer, a 2007 report produced a mean Earth density of 5,480 ± 250 kg·m−3.[24] When compared to the modern figure of 5,515 kg·m−3, it stood as a testament to the accuracy of Maskelyne's astronomical observations.[24]
Schiehallion experiment
110
Mathematical procedure Consider the force diagram to the right, in which the deflection has been greatly exaggerated. The analysis has been simplified by considering the attraction on only one side of the mountain.[20] A plumb-bob of mass m is situated a distance d from P, the centre of mass of a mountain of mass MM and density ρM. It is deflected through a small angle θ due to its attraction F towards P and its weight W directed towards the Earth. The vector sum of W and F results in a tension T in the pendulum string. The Earth has a mass ME, radius rE and a density ρE.
Schiehallion force diagram
The two gravitational forces on the plumb-bob are given by Newton's law of gravitation:
Where G is Newton's gravitational constant. G and m can be eliminated by taking the ratio of F to W:
Where VM and VE are the volumes of the mountain and the Earth. Under static equilibrium, the horizontal and vertical components of the string tension T can be related to the gravitational forces and the deflection angle θ:
Substituting for T:
Since VE, VM, d and rE are all known, and θ and d have been measured, then a value for the ratio ρE : ρM can be obtained:[20]
Notes a. At the time, part of the Viceroyalty of Peru. Contemporary sources therefore refer to the 'Peruvian Expedition'. b. Mason, together with Jeremiah Dixon, had earlier marked the Mason-Dixon line which separated the northern and southern United States. c. These constructions are now ruined, but their remnants may still be found on the mountainside. d. This was arguably a rediscovery: Edmond Halley had plotted lines of equal magnetic variation (isogons) in 1701, and Nicholas Cruquius lines of equal depth (isobaths) in 1727. e. A value of 5,480 kg·m−3 appears in Cavendish's paper. He had however made an arithmetical error: his measurements actually led to a value of 5,448 kg·m−3; a discrepancy that was not found until 1821 by Francis Baily. f. Taking the volume of the Earth to be 1.0832 × 1012 km3.
Schiehallion experiment
References [1] Davies, R.D. (1985). "A Commemoration of Maskelyne at Schiehallion". Royal Astronomical Society Quarterly Journal 26 (3): 289–294. Bibcode 1985QJRAS..26..289D. [2] Newton. Philosophiæ Naturalis Principia Mathematica (http:/ / scanserver. ulib. org/ is/ scanserver/ newton/ xml/ doc. scn?pg=527& rp=_n). II. p. 528. ISBN 0-521-07647-1. . Translated: Andrew Motte, First American Edition. New York, 1846 [3] Sillitto, R.M. (31 October 1990). "Maskelyne on Schiehallion: A Lecture to The Royal Philosophical Society of Glasgow" (http:/ / www. sillittopages. co. uk/ schie/ schie90. html). . Retrieved 28 December 2008. [4] Cornu, A.; Baille, J. B. (1873). "Mutual determination of the constant of attraction and the mean density of the earth". Comptes rendus de l'Académie des sciences 76: 954–958. [5] Poynting, J.H. (1913). The Earth: its shape, size, weight and spin (http:/ / books. google. com/ ?id=whA9AAAAIAAJ& pg=PA50). Cambridge. pp. 50–56. . [6] Poynting, J. H. (1894). The mean density of the earth (http:/ / www. archive. org/ download/ meandensityofear00poynuoft/ meandensityofear00poynuoft. pdf). pp. 12–22. . [7] Maskelyne, N. (1772). "A proposal for measuring the attraction of some hill in this Kingdom". Phil. Trans. Royal Soc. 65: 495–499. Bibcode 1775RSPT...65..495M. [8] Danson, Edwin (2006). Weighing the World (http:/ / books. google. com/ ?id=UNH_Y7ERFeoC& pg=PA146). Oxford University Press. pp. 115–116. ISBN 978-0-19-518169-2. . [9] Danson, Edwin (2006). Weighing the World (http:/ / books. google. com/ ?id=UNH_Y7ERFeoC& pg=PA146). Oxford University Press. p. 146. ISBN 978-0-19-518169-2. . [10] "The "Weigh the World" Challenge 2005" (http:/ / www. countingthoughts. com/ ct/ wtw/ notes. pdf). countingthoughts. 23 April 2005. . Retrieved 28 December 2008. [11] Poynting, J.H. (1913). The Earth: its shape, size, weight and spin (http:/ / books. google. com/ ?id=whA9AAAAIAAJ& pg=PA50). Cambridge. pp. 56–59. . [12] Maskelyne, N. (1775). "An Account of Observations Made on the Mountain Schiehallion for Finding Its Attraction". Phil. Trans. Royal Soc. 65 (0): 500–542. doi:10.1098/rstl.1775.0050. [13] Poynting, J. H.; Thomson, J. J. (1909). A text-book of physics (http:/ / www. archive. org/ download/ textbookofphysic01poynuoft/ textbookofphysic01poynuoft. pdf). pp. 33–35. ISBN 1-4067-7316-6. . [14] Mackenzie, A.S. (1900). The laws of gravitation; memoirs by Newton, Bouguer and Cavendish, together with abstracts of other important memoirs (http:/ / www. archive. org/ download/ lawsofgravitatio00mackrich/ lawsofgravitatio00mackrich. pdf). pp. 53–56. . [15] Chalmers, A. (1816). The General Biographical Dictionary (http:/ / books. google. com/ ?id=Uh8IAAAAQAAJ& pg=PA317). 25. p. 317. . [16] Danson, Edwin (2006). Weighing the World (http:/ / books. google. com/ ?id=UNH_Y7ERFeoC& pg=PA153). Oxford University Press. pp. 153–154. ISBN 978-0-19-518169-2. . [17] Hutton, C. (1778). "An Account of the Calculations Made from the Survey and Measures Taken at Schehallien" (http:/ / www. metapress. com/ content/ hp3604530g7k70x6/ ). Phil. Trans. Royal Soc. 68 (0): 689. doi:10.1098/rstl.1778.0034. . [18] "Planetary Fact Sheet" (http:/ / nssdc. gsfc. nasa. gov/ planetary/ factsheet/ ). Lunar and Planetary Science. NASA. . Retrieved 2 January 2009. [19] McCormmach, Russell; Jungnickel, Christa (1996). Cavendish (http:/ / books. google. com/ ?id=EUoLAAAAIAAJ). American Philosophical Society. pp. 340–341. ISBN 978-0-87169-220-7. . [20] Ranalli, G. (1984). "An Early Geophysical Estimate of the Mean Density of the Earth: Schehallien, 1774" (http:/ / hess. metapress. com/ content/ k43q522gtt440172/ ). Earth Sciences History 3 (2): 149–152. . [21] Hutton, Charles (1821). "On the mean density of the earth" (http:/ / www. archive. org/ details/ onmeandensityofe00huttiala). Proceedings of the Royal Society. . [22] James (1856). "On the Deflection of the Plumb-Line at Arthur's Seat, and the Mean Specific Gravity of the Earth". Proceedings of the Royal Society 146: 591–606. JSTOR 108603. [23] "The "Weigh the World" Challenge Results" (http:/ / www. countingthoughts. com/ ct/ wtw/ schiehallion results june. doc). countingthoughts. . Retrieved 28 December 2008. [24] Smallwood, J.R. (2007). "Maskelyne's 1774 Schiehallion experiment revisited" (http:/ / www. ingentaconnect. com/ content/ geol/ sjg/ 2007/ 00000043/ 00000001/ art00003). Scottish Journal of Geology 43 (1): 15 31. doi:10.1144/sjg43010015. .
111
112
Mechanics Atwood machine The Atwood machine (or Atwood's machine) was invented in 1784 by Rev. George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics. The ideal Atwood Machine consists of two objects of mass m1 and m2, connected by an inextensible massless string over an ideal massless pulley. [1] When m1 = m2, the machine is in neutral equilibrium regardless of the position of the weights. When m1 ≠ m2 both masses experience uniform acceleration.
Illustration of Atwood machine, 1905.
Atwood machine
113
Equation for constant acceleration We are able to derive an equation for the acceleration by using force analysis. If we consider a massless, inextensible string and an ideal massless pulley, the only forces we have to consider are: tension force (T), and the weight of the two masses (W1 and W2). To find an acceleration we need to consider the forces affecting each individual mass. Using Newton's second law (with a sign convention of ) we can derive a system of equations for the acceleration (a). As a sign convention, we assume that a is positive when downward for , and that a is positive when upward for . Weight of and is simply and respectively. Forces affecting m1: Forces affecting m2: and adding the two previous equations we obtain , and our concluding formula for acceleration
Conversely, the acceleration due to gravity, g, can be found by timing the movement of the weights, and calculating a value for the uniform acceleration a:
.
The free body diagrams of the two hanging masses of the Atwood machine. Our sign convention, depicted by the acceleration vectors is that m1 accelerates downward and that m2 accelerates upward, as would be the case if m1 > m2
The Atwood machine is sometimes used to illustrate the Lagrangian method of deriving equations of motion. [2]
Equation for tension It can be useful to know an equation for the tension in the string. To evaluate tension we substitute the equation for acceleration in either of the 2 force equations.
For example substituting into
The tension can be found in using this method.
, we get
Atwood machine
Equations for a pulley with inertia and friction For very small mass differences between m1 and m2, the rotational inertia I of the pulley of radius r cannot be neglected. The angular acceleration of the pulley is given by the no-slip condition:
where
is the angular acceleration. The net torque is then:
Combining with Newton's second law for the hanging masses, and solving for T1, T2, and a, we get: Acceleration:
Tension in string segment nearest m1:
Tension in string segment nearest m2:
Should bearing friction be negligible (but not the inertia of the pulley and not the traction of the string on the pulley rim), these equations simplify as the following results: Acceleration:
Tension in string segment nearest m1:
Tension in string segment nearest m2:
Practical implementations Atwood's original illustrations show the main pulley's axle resting on the rims of another four wheels, to minimise friction forces from the bearings. Many historical implementations of the machine follow this design. An elevator with a counterbalance approximates an ideal Atwood machine and thereby relieves the driving motor from the load of holding the elevator cab — it has to overcome only weight difference and inertia of the two masses. The same principle is used for funicular railways with two connected railway cars on inclined tracks.
114
Atwood machine
Notes [1] Tipler, Paul A. (1991). Physics For Scientists and Engineers, Third Edition, Extended Version. New York: Worth Publishers. ISBN 0-87901-432-6. Chapter 6, example 6-13, page 160. [2] Goldstein, Herbert (1980). Classical Mechanics, second Edition. New Delhi: Addison-Wesley/Narosa Indian Student Edition. ISBN 81-85015-53-8. Section 1-6, example 2, pages 26-27.
• " Atwood's Machine (http://demonstrations.wolfram.com/AtwoodsMachine/)" by Enrique Zeleny, The Wolfram Demonstrations Project.
Barton's Pendulums First demonstrated by Edwin Henry Barton (1858-1925), Professor of Physics at University College, Nottingham, who had a particular interest in the movement and behavior of spherical bodies, a Barton's Pendulums experiment demonstrates the physical phenomenon of resonance and the response of pendulums to vibration at, below and above their resonant frequencies. In its simplest construction, approximately 10 different pendulums are hung from one common string. This system vibrates at the resonance frequency of a center pendulum, causing the target pendulum to swing with the maximum amplitude. The other pendulums to the side do not move as well, thus demonstrating how torquing a pendulum at its resonance frequency is most efficient.[1][2] The driver may be a very heavy pendulum also attached to this common string; the driver is set to swing and move the whole system. java simulation of Barton’s Pendulum [3]
References [1] Barton’s Pendulum (http:/ / www. fas. harvard. edu/ ~scdiroff/ lds/ OscillationsWaves/ BartonsPendulum/ BartonsPendulum. html) [2] G2-12 (http:/ / www. physics. umd. edu/ lecdem/ services/ demos/ demosg2/ g2-12. htm) [3] http:/ / www. phy. ntnu. edu. tw/ ntnujava/ index. php?topic=1598
115
Bedford Level experiment
Bedford Level experiment The Bedford Level Experiment is a series of observations carried out along a six-mile length of the Old Bedford River on the Bedford Level, Norfolk, England, during the nineteenth and early twentieth centuries. It was an attempt to determine the shape of the Earth. Early results seemed to prove the Earth to be flat, but most later attempts to reproduce the observations firmly supported the established view that the Earth is a sphere.
Method At the point chosen for all the experiments the river is a slow-flowing drainage canal running in an uninterrupted straight line for a six-mile stretch to the north-east of the village of Welney. The most famous of the observations, and the one that was taught in schools until photographs of the Earth from space became available,[1][2] involved a set of three poles fixed at equal height above water level along this length. As the surface of the water was assumed to be level, the discovery that the middle pole, when viewed carefully through a theodolite, was almost three feet higher than the poles at each end was finally accepted as a new proof that the surface of the earth was indeed curved.[3]
History The first investigation was carried out by Samuel Birley Rowbotham (1816–1884), in the summer of 1838. He waded into the river and used a telescope held eight inches above the water to watch a boat with a five-foot mast row slowly away from him. He reported that the vessel remained Diagram of Rowbotham's experiment on the Bedford Level, taken from his book constantly in his view for the full six miles "Earth not a globe" to Welney bridge, whereas, had the water surface been curved with the accepted circumference of a spherical earth, the top of the mast should have been some eleven feet below his line of sight. He published this discovery under the title Zetetic Astronomy using the pseudonym Parallax in 1849 and subsequently expanded it into a book published in 1865.[4] Rowbotham repeated his experiments several times over the years but his claims received little attention until, in 1870, a supporter by the name of John Hampden offered a wager that he could show, by repeating Rowbotham's experiment, that the earth was flat. The noted naturalist and qualified surveyor Alfred Russel Wallace accepted the wager. Wallace, by virtue of his surveyor's training and knowledge of physics, avoided the errors of the preceding experiments and won the bet.[5][6] The crucial step was to set a sight line 4 metres (unknown operator: u'strong' ft) above the water.[7] Despite Hampden initially The view through Wallace's level as reproduced refusing to accept the demonstration, Wallace was awarded the bet by in his autobiography the referee, editor of The Field sports magazine. Hampden subsequently published a pamphlet alleging that Wallace had cheated and sued for his money. Several protracted court cases ensued, with the result that Hampden was imprisoned for libel and threatening to kill Wallace.[8][9] Wallace, who had been unaware of Rowbotham's earlier experiments, was criticized by his peers for "his 'injudicious' involvement in a bet to 'decide' the most fundamental and established of scientific facts".[7]
116
Bedford Level experiment In 1901 Henry Yule Oldham, a geography reader at King's College, Cambridge, claimed to have conducted the definitive experiment described in "Method", above.[3][10] The planists, however, were not yet defeated: On 11 May 1904 Lady Elizabeth Anne Blount hired a commercial photographer to use a telephoto lens camera to take a picture from Welney of a large white sheet she had placed, touching the surface of the river, at Rowbotham's original position six miles away. The photographer, Edgar Clifton from Dallmeyer's studio, mounted his camera two feet above the water at Welney and was surprised to be able to obtain a picture of the target, which should have been invisible to him given the low mounting point of the camera. Lady Blount published the pictures far and wide and for those who do not accept the explanation of Superior Mirage due to refraction, these have not been explained.[11] These controversies became a regular feature in the English Mechanic magazine in 1904–5, which published Blount's photo and reported two experiments in 1905 that showed the opposite results. One of these, by Clement Stratton on the Ashby Canal, showed a dip on a sight-line only 4 feet 9 inches (unknown operator: u'strong' m) above the surface.[12]
Refraction Refraction of light can produce the results noted by Rowbotham and Blount. Because the density of air in the Earth's atmosphere decreases with height above the Earth's surface, all light rays travelling nearly horizontally bend downward. This phenomenon is routinely allowed for in levelling and celestial navigation.[13] If the measurement is close enough to the surface, light rays can curve downward at a rate equal to the mean curvature of the Earth's surface. In this case, the two effects of curvature and refraction cancel each other out and the Earth will appear flat in optical experiments. This would have been aided, on each occasion, by a temperature inversion in the atmosphere with temperature increasing with altitude above the canal, similar to the phenomenon of the superior image mirage. Temperature inversions like this are common. An increase in air temperature or lapse rate of 0.11 degrees Celsius per metre of altitude would create an illusion of a flat canal, and all optical measurements made near ground level would be consistent with a completely flat surface. If the lapse rate were higher than this (temperature increasing with height at a greater rate), all optical observations would be consistent with a concave surface, a "bowl-shaped earth". Under average conditions, optical measurements are consistent with a spherical Earth approximately 15% less curved than its true diameter.[14] Repetition of the atmospheric conditions required for each of the many observations is not unlikely, and warm days over still water can produce favourable conditions.[15]
Other experiments On July 25, 1896, Ulysses Grant Morrow, a newspaper editor, conducted a similar experiment on the Old Illinois Drainage Canal, Summit, Illinois. Unlike Rowbotham, he was seeking to demonstrate that the surface of the earth was curved: when he too found that his target marker, eighteen inches above water level and five miles distant, was clearly visible he concluded that the Earth's surface was concavely curved, in line with the expectations of his sponsors, the Koreshan Unity society. The findings were dismissed by critics as the result of atmospheric refraction.[16][17]
117
Bedford Level experiment
118
References [1] Association for Science Education (1942). School Science Review (London: John Murray) 24: 120. ISSN 0036-6811. [2] Richards-Jones, P (1968). "Astronomy at O level". Physics Education 3 (1): 35–39. Bibcode 1968PhyEd...3...35R. doi:10.1088/0031-9120/3/1/310. ISSN 0031-9120. [3] Correspondent (25 September 1901). "The British Association". The Times (London) (36569): 12. "Mr Yule Oldham on his re-measurement of the curvature of the Earth along the Bedford Level." [4] Samuel Birley Rowbotham, writing as "Parallax" (1881): Earth not a globe. Simpkin, Marshall, London. ISBN 0-7661-4945-5. [5] Nature 7 April 1870. [6] "The Form of the Earth—A Shock of Opinions" (http:/ / query. nytimes. com/ mem/ archive-free/ pdf?_r=1& res=9C00EFDF113EEE34BC4852DFBE66838A669FDE& oref=slogin) (PDF). New York Times. 1871-08-10. . Retrieved 2007-11-02. [7] Christine Garwood (2007). Flat Earth. Macmillan. pp. 104–125. ISBN 0-312-38208-1. [8] Hampden, John (1870): The Bedford Canal swindle detected & exposed. A. Bull, London. [9] Correspondent (8 March 1875). "Spring Assizes". The Times (London) (28257): 11. [10] Oldham, H. Yule (1901). "The experimental demonstration of the curvature of the Earth's surface". Annual Report (London: British Association for the Advancement of Science): 725–6. [11] Michell, John (1984): Eccentric Lives and Peculiar Notions. Thames and Hudson, London. ISBN 0-500-01331-4. [12] Clement Stratton (20 January 1905). English Mechanic. [13] Henning Umland. "A short guide to Celestial Navigation" (http:/ / www. celnav. de/ page2. htm). . Retrieved 2010-11-14. [14] Lynch, David K; Livingston, William (2001). Color and Light in Nature. New York: Cambridge University Press. ISBN 0-521-77504-3. [15] Naylor, John (2002). "Mirages". Out of the Blue A 24-Hour Skywatcher's Guide. Cambridge, England: Cambridge University Press. ISBN 0-521-80925-8. [16] Simanek, Donald E. (2003). "Turning the Universe Inside-Out" (http:/ / www. lhup. edu/ ~dsimanek/ hollow/ morrow. htm). Lock Haven University of Pennsylvania. . Retrieved 2007-11-02. [17] Teed, Cyrus; Morrow, Ulysses Grant (1905). The Earth a Concave Sphere. Estero, FL: Guiding Star. p. 160. ISBN 0-87991-026-7.
Beverly Clock The Beverly Clock is a clock situated in the foyer of the Department of Physics at the University of Otago, Dunedin, New Zealand. The clock is still running despite never having been manually wound since its construction in 1864 by Arthur Beverly.
Operation The clock mechanism is driven by variations in atmospheric pressure and by daily temperature variations; of the two, the temperature variations are the more important. Either causes the air in a one cubic-foot air-tight box to expand or contract, pushing on a diaphragm. A six-degree Celsius temperature variation over the course of each day creates enough pressure to raise a one-pound weight by one inch (energy extracted = .11 joules), which drives the clock mechanism. It is therefore not an example of perpetual motion. A similar commercial example of this mechanism is known as the Atmos clock. The Beverly Clock as it now stands in the Physics
While the clock has not been wound since it was made by Arthur Department at the University of Otago Beverly in 1864, it has stopped on a number of occasions: when its mechanism needed cleaning; when there was a mechanical failure; when the Physics Department moved to new quarters; and on
Beverly Clock
119
occasions when the ambient temperature has not fluctuated sufficiently. After environmental parameters readjust, the clock begins operating again.
References • L.E.S. Amon, A. Beverly, and J.N. Dodd (1984). "The Beverly clock" [1] (abstract). European Journal of Physics 5 (4): 1957–197. Bibcode 1984EJPh....5..195A. doi:10.1088/0143-0807/5/4/002. • Marc Abrahams (2001). "The Latest on Long-Running Experiments" [2] (– Scholar search [3]). Annals of Improbable Research 7 (3). • L.E.S. Amon and Hardwicke Knight. "Beverly, Arthur 1822 – 1907" [4]. Dictionary of New Zealand Biography. Ministry for Culture and Heritage. Retrieved 4 April 2011.
The inner mechanism of the Beverly clock showing chain, sprockets and torsional pendulum
References [1] http:/ / www. iop. org/ EJ/ abstract/ 0143-0807/ 5/ 4/ 002 [2] http:/ / www. improbable. com/ airchives/ paperair/ volume7/ v7i3/ long-run-7-3. html [3] http:/ / scholar. google. co. uk/ scholar?hl=en& lr=& q=intitle%3AThe+ Latest+ on+ Long-Running+ Experiments& as_publication=Annals+ of+ Improbable+ Research& as_ylo=& as_yhi=& btnG=Search [4] http:/ / www. teara. govt. nz/ en/ biographies/ 1B20
Galileo's Leaning Tower of Pisa experiment
Galileo's Leaning Tower of Pisa experiment According to a biography by Galileo's pupil Vincenzo Viviani, in 1589 the Italian scientist Galileo had dropped two balls of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass.[1]. Via this method, he supposedly discovered that the objects fell at the same acceleration, proving his prediction true, while at the same time proving Aristotle's theory of gravity (which states that objects fall at speed relative to their mass) false. At the time when Viviani asserts that the experiment took place, Galileo had not yet formulated the final version of his law of free fall. He had, however, formulated an earlier version which predicted that bodies of the same material falling through the same medium would fall at the same speed.[2] This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight.[3][4] While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is accepted by most historians that it was a thought experiment which did not actually take place.[5][6] An exception is Drake,[7] who argues that the experiment did take place, more or less as Viviani described it. Galileo arrived at his hypothesis by a famous thought experiment outlined in his book On Motion[8]. Imagine two objects, one light and one heavier than the other one, are connected to each other by a string. Drop this system of objects from the top of a tower. If we assume heavier objects do indeed fall faster than lighter ones (and conversely, lighter objects fall slower), the string will soon pull taut as the lighter object retards the fall of the heavier object. But the system considered as a whole is heavier than the heavy object alone, and therefore should fall faster. This contradiction leads one to conclude the assumption is false.
Notes [1] [2] [3] [4] [5] [6]
Drake, S. (1978). Galileo At Work. University of Chicago Press. pp. 19–20. ISBN 0-226-16226-5. Drake (1978), p. 20 Drake (1978), p. 9 Sharratt, M. (1994). Galileo: Decisive Innovator. Cambridge University Press. p. 31. ISBN 0-521-56671-1. Groleau, R. (July 2002). "Galileo's Battle for the Heavens" (http:/ / www. pbs. org/ wgbh/ nova/ galileo/ experiments. html). . pen and pencil, P. (30 June 2005). "Science history: Setting the record straight" (http:/ / www. hindu. com/ seta/ 2005/ 06/ 30/ stories/ 2005063000351500. htm). The Hindu. . [7] Drake (1978), pp. 19–21, 414–416 [8] "The Galileo Project - On Motion" (http:/ / galileo. rice. edu/ sci/ theories/ on_motion. html). .
External links • Falling body experiments (http://physicsworld.com/cws/article/print/16806) • Galileo and the Leaning Tower of Pisa (http://www.jimloy.com/physics/galileo.htm) • Newton's Modification to Kepler's Laws (http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html)
120
Heron's fountain
Heron's fountain Heron's fountain is a hydraulic machine invented by the 1st century inventor, mathematician, and physicist Heron, also known as Hero of Alexandria. Heron studied the pressure of air and steam, described the first steam engine, and built toys that would spurt water, one of them known as Heron's fountain. Various versions of Heron's Fountain are used today in physics classes as a demonstration of principles of hydraulics and pneumatics.
Construction Heron's fountain is built as follows: • Start with a basin, open to the air. Run a pipe from a hole in the bottom of that basin to an airtight air supply container. (Glass flasks are shown here, and serve the purpose well. Cans with airtight lids may also be used.) The air supply container stands significantly below the basin. • Run another pipe from the top of that container up to the top of the airtight fountain supply container, which is filled with water. • From the fountain supply container, have a pipe that reaches nearly to the bottom of the container, through the top up to the spout of the fountain. A refinement is to have the spout coming up through the centre of the basin, and the containers may be concealed in a column supporting the basin, as long as the air supply container is lower than the fountain supply container. • Fill the basin with water. • The water from the basin flows by gravity into the air supply container. It fills the container, displacing the air. • The air flows into the fountain supply container, displacing the water, which shoots out higher than the original basin. • The flow will stop when the water supply container is empty (i.e. when the water level drops below the lower end of the outlet pipe).
121
Heron's fountain
Motion Heron's fountain is not a perpetual motion machine.[1] If the nozzle of the spout is narrow, it may play for several minutes, but it eventually comes to a stop. The water coming out of the tube may go higher than the level in any container, but the net flow of water is downward. If, however, the volumes of the air supply and fountain supply containers are designed to be much larger than the volume of the basin, with the flow rate of water from the nozzle of the spout being held constant, the fountain could operate for a far greater time interval. Its action may seem less paradoxical if it considered as a siphon, but with the upper arch of the tube removed, and the air pressure between the two lower containers providing the positive pressure to lift the water over the arch. The device is also known as Heron's siphon. The gravitational potential energy of the water which falls a long way from the basin into the lower container is transferred by pneumatic pressure tube (only air is moved upwards at this stage) to push the water from the upper container a short way above the basin. The fountain can spout (almost) as high above the upper container as the water falls from the basin into the lower container. For maximum effect, place the upper container as closely beneath the basin as possible and place the lower container a long way beneath both. As soon as the water level in the upper container has dropped so low that the water bearing tube no longer touches the water surface, the fountain stops. In order to make the fountain play again, the air supply container is emptied of water, and the fountain supply container and the basin are refilled. Lifting the water provides the energy required.
Geological phenomena It is possible that geysers operate via this mechanism, with the distinction that the spouting of the water at the surface occurs discontinuously. Furthermore, unlike Heron's fountain, which requires that the air supply container be manually emptied of water, geysers have an analogous "air supply container" that is steadily heated by geothermal energy. When the water level in the air supply container becomes too high, the geothermal heat flux causes the water to boil off and therefore naturally empty the container of water and replace it with water vapor instead of air.
In popular culture An example of Heron's fountain, built by Larry Fleinhardt, was featured in the 8th episode (titled "Tabu") of the 4th season of the television show Numb3rs.
Notes [1] Hero's Fountain (http:/ / physics. kenyon. edu/ EarlyApparatus/ Fluids/ Heros_Fountain/ Heros_Fountain. html), physics.kenyon.edu
References • Brown, Henry T.; "507 Mechanical Movements, Mechanisms and Devices", p. 111; 19th edition 1901. • Hiscox, Gardner D.; "1800 Mechanical Movements, Devices and Appliances", p. 162; 16th edition published 1926 under the name "Mechanical Movements, Power and Devices".
122
Heron's fountain
123
External links • R.Ya.Kezerashvili, A.Sapozhnikov. "Magic Fountain" (http://arxiv.org/abs/physics/0310039), at arxiv.org
Magdeburg hemispheres The Magdeburg hemispheres are a pair of large copper hemispheres with mating rims, used to demonstrate the power of atmospheric pressure. When the rims were sealed with grease and the air was pumped out, the sphere contained a vacuum and could not be pulled apart by teams of horses. The Magdeburg hemispheres were designed by a German scientist and mayor of Magdeburg,[1] Otto von Guericke in 1656 to demonstrate the air pump which he had invented, and the concept of atmospheric pressure. The first artificial vacuum had been produced a few years earlier by Evangelista Torricelli, and had inspired von Guericke to design the world's first vacuum pump, which Gaspar Schott's sketch of Otto von Guericke's Magdeburg consisted of a piston and cylinder with one-way flap hemispheres experiment. valves. The hemispheres became popular in physics lectures as an illustration of the power of air pressure, and are still used in education. A pair of the original hemispheres are preserved in the Deutsches Museum in Munich.
Overview The Magdeburg hemispheres, around 50 cm (20 inches) in diameter,[2][3][4][5] were designed to demonstrate the vacuum pump that von Guericke had invented. One of them had a tube connection to attach the pump, with a valve to close it off. When the air was sucked out from inside the hemispheres, and the valve was closed, the hose from the pump could be detached, and they were held firmly together by the air pressure of the surrounding atmosphere.
Original Magdeburg hemispheres and von Guericke's vacuum pump in Deutsches Museum, Munich, Germany
The force holding the hemispheres together was equal to the area bounded by the joint between the hemispheres, a circle with a diameter of 50 cm, multiplied by the difference in air pressure between the inside and the outside. It is unclear how good a vacuum von Guericke's pump was able to achieve, but if it was able to evacuate all of the air from the inside, the hemispheres would have been held together with a force of around 40 000 N (9 000 lbf, or 4½ short tons),[6] equivalent to lifting a car or small elephant; a dramatic demonstration of the pressure of the atmosphere.
Magdeburg hemispheres
124
Demonstrations Von Guericke's demonstration was performed on 8 May 1654 in front of the Reichstag and the Emperor Ferdinand III in Regensburg.[7] Thirty horses, in two teams of 15, could not separate the hemispheres until the valve was opened to equalize the air pressure. In 1656 he repeated the demonstration with 16 horses (2 teams of 8) in his hometown of Magdeburg, where he was mayor. He also took the two spheres, hung the two hemispheres with a support, and removed the air from within. He then strapped weights to the spheres, but the spheres would not budge. Gaspar Schott was the first to describe the experiment in print in his Mechanica Hydraulico-Pneumatica (1657). In 1663 (or according to some sources in 1661) the demonstration was given in Berlin before Frederick William, Elector of Brandenburg with 24 horses. The experiment became a popular way to illustrate the principles of air pressure, and many smaller copies of the hemispheres were made, and are used to this day in science classes. Re-enactments of von Guerike's 1654 experiment are performed in locations around the world by the Otto von Guericke Society. On the 18th of March 2000, a demonstration using 16 horses was conducted in Great Torrington by Barometer World.
Small 4 in. hemispheres, 1870s
The experiment has been commemorated on at least two German stamps. After learning about Guericke's pump through Schott's book, Robert Boyle worked with Robert Hooke to design and build an improved air pump. From this, through various experiments, they formulated what is called Boyle's law, which states that the volume of a body of an ideal gas is inversely proportional to its pressure. Soon the ideal gas law was formulated.
References [1] "Guericke, Otto von" (http:/ / books. google. com/ books?id=GFAEAAAAYAAJ& pg=PA670). Encyclopædia Britannica, 11th Ed.. 12. Cambridge Univ. Press. 1910. pp. 670. . [2] Hablanian, M. H.; Hemeon, C. H. (2003). "Comments about Magdeburg hemispheres reenactment" (http:/ / www2. avs. org/ historybook/ links/ magden. htm). 50 years of the AVS. American Vacuum Society. . [3] Nave, C.R. (2000). "Original Magdeburg Hemispheres" (http:/ / hyperphysics. phy-astr. gsu. edu/ Hbase/ Kinetic/ pmdg. html). Hyperphysics. Dept. of Physics and Astronomy, Georgia State Univ.. . [4] "Magdeburg hemispheres" (http:/ / brunelleschi. imss. fi. it/ museum/ esim. asp?c=500014). Multimedia Catalogue. Institute and Museum of the History of Science, Florence, Italy. 2006. . [5] Hall, Edwin H.; Bergen, Joseph Y. (1903). A Textbook of Physics, 3rd Ed. (http:/ / books. google. com/ books?id=szoAAAAAYAAJ& pg=PA52& dq=Magdeburg+ hemispheres). New York: Henry Holt & Co.. pp. 52. . [6] Calculated using a diameter of 0.5 m with atmospheric pressure; since air pushes in from both hemishperes, we have 2 * P0 * pi * r^2, where P0=air pressure; r=cross-sectional radius of a hemisphere. Due to the inefficiencies of the vacuum pump, the artificial vacuum was likely much weaker. [7] "Von Guericke, Otto" (http:/ / books. google. com/ books?id=GFAEAAAAYAAJ& pg=PA670& ). Encyclopædia Britannica, 11th Edition. 9. The Encyclopædia Britannica Co.. 1910. p. 670. .
• "The Magdeburg hemispheres" (http://www.deutsches-museum.de/sammlungen/ausgewaehlte-objekte/ meisterwerke-i/halbkugel/). Masterpieces from the Deutsches Museum. Retrieved June 27, 2005. • "The Magdeburg hemispheres" (http://www.drafthorsejournal.net/summer2004/feature.htm). The Draft Horse Journal. Retrieved October 31, 2006. published in print Summer 2004.
Magdeburg hemispheres
External links • Magdeburg Hemispheres (http://physics.kenyon.edu/EarlyApparatus/Pneumatics/Magdeburg_Hemispheres/ Magdeburg_Hemispheres.html)
Rubens' tube The Rubens' tube, also known as the standing wave flame tube, or simply flame tube, is a physics experiment demonstrating a standing wave. It shows the relationship between sound waves and sound pressure.
Overview A length of pipe is perforated along the top and sealed at both ends - one seal is attached to a small speaker or frequency generator, the other to a supply of a flammable gas (propane tank). The pipe is filled with the gas, and the gas leaking from the perforations is lit. If a suitable constant frequency is used, a standing wave can form within the tube. When the speaker is turned on, the standing wave will A Rubens' Tube setup create points with oscillating (higher and lower) pressure and points with constant pressure (pressure nodes) along the tube. Where there is oscillating pressure due to the sound waves, less gas will escape from the perforations in the tube, and the flames will be lower at those points. At the pressure nodes, the flames are higher. At the end of the tube gas molecule velocity is zero and oscillating pressure is maximal, thus low flames are observed. It is possible to determine the wavelength from the flame minima and maxima by simply measuring with a ruler.
Explanation Since the time averaged pressure is equal at all points of the tube, it is not straightforward to explain the different flame heights. The flame height is proportional to the gas flow as shown in the figure. Based on Bernoulli's principle, the gas flow is proportional to the square root of the pressure difference between the inside and outside of the tube. This is shown in the figure for a tube without standing sound wave. Based on this argument, the flame height depends non-linearly on the local, time-dependent pressure. The time average of the flow is reduced at the points with oscillating pressure and thus flames are lower.[1]
125
Rubens' tube
126
History Heinrich Rubens was a German physicist born in 1865. Though he allegedly worked with better remembered physicists such as Max Planck at the University of Berlin on some of the ground work for quantum physicists, he is best known for his flame tube, which was demonstrated in 1905. This original Rubens' Tube was a four meter section of pipe with 200 holes spaced evenly along its length. When the ends are sealed and a flammable gas is pumped into the device the building pressure will have only one route to equalize. The escaping gas can be lit to form a row of roughly even flames. Upon introduction of a loud speaker to one of the sealed ends, standing waveforms can be seen in the flames.
Flame height on a Rubens tube (without standing sound wave) for different flows of natural gas. Dashed line is linear fit.
Within the Rubens' tube, as soon as gas is ignited generally uniform flames will be seen. This is because there is very little pressure differential between any given area of the space inside the tube. Once sound is applied from one end, pressure will change within the tube. Should the sound be an easily measurable frequency, the wavelength will be visible in the series of flames, with the highest flames being where condensation is occurring and the lowest where rarefaction is occurring.
Public displays A Rubens' Tube was on display at The Exploratory in Bristol, England until it closed in 1999. A similar exhibit using polystyrene beads instead of flames featured in the At-Bristol science centre until 2009.[2]
Square root of the pressure difference between inside and outisde of Rubens tube (without standing sound wave) for different flows of natural gas. Dashed line is linear fit.
This display is also found in Physics departments at a number of Universities.[3] A number of physics shows also have one, such as: Rino Foundation Fysikshow Aarhus (Denmark), Fizika Ekspres (Croatia) and ÅA Physics show (Finland).[5][6]
[4]
(The Netherlands),
The Mythbusters also included a demonstration on their "Voice Flame Extinguisher" episode in 2007.[7] The Daily Planet's The Greatest Show Ever,[8] ran a competition whereby five Canadian Science Centres competed for the best science centre's experiment/display. Edmonton's Science Centre (Telus World of Science) utilized a Rubens' Tube. In fact, the Rubens' Tube won the competition. The special was filmed on October 10, 2010.
Rubens' tube
References [1] G.W. Ficken, F.C. Stephenson, Rubens flame-tube demonstration, The Physics Teacher, Vol. 17, pp. 306-310 (1979) (http:/ / dx. doi. org/ 10. 1119/ 1. 2340232) [2] "The Exploratory - Exhibits" (http:/ / www. exploratory. org. uk/ exhibits/ sound. htm). . Retrieved November 6, 2006. [3] "Oscillation & Waves" (http:/ / pirt. asu. edu/ detail_3. asp?ID=1462& offset=175). . Retrieved November 8, 2006. [4] "website Rino Foundation" (http:/ / www. stichtingrino. nl). . Retrieved October 29, 2009. [5] "Fizika Ekspres website" (http:/ / fizika-ekspres. hfd. hr/ web2/ index. php). . Retrieved April 20, 2009. [6] "ÅA website" (http:/ / users. abo. fi/ jlinden/ fysikshow. html). . Retrieved April 20, 2009. [7] "Discovery Channel Video" (http:/ / dsc. discovery. com/ videos/ mythbusters-rubens-tube. html). . Retrieved August 11, 2009. [8] "Daily Planet's The Greatest Show Ever" (http:/ / www. discoverychannel. ca/ greatestshowever/ ). . Retrieved October 10, 2010.
External links • Detailed Video including sound board and microphone (http://www.youtube.com/watch?v=oPWucNgN8TQ) • Experiment notes, video & detailed analysis (http://www.vuw.ac.nz/scps-demos/demos/Light_and_Waves/ SoundFlames/SoundFlames.htm) • Flame tube setup and explanation of effects (http://www.fysikbasen.dk/English.php?page=Vis&id=6) • Brief Setup Guide (http://www.physics.umd.edu/lecdem/services/demos/demosh3/h3-17.htm) • Classroom setup guide (http://www.physics.isu.edu/physdemos/waves/flamtube.htm) • Information on Rubens' original design in .doc format (http://web.archive.org/web/20040724131501/http:// www.science-on-stage.de/fileadmin/Materialien/CD_POS3/Luehrs_waterwave_englisch.doc) • Image showing setup (http://groups.physics.umn.edu/demo/old_page/demo_gifs/3D30_50.GIF) • General information (http://physicslearning.colorado.edu/website_new/Common/ViewDemonstration. asp?DemoCode=3D30.50) • Experiment setup - under "Links" heading and photo illustrating this experiment (http://pirt.asu.edu/detail_3. asp?ID=1462&offset=175) • Video various tones and music being played (http://www.richdunajewski.com/videos/YHpovwbPGEoo) • Rubens' Tube performance by Alyce Santoro (http://www.youtube.com/watch?v=cootexkMmrY)
127
Pitch drop experiment
128
Pitch drop experiment The pitch drop experiment is a long-term experiment which measures the flow of a piece of pitch over many years. Pitch is the name for any of a number of highly viscous liquids which appear solid, most commonly bitumen. At room temperature, tar pitch flows at a very slow rate, taking several years to form a single drop.
The pitch drop experiment at the University of Queensland The most famous version of the experiment was started in 1927 by Professor Thomas Parnell of the University of Queensland in Brisbane, Australia, to demonstrate to students that some substances that appear to be solid are in fact very-high-viscosity fluids. Parnell poured a heated sample of pitch into a sealed The University of Queensland pitch funnel and allowed it to settle for three years. In 1930, the seal at the neck of the drop experiment, demonstrating the funnel was cut, allowing the pitch to start flowing. Large droplets form and fall viscosity of bitumen. over the period of about a decade. The eighth drop fell on 28 November 2000, allowing experimenters to calculate that the pitch has a viscosity approximately 230 billion (2.3×1011) times that of water.[1] The ninth drop is expected to fall in 2012 or 2013. [2] This is recorded in the Guinness Book of Records as the world's longest continuously running laboratory experiment, and it is expected that there is enough pitch in the funnel to allow it to continue for at least another hundred years. This experiment is pre-dated by two other still-active scientific devices, the Oxford Electric Bell (1840) and the Beverly Clock (1864). The experiment was not originally carried out under any special controlled atmospheric conditions, meaning that the viscosity could vary throughout the year with fluctuations in temperature. Some time after the seventh drop fell in 1988, air conditioning was added to the location where the experiment resided. The temperature stability has lengthened each drop's stretch before it separates from the rest of the pitch in the funnel. In October 2005, John Mainstone and the late Thomas Parnell were awarded the Ig Nobel Prize in Physics, a parody of the Nobel Prize, for the pitch drop experiment.[3] To date, no one has ever witnessed a drop fall. The experiment is in the view of a webcam but technical problems prevented the most recent drop from being recorded.[4][5] The pitch drop experiment is on public display on Level 2 of Parnell Building in the School of Mathematics and Physics at the St Lucia campus of The University of Queensland.
The University of Queensland pitch drop experiment, featuring its current custodian, Professor John Mainstone (taken in 1990, two years after the seventh drop and 10 years before the eighth drop fell).
Pitch drop experiment
129
Timeline Date
Event
Duration (months) Duration (years)
1927 Experiment set up 1930 The stem was cut December 1938 1st drop fell
96–107
8.0–8.9
February 1947 2nd drop fell
99
8.3
April 1954 3rd drop fell
86
7.2
May 1962 4th drop fell
97
8.1
August 1970 5th drop fell
99
8.3
April 1979 6th drop fell
104
8.7
July 1988 7th drop fell
111
9.3
28 November 2000 8th drop fell
148
12.3
References [1] Edgeworth, R., Dalton, B.J. & Parnell, T.. "The Pitch Drop Experiment" (http:/ / www. physics. uq. edu. au/ physics_museum/ pitchdrop. shtml). . Retrieved 2007-10-15. [2] "Is this the most boring experiment ever? Scientists watch drops of pitch form - and there have been eight in 75 years" (http:/ / www. dailymail. co. uk/ sciencetech/ article-2142928/ Is-boring-experiment-Scientists-watch-drops-pitch-form--75-years. html). . Retrieved 2012-05-13. [3] The 2005 Ig Nobel Prize Winners (http:/ / improbable. com/ ig/ winners/ #ig2005) [4] University of Queensland page on the Pitch Drop experiment (http:/ / www. smp. uq. edu. au/ content/ pitch-drop-experiment) [5] Link to Webcam (http:/ / pitchdrop. physics. uq. edu. au:8081/ flash. html)
External links • The sixth drop shortly after falling (http://www.physics.uq.edu.au/physics_museum/pitch2.gif)
Spouting can
130
Spouting can The Spouting can experiment is a physics experiment designed to show that, according to Torricelli's law, in a liquid with an open surface, pressure increases with depth. It consists of a tube with three separate holes and an open surface. The three holes are blocked, then the tube is filled with water. When it is full, the holes are unblocked. The jets become more powerful, and travel a larger distance, the further down the tube they are.[1]
Vertical nozzles Ignoring viscosity and other losses, if the nozzles point vertically upward then each jet will reach the height of the surface of the liquid in the container.
A diagram of the spouting can experiment. The pressure increases with depth.
References [1] Spouting cylinder fluid flow (http:/ / www. 4physics. com/ phy_demo/ SpoutingCylinder/ SpoutingCylinder. html)
External links • Article on Spouting Cylinder (http://www.4physics.com/phy_demo/SpoutingCylinder/SpoutingCylinder. html)
131
Particle & Nuclear Physics Bevatron The Bevatron was a historic particle accelerator — specifically, a weak-focusing proton synchrotron — at Lawrence Berkeley National Laboratory, U.S.A., which began operating in 1954.[1] The antiproton was discovered there in 1955, resulting in the 1959 Nobel Prize in physics for Emilio Segrè and Owen Chamberlain.[2] It accelerated protons into a fixed target, and was named for its ability to impart energies of billions of eV. (Billions of eV Synchrotron.)
Antiprotons At the time the Bevatron was designed, it was strongly suspected but not known, that each particle had a corresponding anti-particle of opposite charge, identical in all other respects, a property known as charge symmetry. The anti-electron, or positron had been first observed in the early 1930s, and theoretically understood as a consequence of the Dirac equation at about the same time. Following World War II, positive and negative muons and pions were observed in cosmic-ray interactions seen in cloud chambers and stacks of nuclear photographic emulsions. The Bevatron was built to be energetic enough to create antiprotons, and thus test the hypothesis that every particle has a corresponding anti-particle.[3] The antineutron was discovered soon thereafter by Oreste Piccioni and co-workers, also at the Bevatron. Confirmation of the charge symmetry conjecture in 1955 led to the Nobel Prize for physics being awarded to Emilio Segrè and Owen Chamberlain in 1960. Shortly after the Bevatron came into use, it was recognized that parity was not conserved in the weak interactions, which led to resolution of the tau-theta puzzle, the understanding of strangeness, and the establishment of CPT symmetry as a basic feature of relativistic quantum field theories.
Requirements and design In order to create antiprotons (mass ~938 MeV/c2) in collisions with nucleons in a stationary target while conserving both energy and momentum, a proton beam energy of approximately 6.2 GeV is required. At the time it was built, there was no known way to confine a particle beam to a narrow aperture, so the beam space was about four square feet in cross section.[4] The combination of beam aperture and energy required a huge, 10,000 ton iron magnet, and a very large vacuum system. A large motor/generator system was used to ramp up the magnetic field for each cycle of acceleration. At the end of each cycle, after the beam was used or extracted, the large magnetic field energy was returned to spin up the motor, which was then used as a generator to power the next cycle, conserving energy; the entire process required about five seconds. The characteristic rising and falling, wailing, sound of the motor-generator system could be heard in the entire complex when the machine was in operation. In the years following the antiproton discovery, much pioneering work was done here using beams of protons extracted from the accelerator proper, to hit targets and generate secondary beams of elementary particles, not only protons but also neutrons, pions, "strange particles", and many others.
Bevatron
132
The liquid hydrogen bubble chamber The extracted particle beams, both the primary protons and secondaries, could in turn be passed for further study through various targets and specialized detectors, notably the liquid hydrogen bubble chamber. Many thousands of particle interactions, or "events", were photographed, measured, and studied in detail with an automated system of large measuring machines (known as "Frankensteins") allowing human operators (typically the wives of graduate students) to mark points along the particle tracks and punch their coordinates into IBM cards, using a foot pedal. The cards decks were then analyzed by early-generation computers, which reconstructed the three-dimensional tracks through the magnetic fields, and computed the momenta and energy of the particles. Computer programs, extremely complex for their time, then fitted the track data associated with a given event to estimate the energies, masses, and identities of the particles produced. This period, when hundreds of new particles and excited states were suddenly revealed, marked the beginning of a new era in elementary particle physics. Luis Alvarez inspired and directed much of this work, for which he received the Nobel Prize in physics in 1968.
First tracks observed in liquid hydrogen bubble chamber at the Bevatron
BEVALAC The Bevatron received a new lease on life in 1971,[5] when it was joined to the SuperHILAC linear accelerator as an injector for heavy ions.[6] The combination was conceived by Albert Ghiorso, who named it the Bevalac.[7] It could accelerate any nuclei in the periodic table to relativistic energies. It was finally decommissioned in 1993.
End of life The next generation of accelerators used "strong focusing", and required much smaller apertures, and thus much cheaper magnets. The CERN PS (Proton Synchrotron, 1959) and the Brookhaven National Laboratory AGS (Alternating Gradient Synchrotron, 1960) were the first next-generation machines, with an aperture roughly an order of magnitude less in both transverse directions, and reaching 30 GeV proton energy, yet with a less massive magnet ring. For comparison, the circulating beams in the Large Hadron Collider, with ~11,000 times higher energy and enormously higher intensity than the Bevatron, are confined to a space on the order of 1 mm in cross-section, and focused down to 16 micrometres at the intersection collision regions, while the field of the bending magnets is only about five times higher. The demolition of the Bevatron began in 2009 by Clauss Construction of Lakeside CA and is scheduled for completion in 2011.
Bevatron
References [1] UC Radiation Lab Document UCRL-3369, "Experiences with the BEVATRON", E.J. Lofgren, 1956. (http:/ / www. osti. gov/ bridge/ purl. cover. jsp;jsessionid=6048B75D377848FD253FA58CEF6EA860?purl=/ 877349-HaNM39/ ) [2] The History of Antimatter (http:/ / livefromcern. web. cern. ch/ livefromcern/ antimatter/ history/ AM-history01-b. html) [3] Segrè Nobel Lecture, 1960 (http:/ / nobelprize. org/ nobel_prizes/ physics/ laureates/ 1959/ segre-lecture. pdf) [4] E.J. Lofgren, 2005 (http:/ / inpa. lbl. gov/ pbar/ talks/ F2_Lofgren. pdf) [5] Bevalac Had 40-Year Record of Historic Discoveries Goldhaber, J. (1992) Berkeley Lab Archive (http:/ / www. lbl. gov/ Science-Articles/ Archive/ Bevalac-nine-lives. html) [6] Stock, Reinhard (2004). "Relativistic nucleus–nucleus collisions: from the BEVALAC to RHIC". Journal of Physics G: Nuclear and Particle Physics 30 (8): S633–S648. arXiv:nucl-ex/0405007. Bibcode 2004JPhG...30S.633S. doi:10.1088/0954-3899/30/8/001. [7] LBL 3835, "Accelerator Division Annual Report", E.J.Lofgren, October 6, 1975 (http:/ / www. osti. gov/ bridge/ product. biblio. jsp?osti_id=937059)
External links • History of the Bevatron (http://www.lbl.gov/Science-Articles/Research-Review/Magazine/1981/81fchp6. html) • "The Bevatron" E.J. Lofgren historical retrospective account; excellent early pictures. (http://inpa.lbl.gov/pbar/ talks/F2_Lofgren.pdf) • Pictures of the Bevatron (http://www.acme.com/jef/photos/bevatron.html) • Shutdown of the Bevatron (http://www.lbl.gov/Science-Articles/Archive/Bevalac-shutdown.html) • Bevatron Building Slated for Demolition (http://www.dailycal.org/article/101423) • Historic Atom Smasher Reduced to Rubble and Revelry (http://www.wired.com/wiredscience/2009/07/ bevatron/)
133
Chicago Pile-1
134
Chicago Pile-1 Site of the First Self Sustaining Nuclear Reaction U.S. National Register of Historic Places U.S. National Historic Landmark Chicago Landmark
Drawing of the reactor
Location:
Chicago, Cook County, Illinois, USA
Coordinates:
41°47′32″N 87°36′3″W
Built:
1942
Governing body:
Regenstein Library
NRHP Reference#:
66000314
[1]
[2]
Significant dates [2]
Added to NRHP:
October 15, 1966 66000314
Designated NHL:
February 18, 1965
Designated CL:
October 27, 1971
[1]
[3]
Chicago Pile-1 (CP-1) was the world's first man-made nuclear reactor.[4][5][6] CP-1 was built on a rackets court, under the abandoned west stands of the original Alonzo Stagg Field stadium, at the University of Chicago. The first self-sustaining nuclear chain reaction was initiated in CP-1 on December 2, 1942. The site was designated a National Historic Landmark in 1965 and was added to the newly created National Register of Historic Places a little over a year later. The site was named a Chicago Landmark in 1971. It is one of the four Chicago Registered Historic Places from the original October 15, 1966, National Register of Historic Places list with the name Site of First Self-Sustaining Nuclear Reaction.[2]
Chicago Pile-1
135
Reactor The reactor was a pile of uranium and graphite blocks, assembled under the supervision of the renowned physicist Enrico Fermi, in collaboration with Leó Szilárd, discoverer of the chain reaction. It contained a critical mass of fissile material, together with control rods, and was built as a part of the Manhattan Project by the University of Chicago Metallurgical Laboratory. The shape of the pile was intended to be roughly spherical, but as work proceeded Fermi calculated that critical mass could be achieved without finishing the entire pile as planned.[7] A labor strike prevented construction of the pile at the Argonne National Laboratory, so Fermi and his associates Martin Whittaker and Henry Moore's Nuclear Energy Walter Zinn set about building the pile (the term "nuclear reactor" was not used until 1952) in a rackets court under the abandoned west stands of the university's Stagg Field.[8] The pile consisted of uranium pellets as a neutron-producing "core", separated from one another by graphite blocks to slow the neutrons. Fermi himself described the apparatus as "a crude pile of black bricks and wooden timbers." The controls consisted of cadmium-coated rods that absorbed neutrons. Withdrawing the rods would increase neutron activity in the pile, leading to a self-sustaining chain reaction. Re-inserting the rods would dampen the reaction.
First nuclear reaction On December 2, 1942, CP-1 was ready for a demonstration. Before a group of dignitaries, a young scientist named George Weil worked the final control rod while Fermi carefully monitored the neutron activity. The pile reached "criticality" or a self-sustaining reaction at 15:25. Fermi shut it down 28 minutes later. After the first self-sustained nuclear chain reaction was achieved, a coded phone call was made by one of the physicists, Arthur Compton, to James Conant, chairman of the National Defense Research Committee. The conversation was in impromptu code:
“
Compton: The Italian navigator has landed in the New World. Conant: How were the natives? [9] Compton: Very friendly.
”
Unlike most reactors that have been built since, this first one had no radiation shielding and no cooling system of any kind. Fermi had convinced Arthur Compton that his calculations were reliable enough to rule out a runaway chain reaction or an explosion, but, as the official historians of the Atomic Energy Commission later noted, the "gamble" remained in conducting "a possibly catastrophic experiment in one of the most densely populated areas of the nation!"[10] Operation of CP-1 was terminated in February 1943. The reactor was then dismantled and moved to Red Gate Woods, the future site of Argonne National Laboratory, where it was reconstructed using the original materials, plus an enlarged radiation shield, and renamed Chicago Pile-2 (CP-2). CP-2 began operation in March 1943 and was later buried at the same site, now known as the Site A/Plot M Disposal Site.[7]
Chicago Pile-1
Significance and commemoration The site of the first man-made self-sustaining nuclear fission reaction received designation as a National Historic Landmark on February 18, 1965.[1] On October 15, 1966, which is the day that the National Historic Preservation Act of 1966 was enacted creating the National Register of Historic Places, it was added to that as well.[2] The site was named a Chicago Landmark on October 27, 1971.[3] A small graphite block from the pile is on display at the Museum of Science and Industry in Chicago; another can be seen at the Bradbury Science Museum in Los Alamos, NM. The old Stagg Field plot of land is currently home to the Regenstein Library at the University of Chicago. A Henry Moore sculpture, Nuclear Energy, in a small quadrangle commemorates the nuclear experiment.[1]
Notes [1] "Site of the First Self-Sustaining Nuclear Reaction" (http:/ / tps. cr. nps. gov/ nhl/ detail. cfm?ResourceId=204& ResourceType=Site). National Historic Landmark summary listing. National Park Service. . Retrieved 2008-06-11. [2] "National Register Information System" (http:/ / nrhp. focus. nps. gov/ natreg/ docs/ All_Data. html). National Register of Historic Places. National Park Service. 2010-07-09. . [3] "Site of the First Self-Sustaining Controlled Nuclear Chain Reaction" (http:/ / www. cityofchicago. org/ Landmarks/ S/ SiteNuclear. html). City of Chicago Department of Planning and Development, Landmarks Division. 2003. . Retrieved March 31, 2007. [4] Chicago Pile 1 (http:/ / www. ne. anl. gov/ About/ reactors/ early-reactors. shtml), Argonne National Laboratory [5] Atoms Forge a Scientific Revolution (http:/ / www. ne. anl. gov/ About/ legacy/ probo. shtml), Argonne National Laboratory [6] Natural nuclear reactors existed approx. 1.5 billion years ago in Oklo, Africa. [7] Fermi E (1946). "The Development of the first chain reaction pile". Proceedings of the American Philosophical Society 90: 20–24. (http:/ / www. jstor. org/ stable/ 3301034). [8] Zug, James (2003). Squash, A History of the Game. Scribner. pp. 135–136. ISBN 978-0-7432-2990-6. The space is commonly misidentified as having been a squash court. [9] "" (http:/ / www. ne. anl. gov/ About/ legacy/ italnav. shtml). Argonne National Laboratory. November 18, 1942. . [10] "CP-1 GOES CRITICAL Met Lab (December 2, 1942) Events: The Plutonium Path to the Bomb, 1942-1944" (http:/ / web. archive. org/ web/ 20101122183641/ http:/ / www. cfo. doe. gov/ me70/ manhattan/ cp-1_critical. htm). The Manhattan Project An Interactive History. US Dept of Energy. . Retrieved 2012-04-12.
External links • CP-1 Goes Critical (http://web.archive.org/web/20101122183641/http://www.cfo.doe.gov/me70/ manhattan/cp-1_critical.htm) Describes in detail the construction and activation of CP-1. US Department of Energy, Office of History and Heritage Resources. • Photos of CP-1 (http://fermi.lib.uchicago.edu/fermiimages.htm) The University of Chicago Library Archive. Includes photos and sketches of CP-1. • Video Showing the Met Lab, Fermi, and an active experiment using CP-1 (http://www.criticalpast.com/video/ 65675046545_uranium-fission_Institute-of-Study-of-Metal_Enrico-Fermi_lights-indicates-radioactivity) • The First Pile (http://www.atomicarchive.com/History/firstpile/index.shtml) 11 page story about CP-1
136
CowanReines neutrino experiment
Cowan–Reines neutrino experiment The neutrino experiment, also called the Cowan and Reines neutrino experiment, was performed by Clyde L. Cowan and Frederick Reines in 1956. This experiment confirmed the existence of the antineutrino—a neutrally charged subatomic particle with very low mass.
History In the 1930s, through the study of beta decay, it was apparent that a third particle, one of nearly no mass and with neutral charge existed and was not observed. This was due to a continuous spread of kinetic energy and momentum values for electrons emitted in beta decay. The only way this was possible was if there was a particle of neutral charge and almost no mass (or possibly no mass) produced in the decay.
Potential for experiment In beta decay the predicted particle, the electron antineutrino (νe), should interact with a proton (p) to produce a neutron (n) and positron (e+) – the antimatter counterpart of the electron. νe + p → n + e+ The positron quickly finds an electron, and they annihilate each other. The two resulting gamma rays (γ) are detectable. The neutron can be detected by its capture on an appropriate nucleus, releasing a gamma ray. The coincidence of both events - positron annihilation and neutron capture - gives a unique signature of an antineutrino interaction. Most hydrogen atoms bound in water molecules have a single proton for a nucleus. Those protons serve as a target for the antineutrinos from a reactor. For heavier nuclei, with several protons and neutrons, the interaction mechanism is more complicated and is not always well described by considering the constituent protons as free.
Setup Cowan and Reines used a nuclear reactor, as advised by Los Alamos physics division leader J.M.B. Kellogg,[1] as a source of a neutrino flux of 5 × 1013 neutrinos per second per square centimeter;[2] far higher than any attainable flux from other radioactive sources. The neutrinos then interacted (as shown above) with protons in a tank of water, creating neutrons and positrons. Each positron created a pair of gamma rays when it annihilated with an electron. The gamma rays were detected by placing a scintillator material in a tank of water. The scintillator material gives off flashes of light in response to the gamma rays and the light flashes are detected by photomultiplier tubes. This experiment was not conclusive enough, so they devised a second layer of certainty. They detected the neutrons by placing cadmium chloride in the tank. Cadmium is a highly effective neutron absorber and gives off a gamma ray when it absorbs a neutron. n + 108Cd → 109mCd → 109Cd + γ The arrangement was such that the gamma ray from the cadmium would be detected 5 microseconds after the gamma ray from the positron, if it were truly produced by a neutrino.
137
CowanReines neutrino experiment
Results They performed the experiment preliminarily at Hanford Site, but later moved the experiment to the Savannah River Plant in South Carolina near Aiken where they had better shielding against cosmic rays. This shielded location was 11 m from the reactor and 12 m underground. They used two tanks with a total of about 200 liters of water with about 40 kg of dissolved CdCl2. The water tanks were sandwiched between three scintillator layers which contained 110 five-inch (127 mm) photomultiplier tubes. After months of data collection, they had accumulated data on about three neutrinos per hour in their detector. To be absolutely sure that they were seeing neutrino events from the detection scheme described above, they shut down the reactor to show that there was a difference in the number of detected events. They had predicted a cross-section for the reaction to be about 6 × 10−44 cm2 and their measured cross-section was 6.3 × 10−44 cm2. Their results were published in the July 20, 1956 issue of Science.[3][4] Clyde Cowan died in 1974; Frederick Reines was honored with the Nobel Prize in 1995 for his work on neutrino physics.[5]
References [1] "The Reines-Cowan Experiments: Detecting the Poltergeist" (http:/ / library. lanl. gov/ cgi-bin/ getfile?25-02. pdf). Los Alamos Science 25: 3. 1997. . [2] Griffiths, David J. (1987). Introduction to Elementary Particles. John Wiley & Sons. ISBN 0-471-60386-4. [3] C. L Cowan Jr., F. Reines, F. B. Harrison, H. W. Kruse, A. D McGuire (July 20, 1956). "Detection of the Free Neutrino: a Confirmation". Science 124 (3212): 103–4. Bibcode 1956Sci...124..103C. doi:10.1126/science.124.3212.103. PMID 17796274. [4] Winter, Klaus (2000). Neutrino physics (http:/ / books. google. com/ books?id=v_tiL2NlfvMC& pg=PA38). Cambridge University Press. p. 38ff. ISBN 978-0-521-65003-8. . This source reproduces the 1956 paper. [5] "The Nobel Prize in Physics 1995" (http:/ / nobelprize. org/ nobel_prizes/ physics/ laureates/ 1995/ ). The Nobel Foundation. . Retrieved 201-06-29.
Further reading • • • •
Cowan and Reines Neutrino Experiment (http://hyperphysics.phy-astr.gsu.edu/hbase/particles/cowan.html) Decay of the Neutron (http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html#c4) Beta Decay (http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/beta.html#c2) Electron Neutrinos and Antineutrinos (http://hyperphysics.phy-astr.gsu.edu/hbase/particles/neutrino. html#c1) • Subatomic particles • Cowan & Reines Experiments: Poltergeist, Hanford, Savannah River (http://library.lanl.gov/cgi-bin/ getfile?00326606.pdf)
138
GeigerMarsden experiment
Geiger–Marsden experiment The Geiger–Marsden experiment (also called the Gold foil experiment or the Rutherford experiment) was an experiment to probe the structure of the atom performed by Hans Geiger and Ernest Marsden in 1909,[1] under the direction of Ernest Rutherford at the Physical Laboratories of the University of Manchester. The unexpected results of the experiment demonstrated for the first time the existence of the atomic nucleus, leading to the downfall of the plum pudding model of the atom, and the development of the Rutherford (or planetary) model.
Background The popular theory of atomic structure at the time of Rutherford's experiment was the "plum pudding model". This model was developed in 1904 by J. J. Thomson, the scientist who discovered the electron. This theory held that the negatively charged electrons in an atom were floating (sometimes moving) in a sea of positive charge—the electrons being akin to plums in a bowl of pudding. The plum pudding model was the prevailing theory on the structure of the atom until it was disproved by Ernest Rutherford in his analysis of the gold foil experiment, published in 1911. The gold foil experiment was conducted under the supervision of Rutherford at the University of Manchester in 1909 by scientist Hans Geiger and undergraduate student Ernest Marsden. Rutherford, chair of the Manchester physics department at the time of the experiment, is given primary credit for the experiment, as the theories that resulted are primarily his work. Rutherford's gold foil experiment is also sometimes referred to as the Geiger-Marsden experiment.
139
GeigerMarsden experiment
140
Experimental procedure and results The gold foil experiment consisted of a series of tests in which positively charged alpha particles (helium nuclei) were fired at a very thin sheet of gold foil. If Thomson's Plum Pudding model was to be accurate, the big alpha particles should have passed through the gold foil with only a few minor deflections. This is because the alpha particles are heavy and the charge in the "plum pudding model" is widely spread. However, the actual results surprised Rutherford. Although many of the alpha particles did pass through as expected, many others were deflected at large angles while others were reflected back to the alpha source. In detail, a beam of alpha particles, generated by the radioactive decay of radon, was directed normally onto a sheet of very thin gold foil in an evacuated chamber. A zinc sulfide screen at the focus of a microscope was used as a detector; the screen and microscope could be swivelled around the foil to observe particles deflected at any given angle. Under the prevailing plum pudding model, the alpha particles should all have been deflected by, at most, a few degrees; measuring the pattern of scattered particles was expected to provide information about the distribution of charge within the atom. However they observed that a very small percentage of particles were deflected through angles much larger than 90 degrees. According to Rutherford:
Top: Expected results: alpha particles passing through the plum pudding model of the atom undisturbed. Bottom: Observed results: a small portion of the particles were deflected, indicating a small, concentrated positive charge. Note that the image is not to scale; in reality the nucleus is vastly smaller than the electron shell.
It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backward must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive center, carrying a charge.[2] —Ernest Rutherford
Conclusions The data generated from the gold foil experiment demonstrated that the plum pudding model of the atom was incorrect. The fact that many of the alpha particles were deflected or reflected meant that the atom had a concentrated center of positive charge and of relatively large mass. The alpha particles had either hit the positive center directly or passed by it close enough to be affected by its positive charge. Since many other particles passed through the gold foil, the positive center would have to be a relatively small size compared to the rest of the atom meaning that the atom is mostly open space. Because the majority of the positive particles continued on their original path unmoved, Rutherford was forced to conclude that most of the remainder of the atom was a region of very low density. A great deal of charge was also associated with the central region of high density. Rutherford hypothesized that these two properties resided in the same physical structure and termed his discovery "the central charge", a region later named the nucleus. Thus the current view of the nuclear atom - a structure with a positively charged center (nucleus) of high density and negatively charged electron particles moving around the nucleus at relatively large distances compared to the nuclear
GeigerMarsden experiment radius - was created. Rutherford interpreted the experimental results in a famous 1911 paper.[3] He was able to definitively reject J.J. Thomson's plum pudding model of the atom, since none of Thomson's negative "corpuscles" (i.e. electrons) contained enough charge or mass to deflect alphas strongly, nor did the diffuse positive "pudding" or cloudlike positive charge, in which the electrons were embedded in the plum pudding model. Instead, Rutherford suggested that a large amount of the atom's charge and mass is instead concentrated into a very physically small (as compared with the size of the atom) region, giving it a very high electric field. Outside of this "central charge" (later termed the nucleus), he proposed that the atom was mostly empty space. Rutherford was able to say from the experiment that the nuclear charge was positive and used the following language for pictorial purposes: "For concreteness, consider the passage of a high speed Alpha particle through an atom having a positive central charge Ne, and surrounded by a compensating charge of N electrons." From energetic considerations of how far alpha particles of known mass and kinetic energy would be able to penetrate toward a central charge of 100 e (expected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operatorexpected operator×10−17 C), Rutherford was able to calculate that the radius of his gold central charge would need to be physically smaller (how much smaller, could not be told) than 3.4 × 10−14 metres (the modern value for the actual radius is only about a fifth of this). The figure applied in a gold atom which was itself known to be much larger: 1.5 × 10−10 metres or so in radius – a very surprising finding, as it implied a strong central charge less than 1⁄4000 of the diameter of the atom. Rutherford had used strictly Newtonian methods to analyze the relatively low-energy alpha-scattering of this experiment. Later, when full quantum mechanical methods were available, it was found that they gave the same scattering equation which had been derived by Rutherford by classical means. Although Rutherford's model of the atom itself had a number of problems with electron charge placement and motion, which were only resolved following the development of quantum mechanics, the central conclusion from the Geiger–Marsden experiment, the existence of the nucleus, still holds. Rutherford's description of the atom set the foundation for all future atomic models and the development of nuclear physics. Rutherford's model was later refined by physicist Niels Bohr in 1913. Bohr's model of the atom is the basic atomic model used today.
References [1] Geiger H. & Marsden E. (1909). "On a Diffuse Reflection of the α-Particles" (http:/ / www. chemteam. info/ Chem-History/ GM-1909. html). Proceedings of the Royal Society, Series A 82: 495–500. Bibcode 1909RSPSA..82..495G. doi:10.1098/rspa.1909.0054. . [2] David C. Cassidy, Gerald James Holton, Gerald Holton, Floyd James Rutherford, (2002) Understanding Physics Harvard Project Physics Published by Birkhäuser, p. 632 ISBN 0-387-98756-8, ISBN 978-0-387-98756-9 [3] Rutherford E. (1911). "The Scattering of α and β Particles by Matter and the Structure of the Atom" (http:/ / www. chemteam. info/ Chem-History/ Rutherford-1911/ Rutherford-1911. html). Philosophical Magazine, Series 6 21: 669–688. doi:10.1080/14786440508637080. .
External links • Images of Rutherford's 1911 paper (http://www.math.ubc.ca/~cass/rutherford/rutherford.html) • Description of the experiment, from the New Mexico Institute of Mining and Technology (http://www.physics. nmt.edu/~raymond/classes/ph13xbook/node193.html) • Description of the experiment, from cambridgephysics.org (http://www-outreach.phy.cam.ac.uk/camphy/ nucleus/nucleus4_1.htm)
141
Homestake experiment
Homestake experiment The Homestake experiment (sometimes referred to as the Davis experiment) was an experiment headed by astrophysicists Raymond Davis, Jr. and John N. Bahcall in the late 1960s. Its purpose was to collect and count neutrinos emitted by nuclear fusion taking place in the Sun. Bahcall did the theoretical calculations and Davis designed the experiment. After Bahcall calculated the rate at which the detector should capture neutrinos, Davis's experiment turned up only one third of this figure. The experiment was the first to successfully detect and count solar neutrinos, and the discrepancy in results essentially created the solar neutrino problem. The experiment operated continuously from 1970 until 1994. The University of Pennsylvania took it over in 1984. The discrepancy between the predicted and measured rates of neutrino detection was later found to be due to neutrino "flavor" oscillations.
Methodology The experiment took place in the Homestake Gold Mine in Lead, South Dakota. Davis placed 1,478 meter (4,850 feet) underground a 380 cubic meter (100,000 gallon) tank of perchloroethylene, a common dry-cleaning fluid. A big target deep underground was needed to account for the very small probability of a successful neutrino capture, and to prevent interference from other forms of solar radiation. Perchloroethylene was chosen because it is rich in chlorine. Upon collision with a neutrino, a chlorine atom transforms into a radioactive isotope of argon, which can then be extracted and counted. Every few weeks, Davis bubbled helium through the tank to collect the argon that had formed, and was able to determine how many neutrinos had been captured.[1][2]
Conclusions Davis's figures were consistently very close to one-third of Bahcall's calculations. The first response from the scientific community was that either Bahcall or Davis had made a mistake. Bahcall's calculations were checked repeatedly, with no errors found. Davis scrutinized his own experiment and insisted there was nothing wrong with it. The Homestake experiment was followed by other experiments with the same purpose, such as Kamiokande in Japan, SAGE in the former Soviet Union, GALLEX in Italy, Super Kamiokande, also in Japan, and SNO (Sudbury Neutrino Observatory) in Ontario, Canada. SNO was the first detector able to detect neutrino oscillation, solving the solar neutrino problem. The results of the experiment, published in 2001, revealed that of the three "flavors" between which neutrinos are able to oscillate, Davis' detector was sensitive to only one. After it had been proven that his experiment was sound, Davis shared the 2002 Nobel Prize in Physics. Among those sharing the prize was Masatoshi Koshiba of Japan, who worked on the Kamiokande and the Super Kamiokande.
References [1] Martin, B.R.; & Shaw, G (1999). Particle Physics (2nd ed.). Wiley. p. 265. ISBN 0-471-97285-1. [2] B. T. Cleveland et al (1998). "Measurement of the Solar Electron Neutrino Flux with the Homestake Chlorine Detector". Astrophysical Journal 496: 505–526. Bibcode 1998ApJ...496..505C. doi:10.1086/305343.
• Raymond Davis Jr.'s Solar Neutrino Experiments (at BNL.gov) (http://www.bnl.gov/bnlweb/raydavis/ research.htm)
142
Large Hadron Collider
143
Large Hadron Collider Large Hadron Collider (LHC)
LHC experiments ATLAS
A Toroidal LHC Apparatus
CMS
Compact Muon Solenoid
LHCb
LHC-beauty
ALICE
A Large Ion Collider Experiment
TOTEM
Total Cross Section, Elastic Scattering and Diffraction Dissociation
LHCf
LHC-forward
MoEDAL
Monopole and Exotics Detector At the LHC LHC preaccelerators
p and Pb
Linear accelerators for protons (Linac 2) and Lead (Linac 3)
(not marked) Proton Synchrotron Booster PS
Proton Synchrotron
SPS
Super Proton Synchrotron
Hadron colliders Intersecting Storage Rings
CERN, 1971–1984
Super Proton Synchrotron
CERN, 1981–1984
ISABELLE
BNL, cancelled in 1983
Tevatron
Fermilab, 1987–2011
Relativistic Heavy Ion Collider
BNL, 2000–present
Superconducting Super Collider Cancelled in 1993 Large Hadron Collider
CERN, 2009–present
Super Large Hadron Collider
Proposed, CERN, 2019–
Very Large Hadron Collider
Theoretical
The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the European Organization for Nuclear Research (CERN) from 1998 to 2008, with the aim of allowing physicists to test the predictions of different theories of particle physics and high-energy physics, and particularly for the existence of the hypothesized Higgs boson[1] and of the large family of new particles predicted by supersymmetry.[2] The LHC is
Large Hadron Collider
144
expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature. It contains six detectors each designed for specific kinds of exploration. The LHC lies in a tunnel 27 kilometres (unknown operator: u'strong' mi) in circumference, as deep as 175 metres (unknown operator: u'strong' ft) beneath the Franco-Swiss border near Geneva, Switzerland. Its synchrotron is designed to collide opposing particle beams of either protons at up to 7 teraelectronvolts (7 TeV or 1.12 microjoules) per nucleon, or lead nuclei at an energy of 574 TeV (92.0 µJ) per nucleus (2.76 TeV per nucleon-pair).[3][4] It was built in collaboration with over 10,000 scientists and engineers from over 100 countries, as well as hundreds of universities and laboratories.[5] On 10 September 2008, the proton beams were successfully circulated in the main ring of the LHC for the first time,[6] but 9 days later operations were halted due to a magnet quench incident resulting from an electrical fault. The following helium gas explosion damaged over 50 superconducting magnets and their mountings, and contaminated the vacuum pipe.[7][8] On 20 November 2009 they were successfully circulated again,[9] with the first recorded proton–proton collisions occurring 3 days later at the injection energy of 450 GeV per beam.[10] On 30 March 2010, the first collisions took place between two 3.5 TeV beams, setting the current world record for the highest-energy man-made particle collisions,[11] and the LHC began its planned research program. The LHC will operate at 4 TeV per beam until the end of 2012, 0.5 TeV higher than 2010 and 2011. It will then go into shutdown for 20 months for upgrades to allow full energy operation (7 TeV per beam), with reopening planned for late 2014.[12]
Etymology The term hadron refers to composite particles composed of quarks held together by the strong force (as atoms and molecules are held together by the electromagnetic force). The best-known hadrons are protons and neutrons; hadrons also include mesons such as the pion and kaon, which were discovered during cosmic ray experiments in the late 1940s and early 1950s. A collider is a type of a particle accelerator involving directed beams of elementary particles. In particle physics colliders are used as a research tool, by accelerating particles to very high kinetic energy and letting them impact other particles. Analysis of the byproducts of these collisions gives scientists good evidence of the structure of the subatomic world and the laws of nature governing it. These may become apparent only at high energies and for tiny periods of time, and therefore may be hard or impossible to study in other ways.
Purpose Physicists hope that the LHC will help answer some of the fundamental open questions in physics, concerning the basic laws governing the interactions and forces among the elementary objects, the deep structure of space and time, and in particular the intersection of quantum mechanics and general relativity, where current theories and knowledge are unclear or break down altogether. Data is also needed from high energy particle experiments to indicate which versions of scientific models are more likely to be correct – in particular to choose between the Standard Model and Higgsless models and to validate their predictions and allow further theoretical development. Many theorists expect new physics beyond the Standard Model to emerge at the TeV-scale, based on unsatisfactory properties of the Standard Model. Issues possibly to be explored by LHC collisions include:[13]
A simulated event in the CMS detector, featuring the appearance of the Higgs boson
Large Hadron Collider
145
• Is the Higgs mechanism for generating elementary particle masses via electroweak symmetry breaking actually realised in nature?[14] It is expected that the collider will either demonstrate or rule out the existence of the elusive Higgs boson, thereby allowing physicists to determine whether the Standard Model or its Higgsless model alternatives are more likely to be correct.[15][16][17] • Is supersymmetry, an extension of the Standard Model and Poincaré symmetry, realised in nature, implying that all known particles have supersymmetric partners?[18][19][20] • Are there extra dimensions,[21] as predicted by various models based on string theory, and can we detect them?[22] • What is the nature of the dark matter that appears to account for 23% of the mass-energy of the universe? Other open questions that may be explored using high energy particle collisions: • It is already known that electromagnetism and the weak nuclear force are just different manifestations of a single force called the electroweak force. The LHC may clarify whether the electroweak force and the strong nuclear force are similarly just different manifestations of one universal unified force, as predicted by various Grand Unification Theories. • Why is the fourth fundamental force (gravity) so many orders of magnitude weaker than the other three fundamental forces? See also Hierarchy problem. • Are there additional sources of quark flavour mixing, beyond those already predicted within the Standard Model? • Why are there apparent violations of the symmetry between matter and antimatter? See also CP violation. • What are the nature and properties of quark-gluon plasma, believed to have existed in the early universe and in certain compact and strange astronomical objects today? This will be investigated by heavy ion collisions in ALICE.
Design The LHC is the world's largest and highest-energy particle accelerator.[3][23] The collider is contained in a circular tunnel, with a circumference of 27 kilometres (unknown operator: u'strong' mi), at a depth ranging from 50 to 175 metres (unknown operator: u'strong' to unknown operator: u'strong' ft) underground.
A Feynman diagram of one way the Higgs boson may be produced at the LHC. Here, two quarks each emit a W or Z boson, which combine to make a neutral Higgs.
The 3.8-metre (unknown operator: u'strong' ft) wide concrete-lined tunnel, constructed between 1983 and 1988, was formerly used to house the Large Electron–Positron Collider.[24] It crosses the border between Switzerland and France at four points, with most of it in France. Surface buildings hold ancillary equipment such as compressors, ventilation equipment, control electronics and refrigeration plants.
The collider tunnel contains two adjacent parallel beamlines (or beam pipes) that intersect at four points, each containing a proton beam, which travel in opposite directions around the ring. Some 1,232 dipole magnets keep the beams on their circular path, while an additional 392 quadrupole magnets are used to keep the beams focused, in order to maximize the chances of interaction between the particles in the four intersection points, where the two beams will cross. In total, over 1,600
Large Hadron Collider
146
superconducting magnets are installed, with most weighing over 27 tonnes. Approximately 96 tonnes of liquid helium is needed to keep the magnets, made of copper-clad niobium-titanium, at their operating temperature of 1.9 K (−unknown operator: u'strong' °C), making the LHC the largest cryogenic facility in the world at liquid helium temperature.
Map of the Large Hadron Collider at CERN
When running at full design power of 7 TeV per beam, once or twice a day, as the protons are accelerated from 450 GeV to 7 TeV, the field of the superconducting dipole magnets will be increased from 0.54 to 8.3 teslas (T). The protons will each have an energy of 7 TeV, giving a total collision energy of 14 TeV. At this energy the protons have a Lorentz factor of about 7,500 and move at about 0.999999991 c, or about 3 metres per second slower than the speed of light (c).[25] It will take less than 90 microseconds (μs) for a proton to travel once around the main ring – a speed of about 11,000 revolutions per second. Rather Superconducting quadrupole electromagnets are than continuous beams, the protons will be bunched together, into used to direct the beams to four intersection 2,808 bunches, so that interactions between the two beams will take points, where interactions between accelerated place at discrete intervals never shorter than 25 nanoseconds (ns) apart. protons will take place. However it will be operated with fewer bunches when it is first commissioned, giving it a bunch crossing interval of 75 ns.[26] The design luminosity of the LHC is 1034 cm−2s−1, providing a bunch collision rate of 40 MHz.[27] Prior to being injected into the main accelerator, the particles are prepared by a series of systems that successively increase their energy. The first system is the linear particle accelerator LINAC 2 generating 50-MeV protons, which feeds the Proton Synchrotron Booster (PSB). There the protons are accelerated to 1.4 GeV and injected into the Proton Synchrotron (PS), where they are accelerated to 26 GeV. Finally the Super Proton Synchrotron (SPS) is used to further increase their energy to 450 GeV before they are at last injected (over a period of 20 minutes) into the main ring. Here the proton bunches are accumulated, accelerated (over a period of 20 minutes) to their peak 7-TeV energy, and finally circulated for 10 to 24 hours while collisions occur at the four intersection points.[28]
Large Hadron Collider
147
The LHC physics program is mainly based on proton–proton collisions. However, shorter running periods, typically one month per year, with heavy-ion collisions are included in the program. While lighter ions are considered as well, the baseline scheme deals with lead ions[29] (see A Large Ion Collider Experiment). The lead ions will be first accelerated by the linear accelerator LINAC 3, and the Low-Energy Ion Ring (LEIR) will be used as an ion storage and cooler unit. The ions will then be further accelerated by the PS and SPS before being injected into LHC ring, where they will reach an energy of 2.76 TeV per nucleon (or 575 TeV per ion), higher than the energies reached by the Relativistic Heavy Ion Collider. The aim of the heavy-ion program is to investigate quark–gluon plasma, which existed in the early universe. CMS detector for LHC
Detectors Six detectors have been constructed at the LHC, located underground in large caverns excavated at the LHC's intersection points. Two of them, the ATLAS experiment and the Compact Muon Solenoid (CMS), are large, general purpose particle detectors.[23] A Large Ion Collider Experiment (ALICE) and LHCb, have more specific roles and the last two, TOTEM and LHCf, are very much smaller and are for very specialized research. The BBC's summary of the main detectors is:[30] Detector
Description
ATLAS
One of two general purpose detectors. ATLAS will be used to look for signs of new physics, including the origins of mass and extra dimensions.
CMS
The other general purpose detector will, like ATLAS, hunt for the Higgs boson and look for clues to the nature of dark matter.
ALICE
ALICE is studying a "fluid" form of matter called quark–gluon plasma that existed shortly after the Big Bang.
LHCb
Equal amounts of matter and antimatter were created in the Big Bang. LHCb will try to investigate what happened to the "missing" antimatter.
Operational history Inaugural tests The first beam was circulated through the collider on the morning of 10 September 2008.[30] CERN successfully fired the protons around the tunnel in stages, three kilometres at a time. The particles were fired in a clockwise direction into the accelerator and successfully steered around it at 10:28 local time.[31] The LHC successfully completed its major test: after a series of trial runs, two white dots flashed on a computer screen showing the protons travelled the full length of the collider. It took less than one hour to guide the stream of particles around its inaugural circuit.[32] CERN next successfully sent a beam of protons in a counterclockwise direction, taking slightly longer at one and a half hours due to a problem with the cryogenics, with the full circuit being completed at 14:59.
2008 quench incident On 19 September 2008, a magnet quench occurred in about 100 bending magnets in sectors 3 and 4, causing a loss of approximately six tonnes of liquid helium, which was vented into the tunnel, and a temperature rise of about 100 degrees celsius in some of the affected magnets. Vacuum conditions in the beam pipe were also lost, and mechanical damage was caused.[33] Shortly after the incident CERN reported that the most likely cause of the problem was a faulty electrical connection between two magnets, and that – due to the time needed to warm up the affected sectors and then cool them back down to operating temperature – it would take at least two months to fix.[34] Subsequently,
Large Hadron Collider
148
CERN released a preliminary analysis of the incident on 16 October 2008,[35] and a more detailed one on 5 December 2008.[36] Both analyses confirmed that the incident was indeed initiated by a faulty electrical connection. A total of 53 magnets were damaged in the incident and were repaired or replaced during the winter shutdown.[37] In the original timeline of the LHC commissioning, the first "modest" high-energy collisions at a center-of-mass energy of 900 GeV were expected to take place before the end of September 2008, and the LHC was expected to be operating at 10 TeV by the end of 2008.[38] However, due to the delay caused by the above-mentioned incident, the collider was not operational until November 2009.[39] Despite the delay, LHC was officially inaugurated on 21 October 2008, in the presence of political leaders, science ministers from CERN's 20 Member States, CERN officials, and members of the worldwide scientific community.[40] Most of 2009 was spent on repairs and reviews from the damage caused by the quench incident, along with two further vacuum leaks identified in July 2009 which pushed the start of operations to November of that year.[41]
Full operation On 20 November 2009, low-energy beams circulated in the tunnel for the first time since the incident, and shortly after, on 30 November, the LHC achieved 1.18 TeV per beam to become the world's highest-energy particle accelerator, beating the Tevatron's previous record of 0.98 TeV per beam held for eight years.[42] The early part of 2010 saw the continued ramp-up of beam in energies and early physics experiments towards 3.5 TeV per beam and on 30 March 2010, LHC set the present record for high-energy collisions by colliding proton beams at a combined energy level of 7 TeV. The attempt was the third that day, after two unsuccessful attempts in which the protons had to be "dumped" from the collider and new beams had to be injected.[43] This also marked the start of its main research program. The first proton run ended on 4 November 2010. A run with lead ions started on 8 November 2010, and ended on 6 December 2010,[44] allowing the ALICE experiment to study matter under extreme conditions similar to those shortly after the Big Bang.[45] CERN has declared that the LHC will run through to the end of 2012, with a short technical stop at the end of 2011. The energy for 2011 was 3.5 TeV per beam, whereas for 2012 it was decided to run the LHC at 4 TeV per beam. In 2013 the LHC will go into a long shutdown to prepare for higher-energy running starting in 2014.[12]
Timeline of operations Date
Event
10 Sep 2008 CERN successfully fired the first protons around the entire tunnel circuit in stages. 19 Sep 2008 Magnetic quench occurred in about 100 bending magnets in sectors 3 and 4, causing a loss of approximately 6 tonnes of liquid helium. 30 Sep 2008 First "modest" high-energy collisions planned but postponed due to accident. 16 Oct 2008
CERN released a preliminary analysis of the accident.
21 Oct 2008
Official inauguration.
5 Dec 2008
CERN released detailed analysis.
20 Nov 2009 Low-energy beams circulated in the tunnel for the first time since the accident.[46] 23 Nov 2009 First particle collisions in all four detectors at 450 GeV.[10] 30 Nov 2009 LHC becomes the world's highest-energy particle accelerator achieving 1.18 TeV per beam, beating the Tevatron's previous record of [42] 0.98 TeV per beam held for eight years. 28 Feb 2010 The LHC continues operations ramping energies to run at 3.5 TeV for 18 months to two years, after which it will be shut down to [47] prepare for the 14 TeV collisions (7 TeV per beam).
Large Hadron Collider
149
30 Mar 2010 The two beams collided at 7 TeV (3.5 TeV per beam) in the LHC at 13:06 CEST, marking the start of the LHC research program. 8 Nov 2010
Start of the first run with lead ions.
6 Dec 2010
End of the run with lead ions. Shutdown until early 2011.
13 Mar 2011 Beginning of the 2011 run with proton beams.[48] 21 Apr 2011 LHC becomes the world's highest-luminosity hadron accelerator achieving a peak luminosity of 4.67·1032 cm−2s−1, beating the [49] Tevatron's previous record of 4·1032 cm−2s−1 held for one year. [50]
17 Jun 2011
The high luminosity experiments ATLAS and CMS reach 1 fb-1 of collected data.
14 Oct 2011
LHCb reaches 1 fb-1 of collected data.
23 Oct 2011
The high luminosity experiments ATLAS and CMS reach 5 fb-1 of collected data.
5 Apr 2012
First collisions with stable beams in 2012 after the winter shutdown. The energy is increased to 4 TeV per beam (8 TeV in [52] collisions).
[51]
Findings CERN scientists estimate that, if the Standard Model is correct, a single Higgs boson may be produced every few hours. At this rate, it may take about two to three years to collect enough data to discover the Higgs boson unambiguously. Similarly, it may take one year or more before sufficient results concerning supersymmetric particles have been gathered to draw meaningful conclusions.[3] On the other hand, some extensions of the Standard Model predict additional particles, such as the heavy W' and Z' gauge bosons, whose existence might already be probed after a few months of data collection.[53] The first physics results from the LHC, involving 284 collisions which took place in the ALICE detector, were reported on 15 December 2009.[54] The results of the first proton–proton collisions at energies higher than Fermilab's Tevatron proton–antiproton collisions were published by the CMS collaboration in early February 2010, yielding greater-than-predicted charged-hadron production.[55] After the first year of data collection, the LHC experimental collaborations started to release their preliminary results concerning searches for new physics beyond the Standard Model in proton-proton collisions.[56][57][58][59] No evidence of new particles was detected in the 2010 data. As a result, bounds were set on the allowed parameter space of various extensions of the Standard Model, such as models with large extra dimensions, constrained versions of the Minimal Supersymmetric Standard Model, and others.[60][61][62] On 24 May 2011 it was reported that quark–gluon plasma (the densest matter besides black holes) has been created in the LHC.[63] Between July and August 2011, results of searches for the Higgs boson and for exotic particles, based on the data collected during the first half of the 2011 run, were presented in conferences in Grenoble[64] and Mumbai.[65] In the latter conference it was reported that, despite hints of a Higgs signal in earlier data, ATLAS and CMS exclude with 95% confidence level (using the CLs method) the existence of a Higgs boson with the properties predicted by the Standard Model over most of the mass region between 145 and 466 GeV.[66] The searches for new particles did not yield signals either, allowing to further constrain the parameter space of various extensions of the Standard Model, including its supersymmetric extensions.[67][68] On 13 December 2011 CERN reported that the Standard Model Higgs boson, if it exists, is most likely to have a mass constrained to the range 115-130 GeV. Both the CMS and ATLAS detectors have also shown intensity peaks in the 124–125 GeV range, consistent with either background noise or the observation of the Higgs boson. It is expected that there will be sufficient data by the end of 2012 for a definite answer.[69] On 22 December 2011 it was reported that a new particle had been observed, the χb (3P) bottomonium state.[70]
Large Hadron Collider
Proposed upgrade After some years of running, any particle physics experiment typically begins to suffer from diminishing returns: as the key results reachable by the device begin to be completed, later years of operation discover proportionately less than earlier years. A common outcome is to upgrade the devices involved, typically in energy, in luminosity, or in terms of improved detectors. A luminosity upgrade of the LHC, called the Super LHC, has been proposed,[71] to be made in 2018 after ten years of operation. The optimal path for the LHC luminosity upgrade includes an increase in the beam current (i.e. the number of protons in the beams) and the modification of the two high-luminosity interaction regions, ATLAS and CMS. To achieve these increases, the energy of the beams at the point that they are injected into the (Super) LHC should also be increased to 1 TeV. This will require an upgrade of the full pre-injector system, the needed changes in the Super Proton Synchrotron being the most expensive. Currently the collaborative research effort of LHC Accelerator Research Program, LARP is conducting research into how to achieve these goals.[72]
Cost With a budget of 7.5 billion euros (approx. $9bn or £6.19bn as of Jun 2010), the LHC is one of the most expensive scientific instruments[73] ever built.[74] The total cost of the project is expected to be of the order of 4.6bn Swiss francs (approx. $4.4bn, €3.1bn, or £2.8bn as of Jan 2010) for the accelerator and SFr 1.16bn (approx. $1.1bn, €0.8bn, or £0.7bn as of Jan 2010) for the CERN contribution to the experiments.[75] The construction of LHC was approved in 1995 with a budget of SFr 2.6bn, with another SFr 210M towards the experiments. However, cost overruns, estimated in a major review in 2001 at around SFr 480M for the accelerator, and SFr 50M for the experiments, along with a reduction in CERN's budget, pushed the completion date from 2005 to April 2007.[76] The superconducting magnets were responsible for SFr 180M of the cost increase. There were also further costs and delays due to engineering difficulties encountered while building the underground cavern for the Compact Muon Solenoid,[77] and also due to faulty parts provided by Fermilab.[78] Due to lower electricity costs during the summer, it is expected that the LHC will normally not operate over the winter months,[79] although an exception was made to make up for the 2008 start-up delays over the 2009/10 winter.
Computing resources Data produced by LHC, as well as LHC-related simulation, was estimated at approximately 15 petabytes per year (max throughput while running not stated).[80] The LHC Computing Grid[81] was constructed to handle the massive amounts of data produced. It incorporated both private fiber optic cable links and existing high-speed portions of the public Internet, enabling data transfer from CERN to academic institutions around the world.[82] The Open Science Grid is used as the primary infrastructure in the United States, and also as part of an interoperable federation with the LHC Computing Grid. The distributed computing project LHC@home was started to support the construction and calibration of the LHC. The project uses the BOINC platform, enabling anybody with an Internet connection and either OS X or Linux [83] to use their computer's idle time to simulate how particles will travel in the tunnel. With this information, the scientists will be able to determine how the magnets should be calibrated to gain the most stable "orbit" of the beams in the ring.[84]
150
Large Hadron Collider
Safety of particle collisions The experiments at the Large Hadron Collider sparked fears among the public that the particle collisions might produce doomsday phenomena, involving the production of stable microscopic black holes or the creation of hypothetical particles called strangelets.[85] Two CERN-commissioned safety reviews examined these concerns and concluded that the experiments at the LHC present no danger and that there is no reason for concern,[86][87][88] a conclusion expressly endorsed by the American Physical Society.[89]
Operational challenges The size of the LHC constitutes an exceptional engineering challenge with unique operational issues on account of the amount of energy stored in the magnets and the beams.[28][90] While operating, the total energy stored in the magnets is 10 GJ (equivalent to 2.4 tons of TNT) and the total energy carried by the two beams reaches 724 MJ (unknown operator: u'strong' kilograms of TNT).[91] Loss of only one ten-millionth part (10−7) of the beam is sufficient to quench a superconducting magnet, while the beam dump must absorb 362 MJ (unknown operator: u'strong' kilograms of TNT) for each of the two beams. These energies are carried by very little matter: under nominal operating conditions (2,808 bunches per beam, 1.15×1011 protons per bunch), the beam pipes contain 1.0×10−9 gram of hydrogen, which, in standard conditions for temperature and pressure, would fill the volume of one grain of fine sand.
Construction accidents and delays • On 25 October 2005, José Pereira Lages, a technician, was killed in the LHC when a switchgear that was being transported fell on him.[92] • On 27 March 2007 a cryogenic magnet support broke during a pressure test involving one of the LHC's inner triplet (focusing quadrupole) magnet assemblies, provided by Fermilab and KEK. No one was injured. Fermilab director Pier Oddone stated "In this case we are dumbfounded that we missed some very simple balance of forces". This fault had been present in the original design, and remained during four engineering reviews over the following years.[93] Analysis revealed that its design, made as thin as possible for better insulation, was not strong enough to withstand the forces generated during pressure testing. Details are available in a statement from Fermilab, with which CERN is in agreement.[94][95] Repairing the broken magnet and reinforcing the eight identical assemblies used by LHC delayed the startup date, then planned for November 2007. • Problems occurred on 19 September 2008 during powering tests of the main dipole circuit, when an electrical fault in the bus between magnets caused a rupture and a leak of six tonnes of liquid helium. The operation was delayed for several months.[96] It is currently believed that a faulty electrical connection between two magnets caused an arc, which compromised the liquid-helium containment. Once the cooling layer was broken, the helium flooded the surrounding vacuum layer with sufficient force to break 10-ton magnets from their mountings. The explosion also contaminated the proton tubes with soot.[36][97] This accident was thoroughly discussed in a 22 February 2010 Superconductor Science and Technology article by CERN physicist Lucio Rossi.[98] • Two vacuum leaks were identified in July 2009, and the start of operations was further postponed to mid-November 2009.[41]
151
Large Hadron Collider
Popular culture The Large Hadron Collider gained a considerable amount of attention from outside the scientific community and its progress is followed by most popular science media. The LHC has also sparked the imaginations of authors of works of fiction, such as novels, TV series, and video games, although descriptions of what it is, how it works, and projected outcomes of the experiments are often only vaguely accurate, occasionally causing concern among the general public. The novel Angels & Demons, by Dan Brown, involves antimatter created at the LHC to be used in a weapon against the Vatican. In response CERN published a "Fact or Fiction?" page discussing the accuracy of the book's portrayal of the LHC, CERN, and particle physics in general.[99] The movie version of the book has footage filmed on-site at one of the experiments at the LHC; the director, Ron Howard, met with CERN experts in an effort to make the science in the story more accurate.[100] The novel FlashForward, by Robert J. Sawyer, involves the search for the Higgs boson at the LHC. CERN published a "Science and Fiction" page interviewing Sawyer and physicists about the book and the TV series based on it.[101] CERN employee Katherine McAlpine's "Large Hadron Rap"[102] surpassed 7 million YouTube views.[103][104] The band Les Horribles Cernettes was founded by female members of CERN. The name was chosen so to have the same initials as the LHC.[105][106] National Geographic's "World's Toughest Fixes," Season 2 (2010) Episode 6 "Atom Smasher" features the replacement of the last superconducting magnet section in the repair of the supercollider after the 2008 quench incident. The episode includes actual footage from the repair facility to the inside of the supercollider, and explanations of the function, engineering, and purpose of the LHC.[107]
References [1] "Missing Higgs" (http:/ / public. web. cern. ch/ public/ en/ Science/ Higgs-en. html). CERN. 2008. . Retrieved 2008-10-10. [2] "Towards a superforce" (http:/ / public. web. cern. ch/ public/ en/ Science/ Superforce-en. html). CERN. 2008. . Retrieved 2008-10-10. [3] "What is LHCb" (http:/ / cdsmedia. cern. ch/ img/ CERN-Brochure-2008-001-Eng. pdf). CERN FAQ. CERN Communication Group. January 2008. p. 44. . Retrieved 2010-04-02. [4] Amina Khan (31 March 2010). "Large Hadron Collider rewards scientists watching at Caltech" (http:/ / articles. latimes. com/ 2010/ mar/ 31/ science/ la-sci-hadron31-2010mar31). Los Angeles Times. . Retrieved 2010-04-02. [5] Roger Highfield (16 September 2008). "Large Hadron Collider: Thirteen ways to change the world" (http:/ / www. telegraph. co. uk/ earth/ main. jhtml?xml=/ earth/ 2008/ 09/ 16/ sciwriters116. xml). Telegraph (London). . Retrieved 2008-10-10. [6] "First beam in the LHC – Accelerating science" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2008/ PR08. 08E. html) (Press release). CERN Press Office. 10 September 2008. . Retrieved 2008-10-09. [7] Paul Rincon (23 September 2008). "Collider halted until next year" (http:/ / news. bbc. co. uk/ 2/ hi/ science/ nature/ 7632408. stm). BBC News. . Retrieved 2008-10-09. [8] http:/ / www. physics. purdue. edu/ particle/ lhc/ [9] "The LHC is back" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2009/ PR16. 09E. html) (Press release). CERN Press Office. 20 November 2009. . Retrieved 2009-11-20. [10] "Two circulating beams bring first collisions in the LHC" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2009/ PR17. 09E. html) (Press release). CERN Press Office. 23 November 2009. . Retrieved 2009-11-23. [11] "CERN LHC sees high-energy success" (http:/ / news. bbc. co. uk/ 2/ hi/ science/ nature/ 8593780. stm) (Press release). BBC News. 30 March 2010. . Retrieved 2010-03-30. [12] CERN Press Office (13 February 2012). "LHC to run at 4 TeV per beam in 2012" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2012/ PR01. 12E. html). CERN. . [13] Brian Greene (11 September 2008). "The Origins of the Universe: A Crash Course" (http:/ / www. nytimes. com/ 2008/ 09/ 12/ opinion/ 12greene. html?_r=1& oref=slogin). The New York Times. . Retrieved 2009-04-17. [14] "... in the public presentations of the aspiration of particle physics we hear too often that the goal of the LHC or a linear collider is to check off the last missing particle of the Standard Model, this year's Holy Grail of particle physics, the Higgs boson. The truth is much less boring than that! What we're trying to accomplish is much more exciting, and asking what the world would have been like without the Higgs mechanism is a way of getting at that excitement." – Chris Quigg (2005). "Nature's Greatest Puzzles". arXiv:hep-ph/0502070 [hep-ph]. [15] "Why the LHC" (http:/ / public. web. cern. ch/ public/ en/ LHC/ WhyLHC-en. html). CERN. 2008. . Retrieved 2009-09-28.
152
Large Hadron Collider [16] "Zeroing in on the elusive Higgs boson" (http:/ / www. science. doe. gov/ Accomplishments_Awards/ Decades_Discovery/ 35. html). US Department of Energy. March 2001. . Retrieved 2008-12-11. [17] "Accordingly, in common with many of my colleagues, I think it highly likely that both the Higgs boson and other new phenomena will be found with the LHC."..."This mass threshold means, among other things, that something new—either a Higgs boson or other novel phenomena—is to be found when the LHC turns the thought experiment into a real one." Chris Quigg (February 2008). "The coming revolutions in particle physics" (http:/ / www. scientificamerican. com/ article. cfm?id=the-coming-revolutions-in-particle-physics& page=3). Scientific American. pp. 38–45. . Retrieved 2009-09-28. [18] Shaaban Khalil (2003). "Search for supersymmetry at LHC". Contemporary Physics 44 (3): 193–201. Bibcode 2003ConPh..44..193K. doi:10.1080/0010751031000077378. [19] Alexander Belyaev (2009). "Supersymmetry status and phenomenology at the Large Hadron Collider". Pramana 72 (1): 143–160. Bibcode 2009Prama..72..143B. doi:10.1007/s12043-009-0012-0. [20] Anil Ananthaswamy (11 November 2009). "In SUSY we trust: What the LHC is really looking for" (http:/ / www. newscientist. com/ article/ mg20427341. 200-in-susy-we-trust-what-the-lhc-is-really-looking-for. html). New Scientist. . [21] Lisa Randall (2002). "Extra Dimensions and Warped Geometries" (http:/ / randall. physics. harvard. edu/ RandallCV/ Sciencearticle. pdf). Science 296 (5572): 1422–1427. Bibcode 2002Sci...296.1422R. doi:10.1126/science.1072567. PMID 12029124. . [22] Panagiota Kanti (2009). "Black Holes at the LHC". Lecture Notes in Physics. Lecture Notes in Physics 769: 387–423. arXiv:0802.2218. doi:10.1007/978-3-540-88460-6_10. ISBN 978-3-540-88459-0. [23] Joel Achenbach (March 2008). "The God Particle" (http:/ / ngm. nationalgeographic. com/ 2008/ 03/ god-particle/ achenbach-text). National Geographic Magazine. . Retrieved 2008-02-25. [24] "The Z factory" (http:/ / public. web. cern. ch/ PUBLIC/ en/ Research/ LEP-en. html). CERN. 2008. . Retrieved 2009-04-17. [25] "LHC: How Fast do These Protons Go?" (http:/ / journal. batard. info/ post/ 2008/ 09/ 12/ lhc-how-fast-do-these-protons-go). yogiblog. . Retrieved 2008-10-29. [26] "LHC commissioning with beam" (http:/ / lhc-commissioning. web. cern. ch/ lhc-commissioning/ ). CERN. . Retrieved 2009-04-17. [27] "Operational Experience of the ATLAS High Level Trigger with Single-Beam and Cosmic Rays" (http:/ / cdsweb. cern. ch/ record/ 1228285/ files/ ATL-DAQ-PROC-2009-044. pdf) (PDF). . Retrieved 2010-10-29. [28] Jörg Wenninger (November 2007). "Operational challenges of the LHC" (http:/ / irfu. cea. fr/ Phocea/ file. php?class=std& file=Seminaires/ 1595/ Dapnia-Nov07-partB. ppt) (PowerPoint). p. 53. . Retrieved 2009-04-17. [29] "Ions for LHC (I-LHC) Project" (http:/ / project-i-lhc. web. cern. ch/ project-i-lhc/ Welcome. htm). CERN. 1 November 2007. . Retrieved 2009-04-17. [30] Paul Rincon (10 September 2008). "'Big Bang' experiment starts well" (http:/ / news. bbc. co. uk/ 1/ hi/ sci/ tech/ 7604293. stm). BBC News. . Retrieved 2009-04-17. [31] "First beam in the LHC – Accelerating science" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2008/ PR08. 08E. html) (Press release). CERN Press Office. 10 September 2008. . Retrieved 2008-09-10. [32] Mark Henderson (10 September 2008). "Scientists cheer as protons complete first circuit of Large Hadron Collider" (http:/ / www. timesonline. co. uk/ tol/ news/ uk/ science/ article4722261. ece). Times Online (London). . Retrieved 2008-10-06. [33] "Interim Summary Report on the Analysis of the 19 September 2008 Incident at the LHC" (https:/ / edms. cern. ch/ file/ 973073/ 1/ Report_on_080919_incident_at_LHC__2_. pdf) (PDF). CERN. 15 October 2008. EDMS 973073. . Retrieved 2009-09-28. [34] "Incident in LHC sector 3–4" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2008/ PR09. 08E. html) (Press release). CERN Press Office. 20 September 2008. . Retrieved 2009-09-28. [35] "CERN releases analysis of LHC incident" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2008/ PR14. 08E. html) (Press release). CERN Press Office. 16 October 2008. . Retrieved 2009-09-28. [36] "LHC to restart in 2009" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2008/ PR17. 08E. html) (Press release). CERN Press Office. 5 December 2008. . Retrieved 2008-12-08. [37] "Final LHC magnet goes underground" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2009/ PR06. 09E. html) (Press release). CERN Press Office. 30 April 2009. . Retrieved 2009-08-04. [38] "CERN announces start-up date for LHC" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2008/ PR06. 08E. html) (Press release). CERN Press Office. 7 August 2008. . [39] "CERN management confirms new LHC restart schedule" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2009/ PR02. 09E. html) (Press release). CERN Press Office. 9 February 2009. . Retrieved 2009-02-10. [40] "CERN inaugurates the LHC" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2008/ PR16. 08E. html) (Press release). CERN Press Office. 21 October 2008. . Retrieved 2008-10-21. [41] "News on the LHC" (http:/ / user. web. cern. ch/ user/ news/ 2009/ 090716. html). CERN. 16 July 2009. . Retrieved 2009-09-28. [42] "LHC sets new world record" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2009/ PR18. 09E. html) (Press release). CERN. 30 November 2009. . Retrieved 2010-03-02. [43] "Big Bang Machine sets collision record" (http:/ / beta. thehindu. com/ sci-tech/ science/ article329160. ece?homepage=true). Associated Press. The Hindu. 30 March 2010. . [44] "CERN completes transition to lead-ion running at the LHC" (http:/ / public. web. cern. ch/ press/ pressreleases/ Releases2010/ PR21. 10E. html) (Press release). CERN. 8 November 2010. . Retrieved 2010-11-08.
153
Large Hadron Collider [45] "The Latest from the LHC : Last period of proton running for 2010. - CERN Bulletin" (http:/ / cdsweb. cern. ch/ journal/ CERNBulletin/ 2010/ 45/ News Articles/ 1302710?ln=en). Cdsweb.cern.ch. 1 November 2010. . Retrieved 2011-08-17. [46] "The LHC is back" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2009/ PR16. 09E. html) (Press release). CERN. 20 November 2009. . Retrieved 2010-03-02. [47] "Large Hadron Collider to come back online after break" (http:/ / news. bbc. co. uk/ 2/ hi/ science/ nature/ 8524024. stm). BBC News. 19 February 2010. . Retrieved 2010-03-02. [48] "LHC sees first stable-beam 3.5 TeV collisions of 2011" (http:/ / www. symmetrymagazine. org/ breaking/ 2011/ 03/ 13/ lhc-sees-first-3-5-tev-collisions-of-2011/ ). symmetry breaking. 13 March 2011. . Retrieved 2011-03-15. [49] CERN Press Office (22 April 2011). "LHC sets world record beam intensity" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2011/ PR02. 11E. html). Press.web.cern.ch. . Retrieved 2011-05-22. [50] "LHC achieves 2011 data milestone" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2011/ PR06. 11E. html). Press.web.cern.ch. 17 June 2011. . Retrieved 2011-06-20. [51] "One recorded inverse femtobarn" (http:/ / www. quantumdiaries. org/ 2011/ 10/ 18/ one-recorded-inverse-femtobarn/ ). . [52] "LHC physics data taking gets underway at new record collision energy of 8TeV" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2012/ PR10. 12E. html). Press.web.cern.ch. 05 April 2012. . Retrieved 2012-04-05. [53] P. Rincon (17 May 2010). "LHC particle search 'nearing', says physicist" (http:/ / news. bbc. co. uk/ 1/ hi/ sci/ tech/ 8685541. stm). BBC News. . [54] First Science Produced at LHC (http:/ / news. softpedia. com/ news/ First-Science-Produced-at-LHC-129833. shtml) 2009-12-15 [55] V. Khachatryan et al. (CMS collaboration) (2010). "Transverse momentum and pseudorapidity distributions of charged hadrons in pp collisions at √s = 0.9 and 2.36 TeV". Journal of High Energy Physics 2010 (2): 1–35. arXiv:1002.0621. Bibcode 2010JHEP...02..041K. doi:10.1007/JHEP02(2010)041. [56] V. Khachatryan et al. (CMS collaboration) (2011). "Search for Microscopic Black Hole Signatures at the Large Hadron Collider". Physics Letters B 697 (5): 434. arXiv:1012.3375. Bibcode 2011PhLB..697..434C. doi:10.1016/j.physletb.2011.02.032. [57] V. Khachatryan et al. (CMS collaboration) (2011). "Search for Supersymmetry in pp Collisions at 7 TeV in Events with Jets and Missing Transverse Energy". Physics Letters B 698 (3): 196. arXiv:1101.1628. Bibcode 2011PhLB..698..196C. doi:10.1016/j.physletb.2011.03.021. [58] G. Aad et al. (ATLAS collaboration) (2011). "Search for supersymmetry using final states with one lepton, jets, and missing transverse momentum with the ATLAS detector in √s = 7 TeV pp". Physical Review Letters 106 (13): 131802. arXiv:1102.2357. Bibcode 2011PhRvL.106m1802A. doi:10.1103/PhysRevLett.106.131802. [59] G. Aad et al. (ATLAS collaboration) (2011). "Search for squarks and gluinos using final states with jets and missing transverse momentum with the ATLAS detector in √s = 7 TeV proton-proton collisions". Physics Letters B 701 (2): 186–203. arXiv:1102.5290. Bibcode 2011PhLB..701..186A. doi:10.1016/j.physletb.2011.05.061. [60] Chalmers, M. Reality check at the LHC (http:/ / physicsworld. com/ cws/ article/ indepth/ 44805), physicsworld.com (http:/ / physicsworld. com/ ), Jan 18, 2011 [61] McAlpine, K. Will the LHC find supersymmetry? (http:/ / physicsworld. com/ cws/ article/ news/ 45182), physicsworld.com (http:/ / physicsworld. com/ ), Feb 22, 2011 [62] Geoff Brumfiel (2011). "Beautiful theory collides with smashing particle data". Nature 471 (7336): 13–14. Bibcode 2011Natur.471...13B. doi:10.1038/471013a. [63] Densest Matter Created in Big-Bang Machine (http:/ / news. nationalgeographic. com/ news/ 2011/ 05/ 110524-densest-matter-created-lhc-alice-big-bang-space-science/ ), National Geographic Daily News [64] CERN Press Office (21 July 2011). "LHC experiments present their latest results at Europhysics Conference on High Energy Physics" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2011/ PR09. 11E. html). Press.web.cern.ch. . Retrieved 2011-09-01. [65] CERN Press Office (22 August 2011). "LHC experiments present latest results at Mumbai conference" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2011/ PR14. 11E. html). Press.web.cern.ch. . Retrieved 2011-09-01. [66] Pallab Ghosh (22 August 2011). "Higgs boson range narrows at European collider" (http:/ / www. bbc. co. uk/ news/ science-environment-14596367). BBC News. . [67] Pallab Ghosh (27 August 2011). "LHC results put supersymmetry theory 'on the spot'" (http:/ / www. bbc. co. uk/ news/ science-environment-14680570). BBC News. . [68] "LHCb experiment sees Standard Model physics" (http:/ / www. symmetrymagazine. org/ breaking/ 2011/ 08/ 29/ lhcb-experiment-sees-standard-model-physics/ ). Symmetry Breaking. SLAC/Fermilab. 29 August 2011. . Retrieved 2011-09-01. [69] "ATLAS and CMS experiments present Higgs search status" (http:/ / press. web. cern. ch/ press/ PressReleases/ Releases2011/ PR25. 11E. html). CERN. 13 December 2011. . Retrieved 2 January 2012. [70] Jonathan Amos (22 December 2011). "LHC reports discovery of its first new particle" (http:/ / www. bbc. co. uk/ news/ science-environment-16301908). BBC News. . [71] F. Ruggerio (29 September 2005). "LHC upgrade (accelerator)" (http:/ / chep. knu. ac. kr/ ICFA-Seminar/ upload/ 9. 29/ Morning/ session1/ Ruggiero-ICFA-05. pdf). 8th ICFA Seminar. . Retrieved 2009-09-28. [72] "DOE Review of LARP" (http:/ / www-td. fnal. gov/ LHC/ USLARP. html). Fermilab. 5–6 June 2007. . Retrieved 2011-06-09. [73] "CERN — The Large Hadron Collider" (http:/ / public. web. cern. ch/ public/ en/ LHC/ LHC-en. html). Public.web.cern.ch. . Retrieved 2010-08-28.
154
Large Hadron Collider [74] Agence Science-Presse (7 December 2009). "LHC: Un (très) petit Big Bang" (http:/ / www. lienmultimedia. com/ article. php3?id_article=22468) (in French). Lien Multimédia. . Retrieved 2010-10-29. Google translation (http:/ / translate. google. com/ translate?u=http:/ / www. lienmultimedia. com/ article. php3?id_article=22468& hl=en& ie=UTF8& sl=fr& tl=en) [75] "How much does it cost?" (http:/ / askanexpert. web. cern. ch/ AskAnExpert/ en/ Accelerators/ LHCgeneral-en. html#3). CERN. 2007. . Retrieved 2009-09-28. [76] Luciano Maiani (16 October 2001). "LHC Cost Review to Completion" (http:/ / user. web. cern. ch/ User/ LHCCost/ 2001-10-16/ LHCCostReview. html). CERN. . Retrieved 2001-01-15. [77] Toni Feder (2001). "CERN Grapples with LHC Cost Hike" (http:/ / ptonline. aip. org/ journals/ doc/ PHTOAD-ft/ vol_54/ iss_12/ 21_2. shtml). Physics Today 54 (12): 21. Bibcode 2001PhT....54l..21F. doi:10.1063/1.1445534. . [78] "Bursting magnets may delay CERN collider project" (http:/ / www. reuters. com/ article/ scienceNews/ idUSL054919720070405). Reuters. 5 April 2007. . Retrieved 2009-09-28. [79] Paul Rincon (23 September 2008). "Collider halted until next year" (http:/ / news. bbc. co. uk/ 1/ hi/ sci/ tech/ 7632408. stm). BBC News. . Retrieved 2009-09-28. [80] "Worldwide LHC Computing Grid" (http:/ / public. web. cern. ch/ public/ en/ LHC/ Computing-en. html). CERN. 2008. . Retrieved 2 October 2011. [81] "grille de production : les petits pc du lhc" (http:/ / www. cite-sciences. fr/ francais/ ala_cite/ science_actualites/ sitesactu/ question_actu. php?langue=fr& id_article=16043). Cite-sciences.fr. . Retrieved 2011-05-22. [82] "Worldwide LHC Computing Grid" (http:/ / lcg. web. cern. ch/ LCG/ public/ ). Official public website. CERN. . Retrieved 2 October 2011. [83] (http:/ / en. wikipedia. org/ wiki/ BOINC_client-server_technology#Server_design_weaknesses), [] [84] LHC@home (http:/ / boinc. berkeley. edu/ wiki/ LHC@home), BOINC [85] Alan Boyle (2 September 2008). "Courts weigh doomsday claims" (http:/ / cosmiclog. msnbc. msn. com/ archive/ 2008/ 09/ 02/ 1326534. aspx). Cosmic Log. MSNBC. . Retrieved 2009-09-28. [86] J.-P. Blaizot, J. Iliopoulos, J. Madsen, G.G. Ross, P. Sonderegger, H.-J. Specht (2003). "Study of Potentially Dangerous Events During Heavy-Ion Collisions at the LHC" (http:/ / cdsweb. cern. ch/ record/ 613175/ files/ p1. pdf). CERN. . Retrieved 2009-09-28. [87] J. Ellis J, G. Giudice, M.L. Mangano, T. Tkachev, U. Wiedemann (LHC Safety Assessment Group) (5 September 2008). "Review of the Safety of LHC Collisions". Journal of Physics G 35 (11): 115004. arXiv:0806.3414. Bibcode 2008JPhG...35k5004E. doi:10.1088/0954-3899/35/11/115004. [88] "The safety of the LHC" (http:/ / public. web. cern. ch/ public/ en/ LHC/ Safety-en. html). CERN. 2008. . Retrieved 2009-09-28. [89] Division of Particles & Fields (http:/ / www. aps. org/ units/ dpf/ ). "Statement by the Executive Committee of the DPF on the Safety of Collisions at the Large Hadron Collider" (http:/ / www. aps. org/ units/ dpf/ governance/ reports/ upload/ lhc_saftey_statement. pdf). American Physical Society. . Retrieved 2009-09-28. [90] "Challenges in accelerator physics" (http:/ / lhc. web. cern. ch/ lhc/ general/ acphys. htm). CERN. 14 January 1999. . Retrieved 2009-09-28. [91] John Poole (2004). "Beam Parameters and Definitions" (https:/ / edms. cern. ch/ file/ 445830/ 5/ Vol_1_Chapter_2. pdf). . [92] Robert Aymar (26 October 2005). "Message from the Director-General" (http:/ / user. web. cern. ch/ user/ QuickLinks/ Announcements/ 2005/ Accident. html) (Press release). CERN Press Office. . Retrieved 2009-09-28. [93] "Fermilab 'Dumbfounded' by fiasco that broke magnet" (http:/ / web. archive. org/ web/ 20080616063402/ http:/ / www. photonics. com/ content/ news/ 2007/ April/ 4/ 87089. aspx). Photonics.com. 4 April 2007. Archived from the original (http:/ / www. photonics. com/ content/ news/ 2007/ April/ 4/ 87089. aspx) on 2008-06-16. . Retrieved 2009-09-28. [94] "Fermilab update on inner triplet magnets at LHC: Magnet repairs underway at CERN" (http:/ / user. web. cern. ch/ user/ QuickLinks/ Announcements/ 2007/ LHCInnerTriplet_5. html) (Press release). CERN Press Office. 1 June 2007. . Retrieved 2009-09-28. [95] "Updates on LHC inner triplet failure" (http:/ / www. fnal. gov/ pub/ today/ lhc_magnet_archive. html). Fermilab Today. Fermilab. 28 September 2007. . Retrieved 2009-09-28. [96] Paul Rincon (23 September 2008). "Collider halted until next year" (http:/ / news. bbc. co. uk/ 2/ hi/ in_depth/ 7632408. stm). BBC News. . Retrieved 2009-09-29. [97] Dennis Overbye (5 December 2008). "After repairs, summer start-up planned for collider" (http:/ / www. nytimes. com/ 2008/ 12/ 06/ science/ 06cern. html). New York Times. . Retrieved 2008-12-08. [98] L. Rossi (2010). "Superconductivity: its role, its success and its setbacks in the Large Hadron Collider of CERN" (http:/ / iopscience. iop. org/ 0953-2048/ 23/ 3/ 034001/ pdf/ sust10_3_034001. pdf). Superconductor Science and Technology 23 (3): 034001. Bibcode 2010SuScT..23c4001R. doi:10.1088/0953-2048/23/3/034001. . [99] "Angels and Demons" (http:/ / public. web. cern. ch/ Public/ en/ Spotlight/ SpotlightAandD-en. html). CERN. January 2008. . Retrieved 2009-09-28. [100] Ceri Perkins (2 June 2008). "ATLAS gets the Hollywood treatment" (http:/ / atlas-service-enews. web. cern. ch/ atlas-service-enews/ news/ news_angelphoto. php). ATLAS e-News. . Retrieved 2009-09-28. [101] "FlashForward" (http:/ / flashforward. web. cern. ch/ flashforward/ ). CERN. September 2009. . Retrieved 2009-10-03. [102] Katherine McAlpine (28 July 2008). "Large Hadron Rap" (http:/ / www. youtube. com/ watch?v=j50ZssEojtM). YouTube. . Retrieved 2011-05-08. [103] Roger Highfield (6 September 2008). "Rap about world's largest science experiment becomes YouTube hit" (http:/ / www. telegraph. co. uk/ earth/ main. jhtml?xml=/ earth/ 2008/ 08/ 26/ scirap126. xml). Telegraph (London). . Retrieved 2009-09-28.
155
Large Hadron Collider [104] Jennifer Bogo (1 August 2008). "Large Hadron Collider rap teaches particle physics in 4 minutes" (http:/ / www. popularmechanics. com/ blogs/ science_news/ 4276090. html). Popular Mechanics. . Retrieved 2009-09-28. [105] Malcolm W Brown (29 December 1998). "Physicists Discover Another Unifying Force: Doo-Wop" (http:/ / musiclub. web. cern. ch/ MusiClub/ bands/ cernettes/ Press/ NYT. pdf). New York Times (New York, USA). . Retrieved 2010-09-21. [106] Heather McCabe (10 February 1999). "Grrl Geeks Rock Out" (http:/ / musiclub. web. cern. ch/ MusiClub/ bands/ cernettes/ Press/ Wired. pdf). Wired News. . Retrieved 2010-09-21. [107] http:/ / movies. netflix. com/ WiMovie/ World_s_Toughest_Fixes_Season_2_Columbia_River_Dam/ 70144790?trkid=496624 /nofollow
External links • • • • • • • • •
Official website (http://lhc.web.cern.ch/lhc/) Overview of the LHC at CERN's public webpage (http://public.web.cern.ch/public/en/LHC/LHC-en.html) CERN Courier magazine (http://www.cerncourier.com/) CERN (https://twitter.com/cern) on Twitter CMS Experiment at CERN (https://twitter.com/CMSExperiment) on Twitter Unofficial CERN (https://twitter.com/LHCExperiment) on Twitter LHC Portal (http://www.lhcportal.com/) Web portal (http://www.youtube.com/watch?v=1sldBwpvGFg) Youtube video, CERN, how it works (http://www.youtube.com/watch?v=aMG35H0YCUs) Youtube video, Megastructures, Atom Smasher
• Lyndon Evans and Philip Bryant (eds) (2008). "LHC Machine" (http://www.iop.org/EJ/journal/-page=extra. lhc/jinst). Journal of Instrumentation 3 (8): S08001. Bibcode 2008JInst...3S8001E. doi:10.1088/1748-0221/3/08/S08001. Full documentation for design and construction of the LHC and its six detectors (1600p). • symmetry magazine LHC special issue August 2006 (http://www.symmetrymagazine.org/cms/?pid=1000350), special issue December 2007 (http://www.symmetrymagazine.org/cms/?pid=1000562) • New Yorker: Crash Course (http://www.newyorker.com/reporting/2007/05/14/070514fa_fact_kolbert). The world's largest particle accelerator. • NYTimes: A Giant Takes On Physics' Biggest Questions (http://www.nytimes.com/2007/05/15/science/ 15cern.html?ex=1336881600&en=7825f6702d7071e7&ei=5090&partner=rssuserland&emc=rss). • Why a Large Hadron Collider? (http://seedmagazine.com/news/2006/07/why_a_large_hadron_collider.php) Seed Magazine interviews with physicists. • Thirty collected pictures during commissioning and post- 19 September 2008 incident repair (http://www. boston.com/bigpicture/2009/11/large_hadron_collider_ready_to.html), from Boston Globe. • Podcast Interview (http://omegataupodcast.net/2010/03/30-the-large-hadron-collider/) with CERN's Rolf Landua about the LHC and the physics behind it
156
Molten-Salt Reactor Experiment
157
Molten-Salt Reactor Experiment The Molten-Salt Reactor Experiment (MSRE) was an experimental molten-salt nuclear reactor at the Oak Ridge National Laboratory (ORNL) researching this technology through the 1960s; constructed by 1964, it went critical in 1965 and was operated until 1969. The MSRE was a 7.4 MWth test reactor simulating the neutronic "kernel" of a type of inherently safe epithermal thorium breeder reactor called the Liquid fluoride thorium reactor. It used two fuels: uranium-235 and uranium-233. The last, 233UF4 was the result of breeding from thorium. Since this was an engineering test, the large, expensive breeding blanket of thorium salt was omitted in favor of neutron measurements.
MSRE plant diagram: (1) Reactor vessel, (2) Heat exchanger, (3) Fuel pump, (4) Freeze flange, (5) Thermal shield, (6) Coolant pump, (7) Radiator, (8) Coolant drain tank, (9) Fans, (10) Fuel drain tanks, (11) Flush tank, (12) Containment vessel, (13) Freeze valve. Also note Control area in upper left and Chimney upper right.
In the MSRE, the heat from the reactor core was shed via a cooling system using air blowers and radiators. It is thought similar reactors could power high-efficiency heat engines such as closed-cycle gas turbines. The MSRE's piping, core vat and structural components were made from Hastelloy-N and its moderator was a pyrolytic graphite core. The fuel for the MSRE was LiF-BeF2-ZrF4-UF4 (65-29-5-1), the graphite core moderated it, and its secondary coolant was FLiBe (2LiF-BeF2), it operated as hot as 650 °C and operated for the equivalent of about 1.5 years of full power operation. The result promised to be a simple, reliable reactor. The purpose of the Molten-Salt Reactor Experiment was to demonstrate that some of the key features of the proposed molten-salt power reactors could be embodied in a practical reactor that could be operated safely and reliably and be maintained without excessive difficulty. For simplicity, it was to be a fairly small, one-fluid (i.e. non-breeding) reactor operating at 10 MWth or less, with heat rejection to the air via a secondary (fuel-free) salt.
Molten-Salt Reactor Experiment
158
Reactor description
Molten Salt Reactor
Core The Pyrolytic graphite core, grade CGB, also served as the moderator. Before the MSRE development began, tests had shown that salt would not permeate graphite in which the pores were on the order of a micrometer. Graphite with the desired pore structure was available only in small, experimentally prepared pieces, however, and when a manufacturer set out to produce a new grade (CGB) to meet the MSRE requirements, difficulties were encountered.[1]
Fuel/primary coolant The fuel was 7LiF-BeF2-ZrF4-UF4 (65-29.1-5-0.9 mole %). The first fuel was 33% used.
235
U , later a smaller amount of
233
UF4 was
By 1960 a better understanding of fluoride salt based molten-salt reactors had emerged due to earlier molten salt reactor research for the Aircraft Reactor Experiment.
Graphite MSRE core
Fluoride salts are strongly ionic, and when melted, are stable at high temperatures, low pressures, and high radiation fluxes. Low pressure stability requires less robust reactor vessels and increases reliability. The high reactivity of fluorine traps most fission reaction byproducts. It appeared that the fluid salt would permit on-site chemical separation of the fuel and wastes. The fuel system was located in sealed cells, laid out for maintenance with long-handled tools through openings in the top shielding. A tank of LiF-BeF2 salt was used to flush the fuel circulating system before and after maintenance. In a cell adjacent to the reactor was a simple facility for bubbling gas through the fuel or flush salt: H2-HF to remove oxide, F2 to remove uranium as UF6. Haubenreich and Engel,[2] Robertson,[3] and Lindauer[4] provide more detailed descriptions of the reactor and processing plant.
Molten-Salt Reactor Experiment
159
Secondary coolant The secondary salt was LiF-BeF2 (66–34 mole %).
Pump The bowl of the fuel pump was the surge space for the circulating loop, and here about 50 gal/min of fuel was sprayed into the gas space to allow xenon and krypton to escape from the salt. Removing the most significant neutron poison xenon-135 made the reactor safer and easier to restart. In solid-fuel reactors, on restart the 135Xe in the fuel absorbs neutrons, followed by a sudden jump in reactivity as the 135Xe is burned out. Conventional reactors may have to wait hours until xenon-135 decays after shutting down and not immediately restarting (so-called iodine pit).
Molten FLiBe
Also in the pump bowl was a port through which salt samples could be taken or capsules of concentrated fuel-enriching salt (UF4-LiF or PuF3) could be introduced.
Air-cooled heat exchangers At the time, the high temperatures were seen almost as a disadvantage, because they hampered use of conventional steam turbines. Now, such temperatures are seen as an opportunity to use high-efficiency closed-cycle gas turbines. After two months of high-power operation, the reactor was down for 3 months because of the failure of one of the main cooling blowers.
Neutronics and thermal-hydraulics The reactor experienced stable neutronic operation. If either temperatures increased, or bubbles formed, the volume of the fluid fuel salts would increase and some fluid fuel salts would be forced out of the core, thereby reducing the reactivity.
MSRE air-cooled heat exchanger glowing a dull red due to high temperature.
The MSRE development program did not include reactor physics experiments or heat transfer measurements. There was enough latitude in the MSRE that deviations from predictions would not compromise safety or accomplishment of the objectives of the experimental reactor.
Building grounds Construction of the primary system components and alterations of the old Aircraft Reactor Experiment building (which had been partly remodeled for a proposed 60-MW(t) aircraft reactor) were started in 1962. Installation of the salt systems was completed in mid-1964. ORNL was responsible for quality assurance, planning, and management of construction.[5] The primary systems were installed by ORNL personnel; subcontractors modified the building and installed ancillary systems.
Aircraft Reactor Experiment building at ORNL that was retrofitted to house the MSRE
Molten-Salt Reactor Experiment
Structural alloy Hastelloy-N A low chromium, nickel–molybdenum alloy, Hastelloy-N, was used in the MSRE and proved compatible with the fluoride salts FLiBe and FLiNaK. [6] All metal parts contacting salt were made of Hastelloy-N. The choice of Hastelloy-N for the MSRE was on the basis of the promising results of tests at aircraft nuclear propulsion conditions and the availability of much of the required metallurgical data. Development for the MSRE generated the further data required for ASME code approval. It also included preparation of standards for Hastelloy-N procurement and for component fabrication. Almost 200,000 lb (90 Mg) in a variety of shapes of material for the MSRE was produced commercially. Requests for bids on component fabrication went to several companies in the nuclear fabrication industry, but all declined to submit lump-sum bids because of lack of experience with the new alloy. Consequently all major components were fabricated in U.S. Atomic Energy Commission-owned shops at Oak Ridge and Paducah.[7] At the time that design stresses were set for the MSRE, the data that was available indicated that the strength and creep rate of Hastelloy-N were hardly affected by irradiation. After the construction was well along, the stress-rupture life and fracture strain were found to be drastically reduced by thermal neutron irradiation. The MSRE stresses were reanalyzed, and it was concluded that the reactor would have adequate life to reach its goals. At the same time a program was launched to improve the resistance of Hastelloy-N to the embrittlement.[8] An out-of-pile corrosion test program was carried out for Hastelloy-N[9] which indicated extremely low corrosion rates at MSRE conditions. Capsules exposed in the Materials Testing Reactor showed that salt fission power densities of more than 200 W/cm3 had no adverse effects on compatibility of fuel salt, Hastelloy-N, and graphite. Fluorine gas was found to be produced by radiolysis of frozen salts, but only at temperatures below about 100 °C.[10] Components that were developed especially for the MSRE included flanges for 5-inch (unknown operator: u'strong' mm) lines carrying molten salt, freeze valves (an air-cooled section where salt could be frozen and thawed), flexible control rods to operate in thimbles at 1200 °F (650 °C), and the fuel sampler-enricher.[11] Centrifugal pumps were developed similar to those used successfully in the aircraft reactor program, but with provisions for remote maintenance, and including a spray system for xenon removal. Remote maintenance considerations pervaded the MSRE design, and developments included devices for remotely cutting and brazing together 1½-inch pipe, removable heater-insulation units, and equipment for removing specimens of metal and graphite from the core.
Development and construction timeline Most of the MSRE effort from 1960 through 1964 was devoted to design, development, and construction of the MSRE. Production and further testing of graphite and Hastelloy-N, both in-pile and out, were major development activities. Others included work on reactor chemistry, development of fabrication techniques for Hastelloy-N, development of reactor components, and remote-maintenance planning and preparations.[12]
Operation The MSRE operated for 5 years. The salt was loaded in 1964 and nuclear operation ended in December, 1969,[2][13] and all of the objectives of the experiment were achieved during this period. Checkout and prenuclear tests included 1,000 hours of circulation of flush salt and fuel carrier salt. Nuclear testing of the MSRE began in June 1965, with the addition of enriched 235U as UF4-LiF eutectic to the carrier salt to make the reactor critical. After zero-power experiments to measure rod worth and reactivity coefficients,[14] the reactor was shut down and final preparations made for power operation. Power ascension was delayed when vapors from oil that had leaked into the fuel pump were polymerized by the radioactive offgas and plugged gas filters and valves. Maximum power, which was limited to 7.4 MW(t) by the capability of the heat-rejection system, was reached in May 1966.
160
Molten-Salt Reactor Experiment After two months of high-power operation, the reactor was down for three months because of the failure of one of the main cooling blowers. Some further delays were encountered because of offgas line plugging, but by the end of 1966 most of the startup problems were behind. During the next 15 months, the reactor was critical 80% of the time, with runs of 1, 3, and 6 months that were uninterrupted by a fuel drain. By March 1968, the original objectives of the MSRE had been accomplished, and nuclear operation with 235U was concluded. By this time, ample 233U had become available,[15] so the MSRE program was extended to include substitution of 233 U for the uranium in the fuel salt, and operation to observe the new nuclear characteristics. Using the on-site processing equipment the flush salt and fuel salt were fluorinated to recover the uranium in them as UF6.[4] 233 UF4-LiF eutectic was then added to the carrier salt, and in October 1968, the MSRE became the world's first reactor to operate on 233U. The 233U zero-power experiments and dynamics tests confirmed the predicted neutronic characteristics. An unexpected consequence of processing the salt was that its physical properties were altered slightly so that more than the usual amount of gas was entrained from the fuel pump into the circulating loop. The circulating gas and the power fluctuations that accompanied it were eliminated by operating the fuel pump at slightly lower speed. Operation at high power for several months permitted accurate measurement of the capture-to-fission ratio, for 233U in this reactor, completing the objectives of the 233U operation. In the concluding months of operation, xenon stripping, deposition of fission products, and tritium behavior were investigated. The feasibility of using plutonium in molten-salt reactors was emphasized by adding PuF3 as makeup fuel during this period. After the final shutdown in December 1969, the reactor was left in standby for nearly a year. A limited examination program was then carried out, including a moderator bar from the core, a control rod thimble, heat exchanger tubes, parts from the fuel pump bowl, and a freeze valve that had developed a leak during the final reactor shutdown. The radioactive systems were then closed to await ultimate disposal.
Statistics Other operational statistics:[16] • Hours critical: 17,655 • Circulating fuel loop hours: 21,788 • Core volume: less than 2 m3 U-235 fuel operation • • • •
Critical June 1, 1965 Full power May 23, 1966 End operation March 26, 1968 Equivalent full power hours: 9,005
U-233 fuel operation • • • •
Critical October 2, 1968 Full power January 28, 1969 Reactor shutdown December 12, 1969 Equivalent full power hours: 4,167
161
Molten-Salt Reactor Experiment
Results The broadest and perhaps most important conclusion from the MSRE experience was that a molten salt fueled reactor concept was viable. It ran for considerable periods of time, yielding valuable information, and maintenance was accomplished safely and without excessive delay. The MSRE confirmed expectations and predictions.[13] For example, it was demonstrated that: the fuel salt was immune to radiation damage, the graphite was not attacked by the fuel salt, and the corrosion of Hastelloy-N was negligible. Noble gases were stripped from the fuel salt by a spray system, reducing the 135Xe poisoning by a factor of about 6. The bulk of the fission product elements remained stable in the salt. Additions of uranium and plutonium to the salt during operation were quick and uneventful, and recovery of uranium by fluorination was efficient. The neutronics, including critical loading, reactivity coefficients, dynamics, and long-term reactivity changes, agreed with prior calculations. In other areas, the operation resulted in improved data or reduced uncertainties. The 233U capture-to-fission ratio in a typical MSR neutron spectrum is an example of basic data that was improved. The effect of fissioning on the redox potential of the fuel salt was resolved. The deposition of some elements (“noble metals”) was expected, but the MSRE provided quantitative data on relative deposition on graphite, metal, and liquid-gas interfaces. Heat transfer coefficients measured in the MSRE agreed with conventional design calculations and did not change over the life of the reactor. Limiting oxygen in the salt proved effective, and the tendency of fission products to be dispersed from contaminated equipment during maintenance was low. Operation of the MSRE provided insights into the problem of tritium in a molten-salt reactor. It was observed that about 6–10% of the calculated 54 Ci/day (2.0 TBq) production diffused out of the fuel system into the containment cell atmosphere and another 6–10% reached the air through the heat removal system.[17] The fact that these fractions were not higher indicated that something partially negated the transfer of tritium through hot metals. One unexpected finding was shallow, inter-granular cracking in all metal surfaces exposed to the fuel salt. The cause of the embrittlement was tellurium - a fission product generated in the fuel. This was first noted in the specimens that were removed from the core at intervals during the reactor operation. Post-operation examination of pieces of a control-rod thimble, heat-exchanger tubes, and pump bowl parts revealed the ubiquity of the cracking and emphasized its importance to the MSR concept. The crack growth was rapid enough to become a problem over the planned thirty-year life of a follow-on thorium breeder reactor. This cracking could be reduced by adding small amounts of niobium to the Hastelloy-N.[18]
Decommissioning After shutdown the salt was believed to be in long-term safe storage, but beginning in the mid-1980s, there was concern that radioactivity was migrating through the system. Sampling in 1994 revealed concentrations of uranium that created a potential for a nuclear criticality accident, as well as a potentially dangerous build-up of fluorine gas — the environment above the solidified salt is approximately one atmosphere of fluorine. The ensuing decontamination and decommissioning project was called "the most technically challenging" activity assigned to Bechtel Jacobs under its environmental management contract with the U.S. Department of Energy's Oak Ridge Operations organization. In 2003, the MSRE cleanup project was estimated at about $130 million, with decommissioning expected to be completed in 2009.[19] A detailed description of potential decommissioning processes is described here.;[20] uranium is to be removed from the fuel as the hexafluoride by adding excess fluorine, and plutonium as the plutonium dioxide by adding sodium carbonate.
162
Molten-Salt Reactor Experiment
References [1] Briggs 1964, pp. 373–309. [2] P.N. Haubenreich and J.R. Engel (1970). "Experience with the Molten-Salt Reactor Experiment" (http:/ / www. energyfromthorium. com/ pdf/ NAT_MSREexperience. pdf) (PDF, reprint). Nuclear Applications and Technology 8: 118–136. . [3] R.C. Robertson (January 1965). MSRE Design and Operations Report, Part I, Description of Reactor Design. ORNL-TM-0728. [4] R.B. Lindauer (August 1969). Processing of the MSRE Flush and Fuel Salts. ORNL-TM-2578. [5] B.H. Webster (April 1970). Quality-Assurance Practices in Construction and Maintenance of the MSRE. ORNL-TM-2999. [6] DeVan, Jackson H. "EFFECT OF ALLOYING ADDITIONS ON CORROSION BEHAVIOR OF NICKEL - MOLYBDENUM ALLOYS IN FUSED FLUORIDE MIXTURES." Thesis. University of Tennessee, 1960. Web.
. [7] Briggs 1964, pp. 63–52. [8] H.E. McCoy et al. (1970). "New Developments in Materials for Molten-Salt Reactors". Nuclear Applications and Technology 8: 156. [9] Briggs 1964, pp. 334–343. [10] Briggs 1964, pp. 252–257. [11] Briggs 1964, pp. 167–190. [12] Briggs 1964. [13] M.W. Rosenthal, P.N. Haubenreich, H.E. McCoy, and L.E. McNeese (1971). "Current Progress in Molten-Salt Reactor Development". Atomic Energy Review IX: 601–50. [14] B.E. Prince, S.J. Ball, J.R. Engel, P.N. Haubenreich, and T.W. Kerlin (February 1968). Zero-Power Physics Experiments on the MSRE. ORNL-4233. [15] (https:/ / twugbcn. files. wordpress. com/ 2010/ 10/ lftr-and-anti-proliferation. pdf) (see PDF page 10) "The MSRE was fueled with 39 kilograms of 233U that contained ~220 parts per million (ppm) of 232U [...which was bred in] various Light Water Reactors that had operated on 235U (such as the Indian Point PWR)" [16] Molten Salt Reactor Experience Applicable to LS-VHTR Refueling (http:/ / www. ornl. gov/ ~webworks/ cppr/ y2001/ pres/ 124832. pdf) [17] R.B. Briggs (Winter 1971–72). "Tritium in Molten-Salt Reactors". Reactor Technology 14: 335–42. [18] Keiser, J.R. (1977), "Status of Tellurium-Hastelloy N Studies in Molten Fluoride Salts" (http:/ / www. moltensalt. org/ references/ static/ downloads/ pdf/ ORNL-TM-6002. pdf), Oak Ridge National Laboratories, ORNL/TM-6002, [19] R. Cathey Daniels, Elegant experiment puts wallop on cleanup (http:/ / nl. newsbank. com/ nl-search/ we/ Archives?p_action=doc& p_docid=110AF8020E01FF40& p_docnum=2& p_theme=gatehouse& s_site=TORB& p_product=TORB), The Oak Ridger, April 8, 2003. [20] Evaluation of the U.S. Department of Energy's Alternatives for the Removal and Disposition of Molten Salt Reactor Experiment Fluoride Salts (http:/ / books. nap. edu/ openbook. php?record_id=5538& page=R1) (1997), Commission on Geosciences, Environment and Resources
• Briggs, R. B. (1964). MSR Program Semiannual Progress Report for the period ending July 31, 1964 (http:// www.energyfromthorium.com/pdf/ORNL-3708.pdf). (ORNL-3708) (66.3 MB PDF), Oak Ridge National Laboratory, U.S. AEC (published November 1964). Retrieved 2008-05-21
163
PS210 experiment
PS210 experiment The PS210 experiment was the first experiment that led to the observation of antihydrogen atoms produced at the Low Energy Antiproton Ring (LEAR) at CERN in 1995. The antihydrogen atoms were produced in flight and moved at nearly the speed of light. They made unique electrical signals in detectors that destroyed them almost immediately after they formed by matter–antimatter annihilation. Eleven signals were observed, of which two were attributed to other processes. In 1997 similar observations were announced at Fermilab from the E862 experiment. The first measurement demonstrated the existence of antihydrogen, the second (with improved setup and intensity monitoring) measured the production rate. Both experiments, one at each of the only two facilities with suitable antiprotons, were stimulated by calculations which suggested the possibility of making very fast antihydrogen within existing circular accelerators.
Literature • A. Aste et al. (1994). "Electromagnetic pair production with capture". Physical Review A 50 (5): 3980–3983. Bibcode 1994PhRvA..50.3980A. doi:10.1103/PhysRevA.50.3980. PMID 9911369. • G. Baur et al. (1996). "Production of Antihydrogen". Physics Letters B 368 (3): 251. Bibcode 1996PhLB..368..251B. doi:10.1016/0370-2693(96)00005-6. • G. Blanford et al. (1998). "Observation of Antihydrogen". Physical Review Letters 80 (14): 3037. Bibcode 1998PhRvL..80.3037B. doi:10.1103/PhysRevLett.80.3037.
External links • http://hussle.harvard.edu/~atrap/Background/HotAntihydrogen.html
164
Trinity
165
Trinity Trinity
The Trinity explosion, 0.016 seconds after detonation. The fireball is about 600 feet (200 m) wide. The black specks silhouetted along the horizon are trees. Information Country
United States
Test site
Trinity Site, New Mexico
Date
July 16, 1945
Test type
Atmospheric
Device type
Fission
Yield
20 kilotons of TNT (unknown operator: u'strong' TJ) Navigation
Previous test
none
Next test
Operation Crossroads
Trinity Site U.S. National Register of Historic Places U.S. National Historic Landmark District
Trinity Site Obelisk
Trinity
166
Location:
White Sands Missile Range
Nearest city:
San Antonio, New Mexico
Coordinates:
33°40′38.28″N 106°28′31.44″W
Area:
36480 acres (unknown operator: u'strong' km2)
Built:
1945
[1]
NRHP Reference#: 66000493 Significant dates Added to NRHP:
[2]
October 15, 1966
Designated NHLD: December 21, 1965[3]
Trinity was the code name of the first detonation of a nuclear device. This test was conducted by the United States Army on July 16, 1945,[4][5][6][7][8] in the Jornada del Muerto desert about 35 miles (56 km) southeast of Socorro, New Mexico, at the new White Sands Proving Ground, which incorporated the Alamogordo Bombing and Gunnery Range. (The site is now the White Sands Missile Range.)[9][10] The date of the test is usually considered to be the beginning of the Atomic Age. Trinity was a test of an implosion-design plutonium device. The weapon's informal nickname was "The Gadget".[11] Using the same conceptual design, the Fat Man device was detonated over Nagasaki, Japan, on August 9, 1945. The Trinity detonation produced the explosive power of about 20 kilotons of TNT.
History The creation of atomic weapons arose out of political and scientific developments of the late 1930s. The rise of fascist governments in Europe, new discoveries about the nature of atoms and the fear that Nazi Germany was working on developing atomic bombs converged in the plans of the United States, the United Kingdom, and Canada to develop powerful weapons using nuclear fission as their primary source of energy. The Manhattan Project, as the American nuclear physics effort was called, culminated in the test of a nuclear weapon at what is now called the Trinity Site on July 16, 1945, and the atomic bombings of Hiroshima and Nagasaki just a few weeks later.
Trinity
167
The Manhattan Project U.S. and British researchers were investigating the feasibility of nuclear weapons as early as 1939. Practical development began in earnest in 1942 when these efforts were transferred to the authority of the U.S. Army and became the Manhattan Project. The weapons-development portion of this project was located at the Los Alamos Laboratory in northern New Mexico, though much other development and production work was carried out at the Clinton Engineer Works near Oak Ridge, Tennessee (the separation of uranium-235); the Hanford Engineer Works near Hanford, Washington (the production and separation of plutonium-239); in and near Chicago, Illinois (at the University of Chicago and at the Argonne National Laboratories); and at the University of California, Berkeley. These research, development, and production efforts focused both on the development of the necessary fissile materials to power the nuclear chain reactions in the atomic bombs and on the design, testing, and manufacture of the bombs themselves.[12]
The two types of fission-bomb assembly methods investigated during the Manhattan Project. The gun-type assembly was not tested before it was detonated at Hiroshima. However, because of the novel and untried features of the implosion-bomb design, Fat Man, J. Robert Oppenheimer and the other scientists at Los Alamos decided that it was necessary to test this one before attempting to utilize one as a weapon against the enemy.
From January 1944 until July 1945, large-scale production plants were set in operation, and the fissile material thus produced was then used to determine the features of the weapons. Multi-pronged research was undertaken to pursue several possibilities for bomb design. Early decisions about weapon design had been based on minute quantities of uranium-235 and plutonium that had been created in pilot plants and in physics-laboratory cyclotrons. From these experimental results, it was thought that the creation of a bomb was as simple as forming a critical mass of fissile material.[13] The productions of both uranium-235 and plutonium-239 were massive undertakings given the technology of the 1940s and accounted for 80% of the total costs of the project.[14] Theoretically, enriching uranium was feasible through pre-existing techniques in physics (e.g., modifying particle accelerator technology), though it proved difficult to scale to industrial levels and was extremely costly. Plutonium, by contrast, could theoretically be produced most easily in nuclear reactors, but the technology and science involved was wholly new. The first experimental nuclear reactor had been developed and constructed by Enrico Fermi and his team of co-workers by the end of 1942 at the University of Chicago (CP-1), which proved that there were no obvious physical limitations to producing a slow-neutron nuclear chain reaction. Work began on constructing massive plutonium-breeding reactors at Hanford, Washington, in October 1943. The first reactor-bred plutonium was produced in the B-Reactor, the first full-scale plutonium-production reactor in the world. The first large batch of plutonium was refined at Hanford in the "221-T plant", using the bismuth phosphate process, from December 26, 1944, to February 2, 1945. This was delivered to Oppenheimer's team at the Los Alamos laboratory on February 5, 1945. In the meantime, the X-10 Graphite Reactor, a scaled-down version of the Hanford reactors, was built in Oak Ridge, Tennessee, and went into operation in November 1943. Plutonium is a synthetic element not found in nature in appreciable quantities. It also has relatively complicated physics, chemistry, and metallurgy compared to most other elements in the periodic table. The only prior plutonium isolated for the project had been produced in cyclotrons in very minute amounts. In April 1944, Emilio Segrè received the first sample of reactor-bred plutonium from the X-10 reactor and discovered that reactor-grade plutonium was not as pure as cyclotron-produced plutonium by a significant degree. Specifically, the longer the plutonium remained irradiated inside the reactor — which is necessary for high yields of the metal — the greater its
Trinity content of the isotope plutonium-240. Pu-240 undergoes spontaneous fission at an appreciable rate, and that releases plenty of excess thermal neutrons. These extra neutrons implied a high probability that a gun-type bomb with plutonium would detonate too early, before a critical mass was formed, scattering the plutonium and producing a small "fizzle" of a nuclear explosion many times smaller than a full explosion. The practical result is that a simple gun-type atomic bomb (the proposed Thin Man) would not work as had been hoped. The impossibility of solving this problem of a gun-type bomb with plutonium was decided upon in a meeting in Los Alamos on June 17, 1944.[15] This forced a search for a different, more practical design of a plutonium-fueled bomb, and an implosion-type atomic-bomb design (i.e., the Fat Man design) was selected as the most practical one at that time. However, even this notion required a great deal of research work and experimentation in engineering and hydrodynamics before a practical design could be worked out. In an implosion bomb, a small spherical core of plutonium would be A diagram showing the bottom half of an surrounded by high explosives that burned with different speeds. By implosion design similar to the one used in the alternating the faster and slower burning explosives in a carefully Trinity gadget. The neutron initiator is at the calculated spherical configuration, they would produce a compressive center, surrounded by the plutonium core, wave upon their simultaneous detonation. This "lensing" effect focused surrounded by a pusher and tamper, surrounded by the explosive lenses, all within a casing. This the explosive force inward with enough force to physically compress diagram is not a literal depiction of the Trinity the plutonium core to several times its original density. This would gadget and contains a few elements not found in nearly instantly reduce the necessary size of the critical mass of the the actual gadget. material, making it supercritical. It would also activate a small neutron source kept at the center of the core, which would assure that the chain reaction began in earnest. The advantage of the implosion method was that it was far more efficient in use of material — only 6.2 kg of plutonium would be needed for a full explosion, compared to the 64 kg of enriched uranium used in the "Little Boy" weapon. The engineering difficulties, though, were daunting. Though explosive lenses had been pursued during the war, the art was still very new, and the tolerances required in terms of timing and symmetry were unprecedented. Should the timing or symmetry be off, the bomb would not detonate fully, and instead just disperse the plutonium into the surrounding area. The entire Los Alamos laboratory was reorganized in 1944 to focus on designing a workable implosion bomb. Scientists were confident that an implosion device would work, but these new design difficulties were great. It was decided that a full-sized test would be required before any military use, even though it would sacrifice one of a very small number of bombs. In early 1944, plans for a July 1945 test were finalized. The uranium weapon would not be tested; its success could be more or less guaranteed by measurements ahead of time. The actual Fat Man atomic bomb, which used the same design as in the Trinity test, was exploded over Nagasaki on August 9, 1945, after the Trinity test had proven its operability in an atomic explosion.
168
Trinity
The gadget "The gadget" was the code name given to the first bomb tested.[16] It was so called because it was not a deployable weapon and because revealing words like bomb were not used during the project for fear of espionage. It was an implosion-type plutonium device, similar in design to the Fat Man bomb used three weeks later in the atomic bombing of Nagasaki, Japan. In the Fat Man design, a subcritical sphere of plutonium was placed in the center of a hollow sphere of high explosive. Numerous exploding-bridgewire detonators located on the surface of the high explosive were fired simultaneously to produce a powerful inward pressure on the core, squeezing it and increasing its density, resulting in a supercritical condition and a nuclear explosion. The actual eventual Fat Man and the "gadget" devices were not strictly "Fat Man type", as the design was modified into a production design, and both were strictly one-off prototypes. The gadget was tested at Trinity Site, New Mexico, near Alamogordo. For the test, the gadget was lifted to the top of a 100-foot (unknown operator: u'strong' m) bomb tower. It was feared by some that the Trinity test might "ignite" the earth's atmosphere, eliminating all life on the planet, although calculations had determined this was unlikely.[17][18] Less wild estimates thought that New Mexico would Schematic cross-section of the gadget. See Fat Man article for details. be incinerated. Calculations showed that the yield of the device would be between 0 (if it did not work) and 20 kilotons (metric, equivalence of TNT). In the aftermath of the test, it appeared to have been a blast equivalent to 18 kt of TNT.
Test planning In March 1944, planning for the test was assigned to Kenneth Bainbridge, a professor of physics at Harvard University, working under explosives expert George Kistiakowsky. A site had to be located that would guarantee secrecy of the project's goals even as a nuclear weapon of unknown strength was detonated. Proper scientific equipment had to be assembled for retrieving data from the test itself, and safety guidelines had to be developed to protect personnel from the unknown results of a highly dangerous experiment. Official test photographer Berlyn Brixner set up dozens of cameras to capture the event on film.
Test site The heads of the project considered eight candidate sites, including San Nicolas Island (California), Padre Island (Texas), San Luis Valley, El Malpais National Monument, and other parts of New Mexico. A Mojave Desert Army base near Rice, California was considered the best location, but was opted against because General Leslie Groves, military head of the project, did not wish to have any dealings with Gen. George S. Patton, commander of the base, whom he disliked.[19] The site finally chosen was at the northern end of the White Sands Proving Ground, in Socorro County between the towns of Carrizozo and San Antonio, in the Jornada del Muerto in the southwestern United Trinity Site (red arrow) near Carrizozo Malpais States (33°40′38″N 106°28′31″W).[20] In late 1944, soldiers started arriving at Trinity Site to prepare for the test. Sgt. Marvin Davis and his military police unit arrived at the site from Los Alamos on December 30, 1944. This unit set up initial security checkpoints around the area, with plans to use horses for patrols. The distances around the site proved too great, so they resorted to using jeeps and trucks for transportation.
169
Trinity
170
Throughout 1945, other personnel arrived at Trinity Site to help prepare for the bomb test. As the soldiers at Trinity Site settled in, they became familiar with Socorro County. They tried to use water out of the ranch wells, but found the water so alkaline they could not drink it. They were forced to use U.S. Navy saltwater soap and hauled drinking water in from the firehouse in Socorro. Gasoline and diesel fuel were purchased from the Standard Oil bulk plant in Socorro. Three bunkers were set up to observe the test.[21] Oppenheimer and Brig. Gen. Thomas Farrell watched from the South bunker 9.1 km (5.7 miles) from the detonation, while Gen. Leslie Groves watched from the base camp 16 km (10 miles) away.[22]
Name The exact origin of the name is unknown, but it is often attributed to laboratory leader J. Robert Oppenheimer as a reference to the poetry of John Donne. In 1962, General Groves wrote to Oppenheimer about the origin of the name, asking if he had chosen it because it was a name common to rivers and peaks in the West and would not attract attention, and elicited this reply:[23] I did suggest it, but not on that ground... Why I chose the name is not clear, but I know what thoughts were in my mind. There is a poem of John Donne, written just before his death, which I know and love. From it a quotation: "As West and East / In all flatt Maps—and I am one—are one, / So death doth touch the Resurrection."[24][25] That still does not make a Trinity, but in another, better known devotional poem Donne opens, "Batter my heart, three person'd God;—."[26][27]
Test predictions The observers set up betting pools on the results of the test.[28][29] Predictions ranged from zero (a complete dud) to 45 kilotons of TNT, to destruction of the state of New Mexico, to ignition of the atmosphere and incineration of the entire planet. This last result had been calculated to be almost impossible,[17][18] although for a while it caused some of the scientists some anxiety. Physicist I. I. Rabi won the pool with a prediction of 18 kilotons.[30]
The explosives of the gadget were raised up to the top of the tower for the final assembly.
Test preparation A pre-test calibration explosion of 108 tons of TNT, spiked with 1000 curies (unknown operator: u'strong' TBq) of fission products from the Hanford reactor, was detonated on a wooden platform 800 yards to the south-east of Trinity ground zero on May 7. For the actual test, the plutonium-core nuclear device, nicknamed "the gadget", was hoisted to the top of a 100-foot-tall steel tower (unknown operator: u'strong' m) for detonation — the height would give a better indication of how the weapon would behave when dropped from High explosive stack of the 100 tons test
Trinity
171
an airplane, as detonation in the air would maximize the amount of energy applied directly to the target (as it expanded in a spherical shape) and would generate less nuclear fallout. The gadget was assembled at the nearby McDonald Ranch House on July 13, the components having arrived on July 12. After assembly, it was carefully winched up the tower the following day. General Groves had ordered the construction of a 214-ton steel canister code-named "Jumbo" to recover valuable plutonium if the five tons of conventional explosives failed to compress it into a chain reaction. The container was constructed at great expense in Pittsburgh, Pennsylvania, and brought to the test site by rail, but by the time it arrived, the confidence The gadget, fully assembled and ready to test of the scientists was high enough that they decided not to use it. Instead, it was hoisted up in a steel tower 800 yards (730 m) from the gadget as a rough measure of how powerful the explosion would be. In the end, Jumbo survived, though its tower did not. The detonation was initially planned for 4:00 am but was postponed because of rain and lightning from early that morning. It was feared that the danger from radiation and fallout would be greatly increased by rain, and lightning had the scientists concerned about accidental detonation.[31]
The 100-foot-tall tower constructed for the test
Trinity
172
Explosion At 4:45 am, a crucial weather report came in favorably, and, at 5:10 am, the twenty-minute countdown began. Most top-level scientists and military officers were observing from a base camp ten miles (16 km) southwest of the test tower. Many other observers were around twenty miles (32 km) away, and some others were scattered at different distances, some in more informal situations (physicist Richard Feynman claimed to be the only person to see the explosion without the dark glasses provided, relying on a truck windshield to screen out harmful ultraviolet wavelengths).[32] The final countdown was read by physicist Samuel K. Allison. At 05:29:45 local time (Mountain War Time), the device exploded with an energy equivalent to around 20 kilotons of TNT (90 TJ). It left a crater of radioactive glass in the desert 10 feet (3 m) deep and 1,100 Color photograph of the Trinity explosion by feet (330 m) wide. At the time of detonation, the surrounding Jack Aeby mountains were illuminated "brighter than daytime" for one to two seconds, and the heat was reported as "being as hot as an oven" at the base camp. The observed colors of the illumination ranged from purple to green and eventually to white. The roar of the shock wave took 40 seconds to reach the observers.[29] The shock wave was felt over 100 miles (160 km) away, and the mushroom cloud reached 7.5 miles (12 km) in height. After the initial euphoria of witnessing the explosion had passed, test director Kenneth Bainbridge commented to Los Alamos director J. Robert Oppenheimer, "Now we are all sons of bitches."[33] Oppenheimer later stated that, while watching the test, he was reminded of a line from the Bhagavad Gita, a Hindu scripture: Now I am become Death, the destroyer of worlds.[34][35] In the official report on the test, General Farrell wrote, "The lighting effects beggared description. The whole country was lighted by a searing light with the intensity many times that of the midday sun. It was golden, purple, violet, gray, and blue. It lighted every peak, crevasse and ridge of the nearby mountain range with a clarity and beauty that cannot be described but must be seen to be imagined..."[36] News reports quoted a forest ranger 150 miles (240 km) west of the site as saying he saw "a flash of fire followed by an explosion and Ground zero after the test black smoke." A New Mexican 150 miles (240 km) north said, "The explosion lighted up the sky like the sun." Other reports remarked that windows were rattled and the sound of the explosion could be heard up to 200 miles (320 km) away. John R. Lugo was flying a U.S. Navy transport at 10000 feet (unknown operator: u'strong' m), 30 miles (unknown operator: u'strong' km) east of Albuquerque, en route to the west coast. "My first impression was, like, the sun was coming up in the south. What a ball of fire! It was so bright it lit up the cockpit of the plane." Lugo radioed Albuquerque. He got no explanation for the blast but was told, "Don't fly south."[37] In the crater, the desert sand, which is largely made of silica, melted and became a mildly radioactive light green glass, which was named Trinitite.[38] The crater was filled in soon after the test.
Trinity
173
The Alamogordo Air Base issued a 50-word press release in response to what it described as "several inquiries" that had been received concerning an explosion. The release explained that "a remotely located ammunitions magazine containing a considerable amount of high explosives and pyrotechnics exploded," but that "there was no loss of life or limb to anyone." A newspaper article published the same day stated that "the blast was seen and felt throughout an area extending from El Paso to Silver City, Gallup, Socorro, and Albuquerque."[39] The actual cause was not publicly acknowledged until after the August 6 bombing of Hiroshima. An aerial photograph of the Trinity crater shortly
The Manhattan Project's official journalist, William L. Laurence, had after the test. The small crater in the southeast corner was from the earlier test explosion of 108 put multiple press releases on file with his office at The New York tons of TNT. Times to be released in case of an emergency, ranging from an account of a successful test (the one which was used) to more macabre scenarios involving serious damage to surrounding communities, evacuation of nearby residents, and a placeholder for the names of those killed in the explosion.[40][41] Around 260 personnel were present, none closer than 5.6 miles (9 km). At the next test series, Operation Crossroads in 1946, over 40,000 people were present.[42] The official technical report (LA-6300-H) on the history of the Trinity test was not released until May 1976.[43]
Test results The results of the test were conveyed to President Harry S. Truman, who was eagerly awaiting them at the Potsdam Conference; the coded message ("Operated this morning. Diagnosis not complete but results seem satisfactory and already exceed expectations. . . . Dr. Groves pleased.") arrived at 7:30 p.m. on July 16 and was at once taken to the president and Secretary of State James F. Byrnes at the "Little White House" in the Berlin suburb of Babelsberg by Secretary of War Henry L. Stimson.[44] Information about the Trinity test was made public shortly after the bombing of Hiroshima. The Smyth Report, released on August 12, 1945, gave some information on the blast, and the hardbound edition released by Princeton University Press a few weeks later contained the famous pictures of a "bulbous" Trinity fireball. Oppenheimer and Groves posed for reporters near the remains of the mangled test tower shortly after the war. In the years after the test, the pictures have become a potent symbol of the beginning of the so-called Atomic Age, and the test has often been featured in popular culture.
Trinity
174
Fallout around the Trinity site in Röntgens. The radioactive cloud moved towards the northeast with high radiation levels within about 100 miles (unknown operator: u'strong' km).
Maj. Gen. Leslie R. Groves and Robert Oppenheimer at the Trinity shot tower remains a few weeks later
First deployment Following the success of the Trinity test, two bombs were prepared for use against Japan during World War II. The first, dropped on Hiroshima, Japan, on August 6, was code-named "Little Boy", and used uranium-235 as its fission source. It was an untested design but was considered very likely to work and was considerably simpler than the implosion model. It could not be tested, because there was only enough uranium-235 for one bomb. The second bomb, dropped on Nagasaki, Japan, on August 9, was code-named "Fat Man" and was a plutonium bomb of the type tested at Trinity. The atomic bombings of Hiroshima and Nagasaki killed at least 148,000 people and many more over time. By 1950, the death toll was over 340,000.[45] They were followed days later by the surrender of Japan. Debate over the justification of the use of nuclear weapons against Japan persists to this day, both in scholarly and popular circles.
Site today In 1952, the site of the explosion was bulldozed, and the remaining trinitite was disposed of. On December 21, 1965, the 51500-acre (unknown operator: u'strong' ha) area Trinity Site was declared a National Historic Landmark district[1][3] and, on October 15, 1966, was listed on the National Register of Historic Places.[2]
Trinity Site Historical Marker
The landmark includes the base camp, where the scientists and support group lived; ground zero, where the bomb was placed for the explosion; and the Schmidt/McDonald ranch house, where the plutonium core to the bomb was assembled. Visitors to a Trinity Site open house are allowed to see the ground zero and ranch house areas. In addition, one of the old instrumentation bunkers is visible beside the road just west of ground zero.
Trinity
175
In September 1953, about 650 people attended the first Trinity Site open house. In recent years, the site has been opened for public visits twice each year, on the first Saturdays in April and October.[46]
Remnants of Jumbo
In 1967, the inner oblong fence was added. In 1972, the corridor barbed wire fence that connects the outer fence to the inner one was completed. Jumbo was moved to the parking lot in 1979. More than sixty years after the test, residual radiation at the site measured about ten times higher than normal.[47] The amount of radioactive exposure received during a one-hour visit to the site is about half of the total radiation exposure which a U.S. adult receives on an average day from natural and medical sources.[48] The Trinity monument, a rough-sided, lava-rock obelisk around 12 feet (3.65 m) high, marks the explosion's hypocenter, and Jumbo is still kept nearby.
Tourists at ground zero
On July 16, 2005, a special tour of the site was conducted to mark the 60th anniversary of the Trinity test, and hundreds (some news sources reported thousands) of visitors arrived to commemorate the occasion. The site is still a popular destination for those interested in atomic tourism, though it is only open to the public twice a year during open houses, on the first Saturdays of April and October.[49]
References [1] Richard Greenwood (January 14, 1975) (PDF). National Register of Historic Places Inventory-Nomination: Trinity Site (http:/ / pdfhost. focus. nps. gov/ docs/ NHLS/ Text/ 66000493. pdf). National Park Service. . Retrieved 2009-06-21 and Accompanying 10 photos, from 1974. (http:/ / pdfhost. focus. nps. gov/ docs/ NHLS/ Photos/ 66000493. pdf)PDF (3.37 MB) [2] "National Register Information System" (http:/ / nrhp. focus. nps. gov/ natreg/ docs/ All_Data. html). National Register of Historic Places. National Park Service. 2007-01-23. . [3] "Trinity Site" (http:/ / tps. cr. nps. gov/ nhl/ detail. cfm?ResourceID=351& resourceType=District). National Historic Landmarks. National Park Service. . Retrieved 2008-01-28. [4] Ferenc Morton Szasz, The Day The Sun Rose Twice: The Story of the Trinity Site Nuclear Explosion July 16, 1945 (University of New Mexico Press, 1984). ISBN 978-0-8263-0768-2 [5] "The First Atomic Bomb Blast, 1945" (http:/ / www. eyewitnesstohistory. com/ atomictest. htm). Eyewitnesstohistory.com. . Retrieved 2010-02-28. [6] Chris Demarest. "Atomic Bomb-Truman Press Release-August 6, 1945" (http:/ / www. trumanlibrary. org/ teacher/ abomb. htm). Trumanlibrary.org. . Retrieved 2010-02-28. [7] "Final Preparations for Rehearsals and Test | The Trinity Test | Historical Documents" (http:/ / www. atomicarchive. com/ Docs/ Trinity/ FinalPreparations. shtml). atomicarchive.com. . Retrieved 2010-02-28. [8] "TRINITY TEST - JULY 16, 1945" (http:/ / www. radiochemistry. org/ history/ nuke_tests/ trinity/ index. html). Radiochemistry.org. . Retrieved 2010-02-28. [9] "Safety and the Trinity Test, July 1945" (http:/ / www. cfo. doe. gov/ me70/ manhattan/ trinity_safety. htm). Cfo.doe.gov. . Retrieved 2010-02-28.
Trinity
176
[10] "Atomic Bomb: Decision - Trinity Test, July 16, 1945" (http:/ / www. dannen. com/ decision/ trin-rad. html). Dannen.com. . Retrieved 2010-02-28. [11] Kathryn Westcott: bbc.co.uk The day the world lit up (http:/ / news. bbc. co. uk/ 2/ hi/ americas/ 4641861. stm), BBC, Friday, 15 July 2005. [12] Hans Bethe (1991), The Road from Los Alamos. American Institute of Physics ISBN 0-671-74012-1 [13] "The Manhattan Project / Making the Atomic Bomb" (http:/ / www. osti. gov/ accomplishments/ pdf/ DE99001330/ DE99001330. pdf) (PDF). United States Department of Energy. 1999. . Retrieved 2008-01-24. [14] The Costs of the Manhattan Project (http:/ / www. brookings. edu/ projects/ archive/ nucweapons/ manhattan. aspx), Brookings Institution (accessed 10 August 2010) [15] Manhattan Project Chronology (http:/ / www. atomicarchive. com/ History/ mp/ chronology. shtml) at AtomicArchive.com [16] Kathryn Westcott: The day the world lit up, BBC, Friday, 15 July 2005, bbc.co.uk (http:/ / news. bbc. co. uk/ 2/ hi/ americas/ 4641861. stm). [17] Richard Hamming (1998). "Mathematics on a Distant Planet" (http:/ / www. jstor. org/ pss/ 2589247). The American mathematical monthly (JSTOR) 105 (7): 640–650. . [18] "Report LA-602, ''Ignition of the Atmosphere With Nuclear Bombs''" (http:/ / www. fas. org/ sgp/ othergov/ doe/ lanl/ docs1/ 00329010. pdf) (PDF). . Retrieved 2011-10-19. [19] "Trinity Atomic Web Site" (http:/ / www. cddc. vt. edu/ host/ atomic/ trinity/ trinity1. html). Walker, Gregory. . Retrieved 2010-08-20. [20] "Trinity Site" (http:/ / web. archive. org/ web/ 20080601033016/ http:/ / www. wsmr. army. mil/ pao/ TrinitySite/ trinst. htm). White Sands Missile Range. Archived from the original (http:/ / www. wsmr. army. mil/ pao/ TrinitySite/ trinst. htm) on 2008-06-01. . Retrieved 2007-07-16. "GPS Coordinates for obelisk (exact GZ) = N33.40.636 W106.28.525" [21] Rhodes, p. 653. [22] Rhodes, p. 675. [23] Richard Rhodes, The Making of the Atomic Bomb (New York: Simon and Shuster, 1986), pp. 571–572. [24] John Donne, "Hymne to God My God, in My Sicknesse". The excerpt is about half of the third five-line stanza out of six. [25] Hymn to god, my god, in my sickness (http:/ / www. luminarium. org/ sevenlit/ donne/ sickness. htm) Source: Donne, John. Poems of John Donne. vol I. E. K. Chambers, ed. London: Lawrence & Bullen, 1896. 211–212. [26] John Donne, Holy Sonnets, XIV. The clause is the truncated first line of a four-line sentence from the (14-line) sonnet. [27] Holy sonnets. XIV (http:/ / www. luminarium. org/ sevenlit/ donne/ sonnet14. php) Source: Donne, John. Poems of John Donne. vol I. E. K. Chambers, ed. London: Lawrence & Bullen, 1896. 165. [28] Rhodes, pages 656 and 664. [29] James Hershberg (1993), James B. Conant: Harvard to Hiroshima and the Making of the Nuclear Age. 948 pp. ISBN 0-394-57966-6 p. 233 [30] Rhodes, p. 677. [31] "Countdown" (http:/ / www. cfo. doe. gov/ me70/ manhattan/ publications/ LANLBeginningofEraPart5. pdf) (PDF). Los Alamos: Beginning of an Era, 1943–1945. Los Alamos Scientific Laboratory. ca. 1967–1971. . Retrieved 2008-01-24. [32] Richard Feynman (2000), The Pleasure of Finding Things Out p. 53–96 ISBN 0-7382-0349-1 [33] "The Trinity Test" (http:/ / www. cfo. doe. gov/ me70/ manhattan/ trinity. htm). United States Department of Energy. . Retrieved 2009-04-08. [34] Variants on this quotation exist, both by Oppenheimer and by others. A more common translation of the passage, from Arthur W. Ryder (from whom Oppenheimer studied Sanskrit at Berkeley in the 1930s), is:
Death am I, and my present task Destruction. (11:32) Since the Gita's first translation into English in 1785, most experts have translated not "Death" but instead "Time". A further elaboration of the supposed Oppenheimer quote often cited is taken from Robert Jungk's 1958 Brighter than a Thousand Suns: If the radiance of a thousand suns were to burst into the sky, that would be like the splendor of the Mighty One— I am become Death, the shatterer of Worlds. For an extensive discussion of the quote, its various translations, and its various reported forms, see James A. Hijiya, "The Gita of Robert Oppenheimer" (http:/ / www. amphilsoc. org/ sites/ default/ files/ Hijiya. pdf) Proceedings of the American Philosophical Society, 144:2 (June 2000). [35] Richard Rhodes, The Making of the Atomic Bomb (New York: Simon and Shuster, 1986). Quotes after the test from p. 675–676. [36] "Chronology on Decision to Bomb Hiroshima and Nagasaki" (http:/ / www. nuclearfiles. org/ menu/ key-issues/ nuclear-weapons/ history/ pre-cold-war/ hiroshima-nagasaki/ decision-drop-bomb-chronology. htm). . [37] The Trinity Test: Eyewitnesses (http:/ / larrycalloway. com/ historic. html?_recordnum=105)
Trinity [38] P.P. Parekh; T.M. Semkow, M.A. Torres, D.K. Haines, J.M. Cooper, P.M. Rosenberg and M.E. Kitto (2006). "Radioactivity in Trinitite six decades later". Journal of Environmental Radioactivity 85 (1): 103–120. doi:10.1016/j.jenvrad.2005.01.017. PMID 16102878. [39] "Army Ammunition Explosion Rocks Southwest Area," El Paso Herald-Post, 1945-7-16, p.1 (quoting the full press release)(retrieved from Newspaperarchive.com 2007-8-15). [40] William L. Laurence, "Now We Are All Sons-of-Bitches," Science News vol. 98, no. 2 (11 July 1970): pp. 39–41. [41] "Weekly Document #1: Trinity test press releases (May 1945)" (http:/ / nuclearsecrecy. com/ blog/ 2011/ 11/ 10/ weekly-document-01/ ). .. Also the text of the press releases (http:/ / nuclearsecrecy. com/ blog/ wp-content/ uploads/ 2011/ 11/ 1945-05-14-Trinity-Test-fake-press-releases. pdf).}} [42] "Operation Crossroads: Fact Sheet" (http:/ / www. history. navy. mil/ faqs/ faq76-1. htm). Department of the navy—naval historical center. 2002-08-11. . Retrieved 2008-01-24. [43] Bainbridge, K.T., Trinity (Report LA-6300-H) (http:/ / www. fas. org/ sgp/ othergov/ doe/ lanl/ docs1/ 00317133. pdf), Los Alamos Scientific Laboratory. [44] Gar Alperovitz, The Decision to Use the Atomic Bomb and the Architecture of an American Myth (New York: Alfred A. Knopf, 1995), p. 240. [45] From: Hughes, Jeff. The Manhattan Project: Big Science and The Atom Bomb. New York: Columbia University Press, 2002. (p.95) [46] "military" (http:/ / www. white-sands-new-mexico. com/ military. htm). White Sands, New Mexico. . Retrieved 2011-10-19. [47] Brian Greene (2003), Nova: The Elegant Universe: Einstein's Dream. PBS Nova transcript (http:/ / www. pbs. org/ wgbh/ nova/ transcripts/ 3012_elegant. html) Regarding residual radiation. [48] WSMR article on Trinity nuclear test site (http:/ / www. wsmr. army. mil/ pao/ TrinitySite/ trnrad. htm) [49] "Entrance fee to be charged for future Trinity Site open houses" (http:/ / www. wsmr. army. mil/ PAO/ Trinity/ Pages/ default. aspx). . Retrieved April 29, 2011.
External links • Official report LA-6300-H (http://library.lanl.gov/cgi-bin/getfile?00317133.pdf) by Bainbridge, declassified as a "comprehensive record" in 1976 and containing "almost all the original text previously published as LA-1012". • Very High Resolution Photograph of The Trinity Obelisk (http://parkerlab.bio.uci.edu/pictures/photography pictures/Trinity Site_Ground Zero Obelisk.jpg) • Trinity Remembered: 60th Anniversary (http://www.trinityremembered.com) • BBC article on the 60th Anniversary (http://news.bbc.co.uk/1/hi/world/americas/4641861.stm) • Atomic tourism: Information for visitors (http://www.atomictourist.com/trinity.htm) • The Trinity test (http://www.lanl.gov/history/atomicbomb/trinity.shtml) on the Los Alamos National Laboratory website • Carey Sublette's Nuclear Weapon Archive Trinity page (http://nuclearweaponarchive.org/Usa/Tests/Trinity. html) • The Trinity test (http://www.sandia.gov/LabNews/LN11-03-00/trinity_story.html) on the Sandia National Laboratories website • The Trinity test (http://www.wsmr.army.mil/wsmr.asp?pg=y&page=579) on the White Sands Missile Range website • Richard Feynman, "Los Alamos from Below" (http://calteches.library.caltech.edu/14/01/ FeynmanLosAlamos.pdf); Surely, You're Joking, Mr. Feynman. • Trinity Test Fallout Pattern (http://www.atomicarchive.com/Maps/TrinityMap.shtml) • Trinity Test Photographs (http://www.atomicarchive.com/Photos/Trinity/index.shtml) • Trinity: First Test of the Atomic Bomb (http://www.olive-drab.com/od_nuclear_trinity.php) • "My Radioactive Vacation" (http://www.randomuseless.info/vacation/vacation.html), report of a visit to the Trinity site, with pictures comparing its past with its present state • Visiting Trinity (http://3quarksdaily.blogs.com/3quarksdaily/2005/08/poison_in_the_i.html) Short article by Ker Than at 3 Quarks Daily (http://3quarksdaily.com) • "War Department release on New Mexico test, July 16, 1945" (http://www.atomicarchive.com/Docs/ SmythReport/smyth_appendix_6.shtml), from the Smyth Report, with eyewitness reports from Gen. Groves and Gen. Farrell (1945)
177
Trinity
178
• Trinity Site National Historic Landmark (http://tps.cr.nps.gov/nhl/detail.cfm?ResourceId=351& ResourceType=District) • Trinity A bomb test photos on The UK National Archives' website. (http://www.nationalarchives.gov.uk/ documentsonline/featuresonline.asp#what) • Annotated bibliography for the Trinity Test from the Alsos Digital Library for Nuclear Issues (http://alsos.wlu. edu/adv_rst.aspx?query=trinity&selection=keyword&results=10) • Video of the Trinity Weapon Test (http://www.sonicbomb.com/modules.php?name=Content& pa=showpage&pid=43) at sonicbomb.com (http://www.sonicbomb.com) • The short film Nuclear Test Film - Trinity Shot (1945) (http://www.archive.org/details/gov.doe.0800001) is available for free download at the Internet Archive [more] • The short film Nuclear Test Film - Nuclear Testing Review (1945) (http://www.archive.org/details/gov.doe. 0800000) is available for free download at the Internet Archive [more] • The short film Atomic Weapons Tests: TRINITY through BUSTER-JANGLE (1952) (http://www.archive.org/ details/AtomicWeaponsTestsTrinitythroughBusterJangle) is available for free download at the Internet Archive [more]
• The short film WORLD CELEBRATES PEACE, VJ DAY, 08/12/1945 (1945) (http://www.archive.org/details/ gov.archives.arc.23976) is available for free download at the Internet Archive [more] (WORLD IN FILM, ISSUE NUMBER 19 - THE ATOM BOMB)
179
Quantum mechanics Afshar experiment The Afshar experiment is an optical experiment, devised and carried out by Shahriar Afshar in 2001, which investigates the principle of complementarity in quantum mechanics. The result of the experiment, that a grid of wires can be ignored when both slits are open, is in accordance with the standard predictions of quantum mechanics; however, it is controversially claimed to violate complementarity[1] and specifically the Englert–Greenberger duality relation; [2] others disagree.[3][4][5][6][7]
Overview Afshar's experiment uses a variant of Thomas Young's classic double-slit experiment to create interference patterns to investigate complementarity. Such interferometer experiments typically have two "arms" or paths a photon may take.[8] One of Afshar's assertions is that, in his experiment, it is possible to check for interference fringes of a photon stream (a measurement of the wave nature of the photons) while at the same time observing each photon's path (a measurement of the particle nature of the photons).[8][9]
History Shahriar S. Afshar's experimental work was done initially at the Institute for Radiation-Induced Mass Studies (IRIMS) in Boston in 2001 and later reproduced at Harvard University in 2003, while he was a research scholar there.[10] The results were presented at a Harvard seminar in March 2004,[11] and published as conference proceeding by the International Society for Optical Engineering (SPIE).[8] The experiment was featured as the cover story in the July 24, 2004 edition of New Scientist.[10][12] The New Scientist feature article itself generated many responses, including various letters to the editor that appeared in the August 7 and August 14, 2004 issues, arguing against the conclusions being drawn by Afshar, with John G. Cramer's response.[13] Afshar presented his work also at the American Physical Society meeting in Los Angeles, in late March 2005.[14] His peer-reviewed paper was published in Foundations of Physics in January 2007.[2] Afshar claims that his experiment invalidates the complementarity principle and has far-reaching implications for the understanding of quantum mechanics, challenging the Copenhagen interpretation. According to Cramer, Afshar's results support Cramer's own transactional interpretation of quantum mechanics and challenge the many-worlds interpretation of quantum mechanics.[15] This claim has not been published in a peer reviewed journal.
Afshar experiment
180
Experimental setup The experiment uses a setup similar to that for the double-slit experiment. In Afshar's variant, light generated by a laser passes through two closely spaced circular pinholes (not slits). After the dual pinholes, a lens refocuses the light so that the image of each pinhole falls on separate photon-detectors (Fig. 1). A photon that goes through pinhole number one impinges only on detector number one, and similarly, if it goes through pinhole two it impinges only on detector number two, which is why we see the pinholes separately in the image plane close to the mirrors before the photon-detectors.
Fig.1 Experiment without obstructing wire grid
Fig.2 Experiment with obstructing wire grid and one pinhole covered
When the light acts as a wave, because of quantum interference one can observe that there are regions that the photons avoid, called dark fringes. A grid of thin wires is placed just before the lens (Fig. 2) so that the wires lie in the dark fringes of an interference pattern which is produced by the dual pinhole setup. If one of the pinholes is blocked, the interference pattern will no longer be formed, and some of the light will be blocked by the wires. Consequently, the image quality is reduced. When one pinhole is closed, the grid of wires causes appreciable diffraction in the light, and blocks a certain amount of light received by the corresponding photon-detector. However, when both pinholes are open, the effect of the wires is negligible, comparable to the case in which there are no wires placed in front of the lens (Fig.3), because the wires lie in the dark fringes, which the photons avoid. The effect is not dependent on the light intensity (photon flux).
Interpretation Afshar's conclusion is that the light exhibits wave-like behavior when going past the wires, since the light goes through the spaces between the wires, but avoids the wires themselves, when both slits were open, but also exhibits particle-like behavior after going through the lens, with photons going to a given photo-detector. Afshar argues that this behavior contradicts the principle of complementarity, since it shows both complementary wave and particle characteristics in the same experiment for the same photons.
Afshar experiment
Specific critiques A number of scientists have published criticisms of Afshar's interpretation of his results. They are united in their rejection of the claims of a violation of complementarity, while differing in the way they explain how complementarity copes with the experiment. Afshar has responded to these critics in his academic talks, his blog, and other forums. The most recent work claims that Afshar's core claim, that the Englert–Greenberger duality relation is violated, is not true. They re-ran the experiment, using a different method for measuring the visibility of the interference pattern than that used by Afshar, and found Fig.3 Experiment with wire grid and both pinholes open. The wires no violation of complementarity, concluding "This lie in the dark fringes and thus block very little light result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics."[5] Below is a synopsis of the papers by critics highlighting their main arguments, and the disagreements they have amongst themselves: Some researchers claim that, while the fringe visibility is high, no which-way information ever exists: • Ruth Kastner [16], Committee on the History and Philosophy of Science, University of Maryland, College Park.[3][17] Kastner's criticism, published in a peer-reviewed paper, proceeds by setting up a gedanken experiment and applying Afshar's logic to it to expose its flaw. She proposes that Afshar's experiment is equivalent to preparing an electron in a spin-up state and then measuring its sideways spin. This does not imply that one has found out the up-down spin state and the sideways spin state of any electron simultaneously. Applied to Afshar's experiment: "Nevertheless, even with the grid removed, since the photon is prepared in a superposition S, the measurement at the final screen at t2 never really is a 'which-way' measurement (the term traditionally attached to the slit-basis observable ), because it cannot tell us 'which slit the photon actually went through.' In addition she underscores her conclusion with an analysis of the Afshar setup within the framework of the transactional interpretation of quantum mechanics. A follow-up e-print by Kastner "On Visibility in the Afshar Experiment" argues that the commonly referenced inverse relationship between visibility parameter V and which-way parameter K does not apply to the Afshar setup, which post-selects for "which slit" after allowing interference to take place. • Kastner's setup has been criticised, and an alternative proposed: Why Kastner analysis does not apply to a modified Afshar experiment [18] (by Eduardo Flores and Ernst Knoesel [19] [2007/02]) Abstract: In an analysis of the Afshar experiment R.E. Kastner points out that the selection system used in this experiment randomly separates the photons that go to the detectors, and therefore no which-way information is obtained. In this paper we present a modified but equivalent version of the Afshar experiment that does not contain a selection device. The double-slit is replaced by two separate coherent laser beams that overlap under a small angle. At the intersection of the beams an interference pattern can be inferred in a non-perturbative manner, which confirms the existence of a superposition state. In the far field the beams separate without the use of a lens system. Momentum conservation warranties that which-way information is preserved. We also propose an alternative sequence of Stern–Gerlach devices that represents a close analogue to the Afshar experimental set up.
181
Afshar experiment • Daniel Reitzner [20] (Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia), Comment on Afshar’s experiments [21] arXiv:quant-ph/0701152 (2007). Reitzner performed numerical simulations, published in a preprint, of Afshar's arrangement and obtained the same results that Afshar obtained experimentally. From this he argues that the photons exhibit wave behavior, including high fringe visibility but no which-way information, up to the point they hit the detector: "In other words the two-peaked distribution is an interference pattern and the photon behaves as a wave and exhibits no particle properties until it hits the plate. As a result a which-way information can never be obtained in this way." Other researchers agree that the fringe visibility is high and that the which-way information is not simultaneously measured, but they believe that the which-way information does exist under some circumstances. • W. G. Unruh, Professor of Physics at University of British Columbia[22] Unruh, who has published his objections on the web pages of his university, is probably the most prominent critic of Afshar's interpretation. He, like Kastner, proceeds by setting up an arrangement that he feels is equivalent but simpler. The size of the effect is larger so that it is easier to see the flaw in the logic. In Unruh's view that flaw is, in the case that an obstacle exists at the position of the dark fringes, "drawing the inference that IF the particle was detected in detector 1, THEN it must have come from path 1. Similarly, IF it were detected in detector 2, then it came from path 2." In other words, he accepts the existence of an interference pattern but rejects the existence of which-way information when Afshar puts in the wire grid. • Tabish Qureshi [23] (Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi), Modified Two-Slit Experiments and Complementarity [24], arXiv:quant-ph/0701109 (2007). Qureshi, in his preprint, does a wave-packet analysis of the Afshar experiment, and argues that even though Afshar's experiment has genuine interference, individual detectors clicking do not give which-path information. Through a mathematical analysis he argues that in the region of overlap of the wave-packets, if the state is such that the modulus square of the wave-function gives an interference pattern, the which-path information is necessarily lost. Another group does not question the which-way information, but rather contends that the measured fringe visibility is actually quite low: • Luboš Motl, Former Assistant Professor of Physics, Harvard University.[25] Motl's criticism, published in his blog, is based on an analysis of Afshar's actual setup, instead of proposing a different experiment like Unruh and Kastner. In contrast to Unruh and Kastner, he believes that which-way information always exists, but argues that the measured contrast of the interference pattern is actually very low: "Because this signal (disruption) from the second, middle picture is small (equivalently, it only affects a very small portion of the photons), the contrast V is also very small, and goes to zero for infinitely thin wires." He also argues that the experiment can be understood with classical electrodynamics and has "nothing to do with quantum mechanics". • Aurelien Drezet [26], Néel Institute, Grenoble, France.[27][28] Drezet argues that the classical concept of a "path" leads to much confusion in this context, but "The real problem in Afshar's interpretation comes from the fact that the interference pattern is not actually completely recorded." The argument is similar to that of Motl's, that the observed visibility of the fringes is actually very small. Another way he looks at the situation is that the photons used to measure the fringes are not the same photons that are used to measure the path. The experimental setup he analyzes is only a "slightly modified version" of the one used by Afshar. • Ole Steuernagel [29], School of Physics, Astronomy and Mathematics, University of Hertfordshire, UK.[4] Steuernagel makes a quantitative analysis of the various transmitted, refracted, and reflected modes in a setup that differs only slightly from Afshar's. He concludes that the Englert-Greenberger duality relation is strictly
182
Afshar experiment satisfied, and in particular that the fringe visibility for thin wires is small. Like some of the other critics, he emphasizes that inferring an interference pattern is not the same as measuring one: "Finally, the greatest weakness in the analysis given by Afshar is the inference that an interference pattern must be present." Others question Afshar's interpretation and offer alternatives: • Entanglement and quantum interference [30] (by Paul O'Hara [2006/09]) Abstract: In the history of quantum mechanics, much has been written about the double-slit experiment, and much debate as to its interpretation has ensued. Indeed, to explain the interference patterns for subatomic particles, explanations have been given not only in terms of the principle of complementarity and wave-particle duality but also in terms of quantum consciousness and parallel universes. In this paper, the topic will be discussed from the perspective of spin-coupling in the hope of further clarification. We will also suggest that this explanation allows for a realist interpretation of the Afshar Experiment.
Specific support There also is support for the Afshar interpretation from John Cramer: • A Farewell to Copenhagen? [31] (by John G. Cramer Analog Science Fiction and Fact, October 2004)
References and notes [1] J. Zheng and C. Zheng (2011). "Variant simulation system using quaternion structures" (http:/ / www. tandfonline. com/ doi/ abs/ 10. 1080/ 09500340. 2011. 636152#preview). Journal of Modern Optics. doi:10.1080/09500340.2011.636152. . [2] S. S. Afshar, E. Flores, K. F. McDonald, E. Knoesel (2007). "Paradox in wave-particle duality". Foundations of Physics 37 (2): 295–305. arXiv:quant-ph/0702188. Bibcode 2007FoPh...37..295A. doi:10.1007/s10701-006-9102-8. [3] R. Kastner (2005). "Why the Afshar experiment does not refute complementarity?". Studies in History and Philosophy of Modern Physics 36 (4): 649–658. doi:10.1016/j.shpsb.2005.04.006. [4] O. Steuernagel (2007). "Afshar's experiment does not show a violation of complementarity". Foundations of Physics 37 (9): 1370. arXiv:quant-ph/0512123. Bibcode 2007FoPh...37.1370S. doi:10.1007/s10701-007-9153-5. [5] V. Jacques et al. (2008). "Illustration of quantum complementarity using single photons interfering on a grating". New Journal of Physics 10 (12): 123009. arXiv:0807.5079. Bibcode 2008NJPh...10l3009J. doi:10.1088/1367-2630/10/12/123009. [6] D. D. Georgiev (2007). "Single photon experiments and quantum complementarity" (http:/ / www. ptep-online. com/ index_files/ 2007/ PP-09-19. PDF). Progress in Physics 2: 97–103. . [7] D. D. Georgiev (2012). "Quantum histories and quantum complementarity" (http:/ / www. isrn. com/ journals/ mp/ 2012/ 327278/ ). ISRN Mathematical Physics 2012: 327278. . [8] S. S. Afshar (2005). "Violation of the principle of complementarity, and its implications". Proceedings of SPIE 5866: 229–244. arXiv:quant-ph/0701027. doi:10.1117/12.638774. [9] S. S. Afshar (2006). "Violation of Bohr's complementarity: One slit or both?". AIP Conference Proceedings 810: 294–299. arXiv:quant-ph/0701039. doi:10.1063/1.2158731. [10] M. Chown (2004). "Quantum rebel" (http:/ / www. newscientist. com/ article/ mg18324575. 300. html). New Scientist 183 (2457): 30–35. . [11] S. S. Afshar (2004). "Waving Copenhagen Good-bye: Were the founders of Quantum Mechanics wrong?" (http:/ / tools. fas. harvard. edu/ cgi-bin/ calendar/ exporter. cgi?view=event_detail& id=10416384). Harvard seminar announcement. . [12] Afshar's Quantum Bomshell (http:/ / www. sciencefriday. com/ images/ shows/ 2004/ 073004/ AfsharExperimentSmall. jpg) Science Friday [13] J. G. Cramer (2004). "Bohr is still wrong" (http:/ / www. newscientist. com/ article/ mg18324614. 100. html). New Scientist 183 (2461): 26. . [14] S. S. Afshar (2005). "Experimental Evidence for Violation of Bohr's Principle of Complementarity" (http:/ / meetings. aps. org/ Meeting/ MAR05/ Event/ 26224). APS Meeting, March 21–25, Los Angeles, California. . [15] J. G. Cramer (2005). "A farewell to Copenhagen?" (http:/ / www. analogsf. com/ 0410/ altview2. shtml). Analog Science Fiction and Fact. . [16] http:/ / carnap. umd. edu/ philphysics/ kastner. html [17] R. E. Kastner (2006). "The Afshar Experiment and Complementarity" (http:/ / meetings. aps. org/ Meeting/ MAR06/ Event/ 40525). APS Meeting, March 13–17, Baltimore, Maryland. . [18] http:/ / arxiv. org/ abs/ quant-ph/ 0702210 [19] http:/ / www. rowan. edu/ centers/ materials/ kn. htm [20] http:/ / www. quniverse. sk/ rcqi/ index. php?x=pub_for& for=reitzner [21] http:/ / arxiv. org/ abs/ quant-ph/ 0701152 [22] W. Unruh (2004). "Shahriar Afshar – Quantum Rebel?" (http:/ / www. theory. physics. ubc. ca/ rebel. html). . [23] http:/ / www. ctp-jamia. res. in/ people/ tabish. html
183
Afshar experiment [24] http:/ / arxiv. org/ abs/ quant-ph/ 0701109 [25] L. Motl (2004). "Violation of complementarity?" (http:/ / motls. blogspot. com/ 2004/ 11/ violation-of-complementarity. html). . [26] http:/ / neel. cnrs. fr/ spip. php?article260& personne=aurelien. drezet/ nano [27] Aurelien Drezet (2005). "Complementarity and Afshar's experiment". arXiv:quant-ph/0508091 [quant-ph]. [28] Aurelien Drezet (2011). "Wave particle duality and the Afshar experiment" (http:/ / www. ptep-online. com/ index_files/ 2011/ PP-24-07. PDF). Progress in Physics 1: 57–67. arXiv:1008.4261v1. . [29] http:/ / strc. herts. ac. uk/ ls/ ole/ to. html [30] http:/ / arxiv. org/ abs/ quant-ph/ 0608202 [31] http:/ / www. analogsf. com/ 0410/ altview2. shtml
Further reading • Mir; Lundeen; Mitchell; Steinberg; Garretson; Wiseman (2007). "A double-slit 'which-way' experiment on the complementarity--uncertainty debate". New Journal of Physics 9 (8): 287–287. arXiv:0706.3966. Bibcode 2007NJPh....9..287M. doi:10.1088/1367-2630/9/8/287.
External links Afshar's blog (http://irims.org/blog/index.php/2005/03/13/questions_welcome_1#comments)
Davisson–Germer experiment The Davisson–Germer experiment was a physics experiment conducted by American physicists Clinton Davisson and Lester Germer in 1927, which confirmed the de Broglie hypothesis. This hypothesis advanced by Louis de Broglie in 1924 says that particles of matter such as electrons have wave like properties. The experiment not only played a major role in verifying the de Broglie hypothesis and demonstrated the wave-particle duality, but also was an important historical development in the establishment of quantum mechanics and of the Schrödinger equation
History and Overview According to Maxwell's equations in the late 19th century, light was thought to consist of waves of electromagnetic fields and matter consist of localized particles. However this was challenged in Albert Einstein’s 1905 paper on the photoelectric effect, which described light as discrete and localized quanta of energy (now called photons), and won him the Nobel Prize in Physics in 1921. In 1927 Louis de Broglie presented his thesis concerning the wave-particle duality theory, which proposed the idea that all matter displays the wave-particle duality of photons.[1] According to de Broglie for all matter and for radiation alike, the energy E of the particle was related to the frequency of its associated wave ν by the Planck relation:
And that the momentum of the particle p was related to its wavelength by what is now known as the de Broglie relation:
where h is Planck's constant. An important contribution to the Davisson–Germer experiment was made by Walter M. Elsasser in Göttingen in the 1920s, who remarked that the wave-like nature of matter might be investigated by electron scattering experiments on crystalline solids, just as the wave-like nature of X-rays had been confirmed through X-ray scattering experiments on crystalline solids.[1][2] This suggestion of Elsasser was then communicated by his senior colleague (and later Nobel Prize recipient) Max Born to physicists in England. When the Davisson and Germer experiment was performed, the results of the
184
DavissonGermer experiment experiment were explained by Elsasser's proposition. However the initial intention of the Davisson and Germer experiment was not to confirm the de Broglie hypothesis, but rather to study the surface of nickel. In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline nickel target. The angular dependence of the reflected electron intensity was measured and was determined to have the same diffraction pattern as those predicted by Bragg for X-rays. This experiment was independently replicated by George Paget Thomson, and Davisson and Thomson shared the Nobel Prize in Physics in 1937.[1][3] The Davisson – Germer experiment confirmed the de Broglie hypothesis that matter has wave-like behavior. This, in combination with the Compton effect discovered by Arthur Compton (who won the Nobel Prize for Physics in 1927),[4] established the wave–particle duality hypothesis which was a fundamental step in quantum theory.
Experiment Davisson and Germer's actual objective was to study the surface of a piece of nickel by directing a beam of electrons at the surface and observing how many electrons bounced off at various angles. They expected that for electrons even the smoothest crystal surface would be too rough and so the electron beam would experience diffuse reflection.[5] The experiment consisted of firing an electron beam from an electron gun directed to a piece of nickel crystal at normal incidence (i.e. perpendicular to the surface of the crystal). The experiment included an electron gun consisting of a heated filament that released thermally excited electrons, which were then accelerated through a potential difference giving them a certain amount of kinetic energy towards the nickel crystal. To avoid collisions of the electrons with other molecules on their way towards the surface, the experiment was conducted in a vacuum chamber. To measure the number of electrons that were scattered at different angles, an electron detector that could be moved on an arc path about the crystal was used. The detector was designed to accept only elastically scattered electrons. During the experiment an accident occurred and air entered the chamber, producing an oxide film on the nickel surface. To remove the oxide, Davisson and Germer heated the specimen in a high temperature oven, not knowing that this affected the formerly polycrystalline structure of the nickel to form large single crystal areas with crystal planes continuous over the width of the electron beam.[5] When they started the experiment again and the electrons hit the surface, they were scattered by atoms which originated from crystal planes inside the nickel crystal. As Max von Laue proved in 1912 the crystal structure serves as a type of three dimensional diffraction grating. The angles of maximum reflection are given by Bragg's condition for constructive interference from an array, Bragg's law
for n = 1, θ = 50°, and for the spacing of the crystalline planes of nickel (d = 0.091 nm) obtained from previous X-ray scattering experiments on crystalline nickel.[1] By varying the applied voltage to the electron gun, the maximum intensity of electrons diffracted by the atomic surface was found at different angles. The highest intensity was observed at an angle θ = 50° with a voltage of 54 V, giving the electrons a kinetic energy of 54 eV.[1] According to the de Broglie relation and Bragg's law, a beam of 54 eV had a wavelength of 0.165 nm. The experimental outcome was 0.167 nm, which closely matched the predictions. Davisson and Germer's accidental discovery of the diffraction of electrons was the first direct evidence confirming de Broglie's hypothesis that particles can have wave properties as well.
185
DavissonGermer experiment
References [1] R. Eisberg, R. Resnick (1985). "Chapter 3 – de Broglie's Postulate—Wavelike Properties of Particles". Quantum Physics: of Atoms, Molecules, Solids, Nuclei, and Particles (2nd ed.). John Wiley & Sons. ISBN 0-471-87373-X. [2] H. Rubin (1995). "Walter M. Elsasser" (http:/ / www. nap. edu/ openbook. php?record_id=4990& page=103). Biographical Memoirs. 68. National Academy Press. ISBN 0-308-05238-6 . . [3] The Nobel Foundation (Clinton Joseph Davisson and George Paget Thomson) (1937). "Clinton Joseph Davisson and George Paget Thomson for their experimental discovery of the diffraction of electrons by crystals" (http:/ / www. nobelprize. org/ nobel_prizes/ physics/ laureates/ 1937/ ). The Nobel Foundation 1937. . [4] The Nobel Foundation (Arthur Holly Compton and Charles Thomson Rees Wilson) (1937). "Arthur Holly Compton for his discovery of the effect named after him and Charles Thomson Rees Wilson for his method of making the paths of electrically charged particles visible by condensation of vapour" (http:/ / www. nobelprize. org/ nobel_prizes/ physics/ laureates/ 1927/ ). The Nobel Foundation 1927. . [5] Hugh D. Young, Roger A. Freedman: University Physics, Ed. 11. Pearson Education, Addison Wesley, San Fransisco 2004, 0-321-20469-7, S. 1493-1494.
External links • R. Nave. "Davisson–Germer Experiment" (http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2. html). HyperPhysics. Georgia State University, Physics Departement.
Delayed choice quantum eraser A delayed choice quantum eraser, first performed by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, and Marlan O. Scully,[1] and reported in early 1999, is an elaboration on a quantum eraser experiment involving the concepts considered in Wheeler's delayed choice experiment. It was designed to investigate peculiar consequences of the well-known double slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.
Introduction In the basic double slit experiment, a very narrow beam of coherent light from a source that is far enough away to have almost perfectly parallel wave fronts is directed perpendicularly towards a wall pierced by two parallel slit apertures. The widths of the slits and their separation are approximately the same size as the wavelength of the incident light. If a detection screen (anything from a sheet of white paper to a digital camera) is put on the other side of the double slit wall, a pattern of light and dark fringes, called an interference pattern, will be observed. Early in the history of this experiment, scientists discovered that, by decreasing the brightness of the light source sufficiently, individual particles of light that form the interference pattern are detectable. They next tried to discover by which slit a given unit of light (photon) had traveled. Unexpectedly, the results discovered were that if anything is done to permit determination of which path the photon takes, the interference pattern disappears: there is no interference pattern. Each photon simply hits the detector by going through one of the two slits. Each slit yields a simple single pile of hits; there is no interference pattern. It is counterintuitive that a different outcome results based on whether or not the photon is constrained to follow one or another path well after it goes through the slit but before it hits the detector. Two inconsistent accounts of the nature of light have long contended. The discovery of light's interfering with itself seemed to prove that light could not be a particle. It seemed that it had to be a wave to explain the interference seen in the double-slit experiment (first devised by Thomas Young in his classic interference experiment of the eighteenth century). In the early twentieth century, experiments with the photoelectric effect (the phenomenon that makes the light meters in cameras possible) gave equally strong evidence to support the idea that light is a particle phenomenon. Nothing is
186
Delayed choice quantum eraser
187
observable regarding it between the time a photon is emitted (which experimenters can at least locate in time by determining the time at which energy was supplied to the electron emitter) and the time it appears as the delivery of energy to some detector screen (such as a CCD or the emulsion of a film camera). Nevertheless experimenters have tried to gain indirect information about which path a photon "really" takes when passing through the double-slit apparatus. In the process they learned that constraining the path taken by one of a pair of entangled photons inevitably controls the path taken by the partner photon. Further, if the partner photon is sent through a double-slit device and thus interferes with itself, then very surprisingly the first photon will also behave in a way consistent with its having interfered with itself, even though there is no double-slit device in its way. In a quantum eraser experiment, one arranges to detect which one of the slits the photon passes through, but also to construct the experiment in such a way that this information can be "erased" after the fact. In practice, this "erasure" of path information frequently means removing the constraints that kept photons following two different paths separated from each other. In one experiment, rather than splitting one photon or its probability wave between two slits, the photon is subjected to a beam splitter. If one thinks in terms of a stream of photons being randomly directed by such a beam splitter to go down two paths that are kept from interaction, it is clear that no photon can then interfere with any other or with itself. If the rate of photon production is reduced so that only one photon is entering the apparatus at any one time, however, it becomes impossible to understand the photon as only moving through one path because when their outputs are redirected so that they coincide on a common detector then interference phenomena appear. In the two diagrams to the right, photons are emitted one at a time from the yellow star. They each pass through a 50% beam splitter (green block) that reflects 1/2 of the photons, which travel along two possible paths, depicted by the red or blue lines. In the top diagram, one can see that the trajectories of photons are clearly known — in the sense that if a photon emerges at the top of the apparatus it appears that it had to have come by the path that leads to that point (blue line), and if it emerges at the side of the apparatus it appears that it had to have come by way of the other path (red line). Next, as shown in the bottom diagram, a second beam splitter is introduced at the top right. It can direct either beam towards either path; thus note that whatever emerges from each exit port may have come by way of either path.
Experiment that shows delayed determination of photon path
It is in this sense that the path information has been "erased". Note that total phase differences are introduced along the two paths because of the different effects of passing through a glass plate, being reflected off its first surface, or passing through the back surface of a semi-silvered beam splitter and being reflected by the back (inner side) of the reflective surface. The result is that waves pass out of both the top upwards exit, and also the top-right exit. Specifically, waves passing out the top exit interfere destructively, whereas waves passing out the upper right side exit interfere constructively. A more detailed explanation of the phase changes involved here can be found in the Mach-Zehnder interferometer article. Also, the experiment depicted above is reported in full in a reference.[2]
Delayed choice quantum eraser If the second beam splitter in the lower diagram could be inserted or removed one might assert that a photon must have traveled by way of one path or the other if a photon were detected at the end of one path or the other. The appearance would be that the photon "chose" one path or the other at the only (bottom left) beam splitter, and therefore could only arrive at the respective path end. The subjective assurance that the photon followed a single path is brought into question, however, if (after the photon has presumably "decided" which path to take) a second beam splitter then makes it impossible to say by which path the photon has traveled. What once appeared to be a "black and white" issue now appears to be a "gray" issue. It is the mixture of two originally separated paths that constitutes what is colloquially referred to as "erasure." It is actually more like "a return to indeterminability."
The experiment The experimental setup, described in detail in the original paper[1], is as follows. First, a photon is generated and passes through a double slit apparatus (vertical black line in the upper left hand corner of the diagram). The photon goes through one (or both) of the two slits, whose paths are shown as red or light blue lines, indicating which slit the photon came through (red indicates slit A, light blue indicates slit B). So far, the experiment is like a conventional two-slit experiment. However, after the slits a beta barium borate crystal (labeled as BBO) causes spontaneous parametric down conversion (SPDC), converting the photon (from either slit) into two identical entangled photons with 1/2 the frequency of the original photon. These photons are caused to diverge and follow two paths by the Glan-Thompson Prism. One of these photons, referred to as the "signal" photon (look at the red and light-blue lines going upwards from the Glan-Thompson prism), continues to the target detector called D0. The positions where these "signal" photons detected by D0 occur can later be examined to discover if collectively those positions form an interference pattern. The other entangled photon, referred to as the "idler" photon (look at the red and light-blue lines going downwards from the Glan-Thompson prism), is deflected by a prism that sends it along divergent paths depending on whether it came from slit A or slit B. Somewhat beyond the path split, beam splitters (green blocks) are encountered that each have a 50% chance of allowing the idler to pass through and a 50% chance of causing it to be reflected. The gray blocks in the diagram are mirrors. Because of the way the beam splitters are arranged, the idler can be detected by detectors labeled D1, D2, D3 and D4. Note that: If it is recorded at detector D3, then it can only have come from slit B. If it is recorded at detector D4 it can only have come from slit A.
188
Delayed choice quantum eraser If the idler is detected at detector D1 or D2, it might have come from either slit (A or B). Thus, which detector receives the idler photon either reveals information, or specifically does not reveal information, about the path of the signal photon with which it is entangled. If the idler is detected at either D1 or D2, the which-path information has been "erased", so there is no way of knowing whether it (and its entangled signal photon) came from slit A or slit B. Whereas, if the idler is detected at D3 or D4, it is known that it (and its entangled signal photon) came from slit B or slit A, respectively. By using a coincidence counter, the experimenters were able to isolate the entangled signal from the overwhelming photo-noise of the laboratory - recording only events where both signal and idler photons were detected. When the experimenters looked only at the signal photons whose entangled idlers were detected at D1 or D2, they found an interference pattern. However, when they looked at the signal photons whose entangled idlers were detected at D3 or similarly at D4, they found no interference. This result is similar to that of the double-slit experiment, since interference is observed when it is not known which slit the photon went through, while no interference is observed when the path is known. However, what makes this experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler need not be made until after the position of the signal photon has already been measured by D0. There is never any which-path information determined directly for the photons that are detected at D0, yet detection of which-path information by D3 or D4 means that no interference pattern is observed in the corresponding subset of signal photons at D0. The results from Kim, et al.[1] have shown that whether the idler photon is detected at a detector that preserves its which-path information (D3 or D4) or a detector that erases its which-path information (D1 or D2) determines whether interference is seen at D0, even though the idler photon is not observed until after the signal photon arrives at D0 due to the shorter optical path for the latter. Some have interpreted this result to mean that the delayed choice to observe or not observe the path of the idler photon will change the outcome of an event in the past. However, an interference pattern may only be observed after the idlers have been detected (i.e., at D1 or D2). Note that the total pattern of all signal photons at D0, whose entangled idlers went to multiple different detectors, will never show interference regardless of what happens to the idler photons.[3] One can get an idea of how this works by looking carefully at both the graph of the subset of signal photons whose idlers went to detector D1 (fig. 3 in the paper[1]), and the graph of the subset of signal photons whose idlers went to detector D2 (fig. 4), and observing that the peaks of the first interference pattern line up with the troughs of the second and vice versa (noted in the paper as "a π phase shift between the two interference fringes"), so that the sum of the two will not show interference.
189
Delayed choice quantum eraser
190
Time relations among data By noting which photons reaching Detector 0 correspond with photons reaching Detectors 1, 2, 3, and 4, it is possible to sort photon records collected by Detector 0 into four groups. Only then will it become possible to see interference patterns in two groups and only diffraction patterns in the other two groups. If there were no coincidence counter, then there would be no way to distinguish any photon that arrives at Detector 0 from any other photon that reaches it.
Raw results for D0 are all delivered to the same detector regardless of what happens at the other detectors.
Photons will not reach detectors one through four in regular rotation, so the only way to sort out the photons that are entangled twins with the ones that reached each of those detectors is to group them according to which of those four detectors was activated when a photon reached Detector 0. Note that in the schematic diagrams the fringes or interference patterns imaged by Detector 1 and Detector 2 will add together to form a solid band. The addition of the diffraction patterns paired with the diffraction patterns seen by Detector 3 and Detector 4 will make the center area somewhat brighter than it would otherwise be, but would have no other influence on the confused picture produced by the raw data gathered at Detector 0. It is impossible to know which group a photon appearing at Detector 0 at time T1 may belong to until after its entangled partner is found at one of the other detectors and their coincidence is measured at some slightly later time T2.
Discussion Problems with using retrocausality This delayed choice quantum eraser experiment raises questions about time, time sequences, and thereby brings our usual ideas of time and causal sequence into question. If a determining factor in the complicated (lower) part of the apparatus determines an outcome in the simple part of the apparatus that consists of only a lens and a detection screen, then effect seems to Raw results for D0 can be sorted precede cause. So if the light paths involved in the complicated part of the according to correspondences with the apparatus were greatly extended in order that, e.g., a year might go by before other detectors,1 through 4 a photon showed up at D1, D2, D3, or D4, then when a photon showed up in one of these detectors it would cause the photon in the upper, simple part of the apparatus to have shown up in a certain mode a year earlier. Perhaps by re-routing light paths to the four detectors during that one year so that the number of possible outcomes is reduced to two or even perhaps to one, then the experimenter could send a signal back through time. Changing between the first possible arrangement and second possible arrangement of parts in the complicated part of the experiment would then function like the opening and closing of a telegraph key. An objection that seems fatal is soon raised: The photons that show up in D1 through D4 do not follow some regular rotation. Therefore the photons that show up in D0 pile onto the same detection screen in random order. There is no way to tell, by simply looking at the time and place of each photon detected using D0, which of the other four detectors it corresponds to. So the result will be like trying to watch a motion picture screen on which four projectors are focused. The whole screen will be awash with light. In order to segregate the photons arriving at D0 into the ones that will form one or the other of two overlapping fringe patterns and also the two diffraction patterns, it will be necessary to know how to collect them into four sets. But to do that it is necessary to
Delayed choice quantum eraser get messages from the second part of the experiment about which detector was involved with the detection of the entangled partner of each photon received at D0. To oversimplify a bit, the data collected at D0 would be like an encrypted message. However, it could only be decrypted when the key to the code was delivered by a message that could travel at no faster than the speed of light. This daunting obstacle to sending messages back in time has not, however, stopped all researchers from trying to find some way of getting around the stumbling block.
Details pertaining to retrocausality in the Kim experiment In their paper, Kim, et al.[1] explain that the concept of complementarity is one of the most basic principles of quantum mechanics. According to the Heisenberg Uncertainty Principle, it is not possible to precisely measure both the position and the momentum of a quantum particle at the same time. In other words, position and momentum are complementary. In 1927, Niels Bohr maintained that quantum particles have both "wave-like" behavior and "particle-like" behavior, but can exhibit only one kind of behavior under conditions that prevent exhibiting the complementary characteristics. This complementarity has come to be known as the wave-particle duality of quantum mechanics. Richard Feynman believed that the presence of these two aspects under conditions that prevent their simultaneous manifestation is the basic mystery of quantum mechanics. According to Kim, et al., "The actual mechanisms that enforce complementarity vary from one experimental situation to another."[1] In the double-slit experiment, the common wisdom is that complementarity makes it seemingly impossible to determine which slit the photon passes through without at the same time disturbing it enough to destroy the interference pattern. A 1982 paper by Scully and Drühl circumvented the issue of disturbance due to direct measurement of the photon,[4] according to Kim, et al. Scully and Drühl "found a way around the position-momentum uncertainty obstacle and proposed a quantum eraser to obtain which-path or particle-like information without introducing large uncontrolled phase factors to disturb the interference."[1] Scully and Drühl found that there is no interference pattern when which-path information is obtained, even if this information was obtained without directly observing the original photon, but that if you somehow "erase" the which-path information, an interference pattern is again observed. In the delayed choice quantum eraser discussed here, the pattern exists even if the which-path information is erased shortly later in time than the signal photons hit the primary detector. However, the interference pattern can only be seen retroactively once the idler photons have already been detected and the experimenter has obtained information about them, with the interference pattern being seen when the experimenter looks at particular subsets of signal photons that were matched with idlers that went to particular detectors.
The main stumbling block for using retrocausality to communicate information The total pattern of signal photons at the primary detector never shows interference, so it is not possible to deduce what will happen to the idler photons by observing the signal photons alone, which would open up the possibility of gaining information faster-than-light (since one might deduce this information before there had been time for a message moving at the speed of light to travel from the idler detector to the signal photon detector) or even gaining information about the future (since as noted above, the signal photons may be detected at an earlier time than the idlers), both of which would qualify as violations of causality in physics. The apparatus under discussion here could not communicate information in a retro-causal manner because it takes another signal, one which must arrive via a process that can go no faster than the speed of light, to sort the superimposed data in the signal photons into four streams that reflect the states of the idler photons at their four distinct detection screens. In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects[5] (see reference [6] for a treatment emphasizing the role of conditional probabilities).
191
Delayed choice quantum eraser
Yet there are those who persevere in attempting to communicate retroactively Some physicists have speculated about the possibility that these experiments might be changed in a way that would be consistent with previous experiments, yet which could allow for experimental causality violations.[7][8]
References [1] Kim, Yoon-Ho; R. Yu, S.P. Kulik, Y.H. Shih, and Marlan Scully (2000). "A Delayed Choice Quantum Eraser". Physical Review Letters 84: 1–5. arXiv:quant-ph/9903047. Bibcode 2000PhRvL..84....1K. doi:10.1103/PhysRevLett.84.1. [2] Jacques, Vincent; Wu, E; Grosshans, Frédéric; Treussart, François; Grangier, Philippe; Aspect, Alain; Rochl, Jean-François (2007). "Experimental Realization of Wheeler's Delayed-Choice Gedanken Experiment" (http:/ / www. sciencemag. org/ cgi/ content/ full/ 315/ 5814/ 966). Science 315 (5814): pp. 966–968. arXiv:quant-ph/0610241. Bibcode 2007Sci...315..966J. doi:10.1126/science.1136303. PMID 17303748. . [3] Greene, Brian (2004). The Fabric of the Cosmos. Alfred A. Knopf. p. 198. ISBN 0-375-41288-3. [4] Scully, Marlan O.; Kai Drühl (1982). "Quantum eraser: A proposed photon correlation experiment concerning observation and "delayed choice" in quantum mechanics". Physical Review A 25 (4): 2208–2213. Bibcode 1982PhRvA..25.2208S. doi:10.1103/PhysRevA.25.2208. [5] Eberhard, Phillippe H.; Ronald R. Ross (1989). "Quantum field theory cannot provide faster-than-light communication" (http:/ / www. springerlink. com/ content/ g7w8441j75831k4x/ ). Foundations of Physics Letters 2 (2): p. 127–149. Bibcode 1989FoPhL...2..127E. doi:10.1007/BF00696109. . [6] Bram Gaasbeek. Demystifying the Delayed Choice Experiments (http:/ / arxiv. org/ abs/ 1007. 3977). arXiv preprint, 22 July 2010. [7] John G. Cramer. NASA Goes FTL - Part 2: Cracks in Nature's FTL Armor (http:/ / www. npl. washington. edu/ AV/ altvw70. html). "Alternate View" column, Analog Science Fiction and Fact, February 1995. [8] Paul J. Werbos, Ludmila Dolmatova. The Backwards-Time Interpretation of Quantum Mechanics - Revisited With Experiment (http:/ / arxiv. org/ abs/ quant-ph/ 0008036). arXiv preprint, 7 August 2000.
External links • • • • •
presentation of the experiment (http://strangepaths.com/the-quantum-eraser-experiment/2007/03/20/en/) basic delayed choice experiment (http://www.bottomlayer.com/bottom/basic_delayed_choice.htm) delayed choice quantum eraser (http://www.bottomlayer.com/bottom/kim-scully/kim-scully-web.htm) the notebook of philosophy and physics (http://www.bottomlayer.com/) Comprehensive experimental test of quantum erasure, Alexei Trifonov, Gunnar Bjork, Jonas Soderholm, and Tedros Tsegaye (http://arxiv.org/abs/quant-ph/0009097) ( doi:10.1140/epjd/e20020030 (http://dx.doi.org/ 10.1140/epjd/e20020030))
192
Double-slit experiment
Double-slit experiment The double-slit experiment, sometimes called Young's experiment, is a demonstration that matter and energy can display characteristics of both waves and particles, and demonstrates the fundamentally probabilistic nature of quantum mechanical phenomena. In the basic version of the experiment, a coherent light source such as a laser beam illuminates a thin plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen — a result that would not be expected if light consisted strictly of particles. However, on the screen, the light is always found to be absorbed as though it were composed of discrete particles or photons.[1][2] This establishes the principle known as wave–particle duality. Additionally, the detection of individual photons is observed to be inherently probabilistic, which is inexplicable using classical mechanics.[3]
Overview If light consisted strictly of ordinary or classical particles, and these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit. However, when this "single-slit experiment" is actually performed, the pattern on the screen is a diffraction pattern, a fairly narrow central band with dimmer bands parallel to it on each side. (See the top photograph to the right.) Similarly, if light consisted strictly of classical particles and we illuminated Same double-slit assembly (0.7mm between slits); in top image, one slit is closed. Note two parallel slits, the expected pattern that the single-slit diffraction pattern — the faint spots on either side of the main band — on the screen would simply be the sum is also seen in the double-slit image, but at twice the intensity and with the addition of of the two single-slit patterns. In many smaller interference fringes. actuality, however, the pattern becomes wider and much more detailed, including a series of light and dark bands. (See the bottom photograph to the right.) When Thomas Young first demonstrated this phenomenon, it indicated that light consists of waves, as the distribution of brightness can be explained by the alternately additive and subtractive interference of wavefronts.[3] Young's experiment played a vital part in the acceptance of the wave theory of light in the early 1800s, vanquishing the corpuscular theory of light proposed by Isaac Newton, which had been the accepted model of light propagation in the 17th and 18th centuries. However, the later discovery of the photoelectric effect demonstrated that under different circumstances, light can behave as if it is composed of discrete particles. These seemingly contradictory discoveries made it necessary to go beyond classical physics and take the quantum nature of light into account. The double-slit experiment (and its variations), conducted with individual particles, has become a classic thought experiment for its clarity in expressing the central puzzles of quantum mechanics. Because it demonstrates the fundamental limitation of the observer to predict experimental results, Richard Feynman called it "a phenomenon which is impossible ... to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]."[3], and was fond of saying that all of quantum mechanics can
193
Double-slit experiment be gleaned from carefully thinking through the implications of this single experiment[4]. Časlav Brukner and Anton Zeilinger have succinctly expressed this limitation as follows: [T]he observer can decide whether or not to put detectors into the interfering path. That way, by deciding whether or not to determine the path through the two-slit experiment, he/she can decide which property can become reality. If he/she chooses not to put the detectors there, then the interference pattern will become reality; if he/she does put the detectors there, then the beam path will become reality. Yet, most importantly, the observer has no influence on the specific element of the world that becomes reality. Specifically, if he/she chooses to determine the path, then he/she has no influence whatsoever over which of the two paths, the left one or the right one, nature will tell him/her is the one in which the particle is found. Likewise, if he/she chooses to observe the interference pattern, then he/she has no influence whatsoever over where in the observation plane he/she will observe a specific particle. Both outcomes are completely random.[5] The Englert–Greenberger duality relation provides a detailed treatment of the mathematics of double-slit interference in the context of quantum mechanics. A low-intensity double-slit experiment was first performed by G. Taylor in 1909,[6] by reducing the level of incident light until photon emission/absorption events were mostly nonoverlapping. A double-slit experiment was not performed with anything other than light until 1961, when Clauss Jönsson of the University of Tübingen performed it with electrons.[7][8] In 2002, Jönsson's double-slit experiment was voted "the most beautiful experiment" by readers of Physics World.[9] In 1999, objects large enough to be seen under an electron microscope — buckyball molecules (diameter about 0.7 nm, nearly half a million times larger than a proton) — were found to exhibit wave-like interference.[10][11] The appearance of interference built up from individual photons could seemingly be explained by assuming that a single photon has its own associated wavefront that passes through both slits, and that the single photon will show up on the detector screen according to the net probability values resulting from the co-incidence of the two probability waves coming by way of the two slits.[12] However, more complicated systems that involve two or more particles in superposition are not amenable to such a simple, classically intuitive explanation.[13]
194
Double-slit experiment
Variations of the experiment Interference of individual particles An important version of this experiment involves single particles (or waves — for consistency, they are called particles here). Sending particles through a double-slit apparatus one at a time results in single particles appearing on the screen, as expected. Remarkably, however, an interference pattern emerges when these particles are allowed to build up one by one (see the image to the right). For example, when a laboratory apparatus was developed that could reliably fire one electron at a time through the double slit,[14] the emergence of an interference pattern suggested that each electron was interfering with itself, and therefore in some sense the electron had to be going through both slits at once[15] — an idea that contradicts our everyday experience of discrete objects. This phenomenon has also been shown to occur with atoms and even some molecules, including buckyballs.[10][16][17] So experiments with electrons add confirmatory evidence to the view of Dirac that electrons, protons, neutrons, and even larger entities that are ordinarily called particles nevertheless have their own wave nature and even their own specific frequencies. This experimental fact is highly reproducible, and the mathematics of quantum mechanics (see below) allows us to predict the exact probability of an electron striking the screen at any particular point. However, the electrons do not arrive at the screen in any predictable order. In other words, knowing where all the previous electrons appeared on the screen and in what order tells us nothing about where any future electron will hit, even though the probabilities at specific points can be calculated.[18] (Note that it is not the probabilities of photons appearing at various Electron buildup over time points along the detection screen that add or cancel, but the amplitudes. Probabilities are the squares of amplitudes. Also note that if there is a cancellation of waves at some point, that does not mean that a photon disappears; it only means that the probability of a photon's appearing at that point will decrease, and the probability that it will appear somewhere else increases.) Thus, we have the appearance of a seemingly causeless selection event in a highly orderly and predictable formulation of the interference pattern. Ever since the origination of quantum mechanics, some theorists have searched for ways to incorporate additional determinants or "hidden variables" that, were they to become known, would account for the location of each individual impact with the target.[19]
With particle detectors at the slits The double-slit apparatus can be modified by adding particle detectors positioned at the slits. This enables the experimenter to find the position of a particle not when it impacts the screen, but rather, when it passes through the double-slit — did it go through only one of the slits, as a particle would be expected to do, or through both, as a wave would be expected to do? Many early experiments found that modification of the apparatus that can determine which slit a particle passes through reduces the visibility of interference at the screen,[3] thereby illustrating the complementarity principle: that light (and electrons, etc.) can behave as either particles or waves, but not both at the same time.[20][21][22] But an experiment performed in 1987[23] produced results that demonstrated that information could be obtained regarding which path a particle had taken, without destroying the interference altogether. This showed the effect of measurements that disturbed the particles in transit to a lesser degree and thereby influenced the interference pattern only to a comparable extent. And in 2012, researchers finally succeeded in correctly identifying the path each particle had taken without any adverse effects at all on the interference pattern generated by the
195
Double-slit experiment
196
particles.[24] There are many methods to determine whether a photon passed through a slit, for instance by placing an atom at the position of each slit. Interesting experiments of this latter kind have been performed with photons[23] and with neutrons.[25]
Delayed choice and quantum eraser variations The delayed-choice experiment and the quantum eraser are sophisticated variations of the double-slit with particle detectors placed not at the slits but elsewhere in the apparatus. The first demonstrates that extracting "which path" information after a particle passes through the slits can seem to retroactively alter its previous behavior at the slits. The second demonstrates that wave behavior can be restored by erasing or otherwise making permanently unavailable the "which path" information.
Other variations In 1967 Pfleegor and Mandel demonstrated two-source interference using two separate lasers as light sources.[26][27] It was shown experimentally in 1972 that in a double-slit system where only one slit was open at any time, interference was nonetheless observed provided the path difference was such that the detected photon could have come from either slit.[28][29] The experimental conditions were such that the photon density in the system was much less than unity. The experiment has been performed with particles as large as C60 (Buckminsterfullerene).[30]
A laboratory double-slit assembly; distance between top posts approximately one inch.
Classical wave-optics formulation Much of the behaviour of light can be modelled using classical wave theory. The Huygens–Fresnel principle is one such model; it states that each point on a wavefront generates a secondary spherical wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual wavelets at that point. This summation needs to take into account the phase as well as the amplitude of the individual wavelets. It should be noted that only the intensity of a light field can be measured – this is proportional to the square of the amplitude. In the double-slit experiment, the two slits are illuminated by a single laser beam. If the width of the slits is small enough (less than the wavelength of the laser light), the slits diffract the light into cylindrical Two slits diffraction pattern by a plane wave waves. These two cylindrical wavefronts are superimposed, and the amplitude, and therefore the intensity, at any point in the combined wavefronts depends on both the magnitude and the phase of the two wavefronts. The difference in phase between the two waves is determined by the difference in the distance travelled by the two waves.
Double-slit experiment
197
If the viewing distance is large compared with the separation of the slits (the far field), the phase difference can be found using the geometry shown in the figure below right. The path difference between two waves travelling at an angle θ is given by:
When the two waves are in phase, i.e. the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximum, and when they are in anti-phase, i.e. the path difference is equal to half a wavelength, one and a half wavelengths, etc., then the two waves cancel and the summed intensity is zero. This effect is known as interference. The interference fringe maxima occur at angles Two slits are illuminated by a plane wave
where λ is the wavelength of the light. The angular spacing of the fringes is θf is given by The spacing of the fringes at a distance z from the slits is given by
For example, if two slits are separated by 0.5mm (d), and are illuminated with a 0.6μm wavelength laser (λ), then at a distance of 1m (z), the spacing of the fringes will be 1.2mm. Geometry for far field fringes
If the width of the slits b is greater than the wavelength, the Fraunhofer diffraction equation gives the intensity of the diffracted light as:[31]
This is illustrated in the figure above, where the first pattern is the diffraction pattern of a single slit, given by the sinc function in this equation, and the second figure shows the combined intensity of the light diffracted from the two slits, where the cos function represent the fine structure, and the coarser structure represents diffraction by the individual slits as described by the sinc function. Similar calculations for the near field can be done using the Fresnel diffraction equation. As the plane of observation gets closer to the plane in which the slits are located, the diffraction patterns associated with each slit decrease in size, so that the area in which interference occurs is reduced, and may vanish altogether when there is no overlap in the two diffracted patterns.[32]
Double-slit experiment
198
Interpretations of the experiment Like the Schrödinger's cat thought experiment, the double-slit experiment is often used to highlight the differences and similarities between the various interpretations of quantum mechanics.
Copenhagen interpretation The Copenhagen interpretation is a consensus among some of the pioneers in the field of quantum mechanics that it is undesirable to posit anything that goes beyond the mathematical formulae and the kinds of physical apparatus and reactions that enable us to gain some knowledge of what goes on at the atomic scale. One of the mathematical constructs that enables experimenters to predict very accurately certain experimental results is sometimes called a probability wave. In its mathematical form it is analogous to the description of a physical wave, but its "crests" and "troughs" indicate levels of probability for the occurrence of certain phenomena (e.g., a spark of light at a certain point on a detector screen) that can be observed in the macro world of ordinary human experience. The probability "wave" can be said to "pass through space" because the probability values that one can compute from its mathematical representation are dependent on time. One cannot speak of the location of any particle such as a photon between the time it is emitted and the time it is detected simply because in order to say that something is located somewhere at a certain time one has to detect it. The requirement for the eventual appearance of an interference pattern is that particles be emitted, and that there be a screen with at least two distinct paths for the particle to take from the emitter to the detection screen. Experiments observe nothing whatsoever between the time of emission of the particle and its arrival at the detection screen. If a ray tracing is then made as if a light wave (as understood in classical physics) is wide enough to take both paths, then that ray tracing will accurately predict the appearance of maxima and minima on the detector screen when many particles pass through the apparatus and gradually "paint" the expected interference pattern.
Path-integral formulation The Copenhagen interpretation is similar to the path integral formulation of quantum mechanics provided by Feynman. The path integral formulation replaces the classical notion of a single, unique trajectory for a system, with a sum over all possible trajectories. The trajectories are added together by using functional integration. Each path is considered equally likely, and thus contributes the same amount. However, the phase of this contribution at any given point along the path is determined by the action along the path (see Euler's formula):
All these contributions are then added together, and the magnitude of the final result is squared, to get the probability distribution for the position of a particle:
One of an infinite number of equally likely paths used in the Feynman path integral. (see also: Wiener process.)
As is always the case when calculating probability, the results must then be normalized:
Double-slit experiment To summarize, the probability distribution of the outcome is the normalized square of the norm of the superposition, over all paths from the point of origin to the final point, of waves propagating proportionally to the action along each path. The differences in the cumulative action along the different paths (and thus the relative phases of the contributions) produces the interference pattern observed by the double-slit experiment. Feynman stressed that his formulation is merely a mathematical description, not an attempt to describe a real process that we cannot measure.
Relational interpretation According to the relational interpretation of quantum mechanics, first proposed by Carlo Rovelli,[33] observations such as those in the double-slit experiment result specifically from the interaction between the observer (measuring device) and the object being observed (physically interacted with), not any absolute property possessed by the object. In the case of an electron, if it is initially "observed" at a particular slit, then the observer–particle (photon–electron) interaction includes information about the electron's position. This partially constrains the particle's eventual location at the screen. If it is "observed" (measured with a photon) not at a particular slit but rather at the screen, then there is no "which path" information as part of the interaction, so the electron's "observed" position on the screen is determined strictly by its probability function. This makes the resulting pattern on the screen the same as if each individual electron had passed through both slits. It has also been suggested that space and distance themselves are relational, and that an electron can appear to be in "two places at once" – for example, at both slits – because its spatial relations to particular points on the screen remain identical from both slit locations.[34]
References [1] . ISBN 0-201-02118-8P. [2] Darling, David (2007). "Wave - Particle Duality" (http:/ / www. daviddarling. info/ encyclopedia/ W/ wave-particle_duality. html). The Internet Encyclopedia of Science. The Worlds of David Darling. . Retrieved 2008-10-18. [3] Feynman, Richard P.; Robert Leighton, Matthew Sands (1965). The Feynman Lectures on Physics, Volume III. Massachusetts, USA: Addison-Wesley. pp. 1–1 to 1–9. ISBN 0-201-02118-8P. [4] Greene, Brian (1999). The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. New York: W.W. Norton. pp. 97–109. ISBN 0-393-04688-5. [5] Brukner C, Zeilinger A (2002). "Young’s experiment and the finiteness of information". Philos. Trans. R. Soc. Lond. 360: 1061-1069. [6] Sir Geoffrey Ingram Taylor, "Interference Fringes with Feeble Light", Proc. Cam. Phil. Soc. 15, 114 (1909). [7] Jönsson C,(1961) Zeitschrift für Physik, 161:454–474 [8] Jönsson C (1974). Electron diffraction at multiple slits. American Journal of Physics, 4:4–11. [9] "The most beautiful experiment" (http:/ / physicsworld. com/ cws/ article/ print/ 9746). Physics World 2002. [10] New Scientist: Quantum wonders: Corpuscles and buckyballs, 2010 (http:/ / www. newscientist. com/ article/ mg20627596. 100-quantum-wonders-corpuscles-and-buckyballs. html) (Introduction, subscription needed for full text, quoted in full in (http:/ / postbiota. org/ pipermail/ tt/ 2010-May/ 007336. html)) [11] Nature: Wave–particle duality of C60 molecules, 14 October 1999 (http:/ / www. nature. com/ nature/ journal/ v401/ n6754/ abs/ 401680a0. html). Abstract, subscription needed for full text [12] de Broglie, Louis (1953). The Revolution in Physics; a Mon-Mathematical Survey of Quanta. Translated by Ralph W. Niemeyer. New York: Noonday Press. pp. 47, 117, 178–186. [13] Baggott, Jim (2011). The Quantum Story: A History in 40 Moments. New York: Oxford University Press. pp. 76. ("The wavefunction of a system containing N particles depends on 3N position coordinates and is a function in a 3N-dimensional configuration space or 'phase space'. It is difficult to visualize a reality comprising imaginary functions in an abstract, multi-dimensional space. No difficulty arises, however, if the imaginary functions are not to be given a real interpretation.") [14] O Donati G F Missiroli G Pozzi May 1973 An Experiment on Electron Interference American Journal of Physics 41 639–644 [15] Brian Greene, The Elegant Universe, p. 110 [16] Olaf Nairz, Björn Brezger, Markus Arndt, and Anton Zeilinger, Abstract, " Diffraction of Complex Molecules by Structures Made of Light (http:/ / prl. aps. org/ abstract/ PRL/ v87/ i16/ e160401)," Phys. Rev. Lett. 87, 160401 (2001) [17] Nairz O, Arndt M, and Zeilinger A. Quantum interference experiments with large molecules (http:/ / hexagon. physics. wisc. edu/ teaching/ 2010s ph531 quantum mechanics/ interesting papers/ zeilinger large molecule interference ajp 2003. pdf). American Journal of Physics, 2003; 71:319–325. doi:10.1119/1.1531580 [18] Brian Greene, The Elegant Universe, p. 104, pp. 109–114 [19] Greene, Brian (2004). The Fabric of the Cosmos: Space, Time, and the Texture of Reality. Knopf. pp. 204–213. ISBN 0-375-41288-3.
199
Double-slit experiment [20] Harrison, David (2002). "Complementarity and the Copenhagen Interpretation of Quantum Mechanics" (http:/ / www. upscale. utoronto. ca/ GeneralInterest/ Harrison/ Complementarity/ CompCopen. html). UPSCALE. Dept. of Physics, U. of Toronto. . Retrieved 2008-06-21. [21] Cassidy, David (2008). "Quantum Mechanics 1925–1927: Triumph of the Copenhagen Interpretation" (http:/ / www. aip. org/ history/ heisenberg/ p09. htm). Werner Heisenberg. American Institute of Physics. . Retrieved 2008-06-21. [22] Boscá Díaz-Pintado, María C. (29–31 March 2007). "Updating the wave-particle duality" (http:/ / philsci-archive. pitt. edu/ archive/ 00003568/ ). 15th UK and European Meeting on the Foundations of Physics. Leeds, UK. . Retrieved 2008-06-21. [23] P. Mittelstaedt; A. Prieur, R. Schieder (1987). "Unsharp particle-wave duality in a photon split-beam experiment". Foundations of Physics 17 (9): 891–903. Bibcode 1987FoPh...17..891M. doi:10.1007/BF00734319. Also D.M. Greenberger and A. Yasin, "Simultaneous wave and particle knowledge in a neutron interferometer", Physics Letters A 128, 391–4 (1988). [24] http:/ / arstechnica. com/ science/ 2012/ 05/ disentangling-the-wave-particle-duality-in-the-double-slit-experiment/ [25] J. Summhammer; H. Rauch, D. Tuppinger (1987). "Stochastic and deterministic absorption in neutron-interference experiments.". Phys. Rev. A 36 (9): 4447. Bibcode 1987PhRvA..36.4447S. doi:10.1103/PhysRevA.36.4447. PMID 9899403. [26] Pfleegor, R. L. and Mandel, L. (July 1967). "Interference of Independent Photon Beams". Phys. Rev. 159 (5): 1084–1088. Bibcode 1967PhRv..159.1084P. doi:10.1103/PhysRev.159.1084. [27] http:/ / scienceblogs. com/ principles/ 2010/ 11/ interference_of_independent_ph. php> [28] Sillitto, R.M. and Wykes, Catherine (1972). "An interference experiment with light beams modulated in anti-phase by an electro-optic shutter" (http:/ / www. sciencedirect. com/ science/ article/ pii/ 0375960172910158). Physics Letters A 39 (4): 333–334. Bibcode 1972PhLA...39..333S. doi:10.1016/0375-9601(72)91015-8. . [29] http:/ / www. sillittopages. co. uk/ 80rms_35. html "To a light particle" [30] Wave Particle Duality of C60 (http:/ / www. quantum. at/ research/ molecule-interferometry-foundations/ wave-particle-duality-of-c60. html) [31] Jenkins FA and White HE, Fundamentals of Optics, 1967, McGraw Hill, New York [32] Longhurst RS, Physical and Geometrical Optics, 1967, 2nd Edition, Longmans [33] Rovelli, Carlo (1996). "Relational Quantum Mechanics". International Journal of Theoretical Physics 35 (8): 1637–1678. arXiv:quant-ph/9609002. Bibcode 1996IJTP...35.1637R. doi:10.1007/BF02302261. [34] Filk, Thomas (2006). "Relational Interpretation of the Wave Function and a Possible Way Around Bell’s Theorem" (http:/ / www. springerlink. com/ content/ v775765467462313/ ). International Journal of Theoretical Physics 45: 1205–1219. arXiv:quant-ph/0602060. Bibcode 2006IJTP...45.1166F. doi:10.1007/s10773-006-9125-0. .
Further reading • Al-Khalili, Jim (2003). Quantum: A Guide for the Perplexed. London: Weidenfeld and Nicholson. ISBN 0-297-84305-2. • Feynman, Richard P. (1988). QED: The Strange Theory of Light and Matter. Princeton University Press. ISBN 0-691-02417-0. • Frank, Philipp (1957). Philosophy of Science. Prentice-Hall. • French, A.P.; Taylor, Edwin F. (1978). An Introduction to Quantum Physics. Norton. ISBN 0-393-09106-6. • Greene, Brian (2000). The Elegant Universe. Vintage. ISBN 0-375-70811-1. • Greene, Brian (2005). The Fabric of the Cosmos. Vintage. ISBN 0-375-72720-5. • Gribbin, John (1999). Q is for Quantum: Particle Physics from A to Z. Weidenfeld & Nicolson. ISBN 0-7538-0685-1. • Hey, Tony (2003). The New Quantum Universe. Cambridge University Press. ISBN 0-521-56457-3. • Sears, Francis Weston (1949). Optics. Addison Wesley. • Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
200
Double-slit experiment
External links • • • • • • •
• •
Java demonstration of double slit experiment, animated (http://www.falstad.com/ripple/ex-2slit.html) Java demonstration of double slit experiment, point by point (http://www.ianford.com/dslit) Java demonstration of Young's double slit interference (http://vsg.quasihome.com/interf.htm) Double-slit experiment animation (http://homepage.univie.ac.at/Franz.Embacher/KinderUni2005/waves. gif) Caltech: The Mechanical Universe, chapter 50 – Particles and Waves (http://video.google.com/ videoplay?docid=5063999801799851614) Electron Interference movies from the Merli Experiment (Bologna-Italy, 1974) (http://www.bo.imm.cnr.it/ users/lulli/downintel/index.html) Movie showing single electron events build up to form an interference pattern in double-slit experiments. Several versions with and without narration (File size = 3.6 to 10.4 MB) (Movie Length = 1m 8s) (http://www.hitachi. com/rd/research/em/movie.html) Freeview video 'Electron Waves Unveil the Microcosmos' A Royal Institution Discourse by Akira Tonomura provided by the Vega Science Trust (http://www.vega.org.uk/video/programme/66) Hitachi website that provides background on Tonomura video and link to the video (http://www.hitachi.com/ rd/research/em/doubleslit.html)
• Simple Derivation of Interference Conditions (http://schools.matter.org.uk/Content/Interference/formula. html) • Carnegie Mellon department of physics, photo images of Newton's rings (http://physdemo.phys.cmu.edu/ newton_rings.htm) • "Single-particle interference observed for macroscopic objects" (http://www.physorg.com/news78650511. html) • Huygens and interference (http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm) • Huygens and interference (http://www.strings.ph.qmw.ac.uk/~jmc/sefp/week9.pdf) • A simulation that runs in Mathematica Player, in which the number of quantum particles, the frequency of the particles, and the slit separation can be independently varied (http://demonstrations.wolfram.com/ WaveParticleDualityInTheDoubleSlitExperiment/) • Wave Nature Of Light (High School Level) – Lots of graphics and simulations; double-slit equation with examples (http://www.stmary.ws/highschool/physics/home/notes/waves/WaveNatureOfLight.htm) • To a light particle (http://www.sillittopages.co.uk/80rms_35.html)
201
ElitzurVaidman bomb tester
202
Elitzur–Vaidman bomb tester In physics, the Elitzur–Vaidman bomb-testing problem is a thought experiment in quantum mechanics, first proposed by Avshalom Elitzur and Lev Vaidman in 1993.[1] An actual experiment demonstrating the solution was constructed and successfully tested by Anton Zeilinger, Paul Kwiat, Harald Weinfurter, and Thomas Herzog From the University of Innsbruck, Austria and Mark A. Kasevich of Stanford University in 1994.[2] It employs a Mach–Zehnder interferometer for ascertaining whether a measurement has taken place. It was chosen by the New Scientist magazine as one of the seven wonders of quantum world.[3]
Bomb-testing problem diagram. A - photon emitter, B - bomb to be tested, C,D - photon detectors. Mirrors in the lower left and upper right corners are half-silvered.
Problem Consider a collection of bombs, some of which are duds. Suppose these bombs carry a certain perfect property: usable bombs have a photon-triggered sensor which will absorb a photon and detonate. Dud bombs have a malfunctioning sensor which will not interfere with any photons.[4] The problem is how to separate at least some of the usable bombs from the duds. A bomb sorter could accumulate dud bombs by attempting to detonate each one. Unfortunately, this naive process destroys all the usable bombs.
Solution A solution is for the sorter to use a mode of observation known as counterfactual measurement, which relies on properties of quantum mechanics.[5] Start with a Mach–Zehnder interferometer and a light source which emits single photons. When a photon emitted by the light source reaches a half-silvered plane mirror, it has equal chances of passing through or reflecting.[6] On one path, place a bomb (B) for the photon to encounter. If the bomb is working, then the photon is absorbed and triggers the bomb. If the bomb is non-functional, the photon will pass through the dud bomb unaffected. When a photon's state is non-deterministically altered, such as interacting with a half-silvered mirror where it non-deterministically passes through or is reflected, the photon undergoes quantum superposition, whereby it takes on all possible states and can interact with itself. This phenomenon continues until an 'observer' (detector) interacts with it, causing the wave function to collapse and returning the photon to a deterministic state.
ElitzurVaidman bomb tester
Step-by-step explanation • After being emitted, the photon 'probability wave' will both pass through the 1st half-silvered mirror (take the lower-route) and be reflected (take the upper-route). If the bomb is a dud: • The bomb will not absorb a photon, and so the wave continues along the lower route to the second half silvered mirror (where it will encounter the upper wave and cause self-interference). • The system reduces to the basic Mach–Zehnder apparatus with no sample bomb, in which constructive interference occurs along the path horizontally exiting towards (D) and destructive interference occurs along the path vertically exiting towards (C). • Therefore, the detector at (D) will detect a photon, and the detector at (C) will not. If the bomb is usable: • Upon meeting the observer (the bomb), the wave function collapses and the photon must be either on the lower route or on the upper route, but not both. • If the photon is measured on the lower route: • Because the bomb is usable, the photon is absorbed and triggers the bomb which explodes. • If the photon is measured on the upper route: • It will not encounter the bomb - but since the lower route can not have been taken, there will be no interference effect at the 2nd half-silvered mirror. • The photon on the upper route now both (i) passes through the 2nd half-silvered mirror and (ii) is reflected. • Upon meeting further observers (detector C and D), the wave function collapses again and the photon must be either at detector C or at detector D, but not both. Thus we can state that if any photons are detected at (C), there must have been a working detector at (B) – the bomb position. With this process, 25% of the usable bombs can be identified as usable without being consumed.[1] whilst 50% of the usable bombs will be consumed and 25% remain 'unknown'. By repeating the process with the 'unknowns', the ratio of surviving, identified, usable bombs approaches 33% of the initial population of usable bombs. See Experiments section below for a modified experiment that can identify the usable bombs with a yield rate approaching 100%.
Many-worlds interpretation One conceptual way to understand this phenomenon is through the Everett many-worlds interpretation. The superposition behaviour is analogous to having parallel worlds for all possible states of the photon. Therefore, when a photon encounters a half-silvered mirror, in one world it passes through, and in another world it reflects off the mirror. These two worlds are completely separate except for the particle in superposition. The photon that passes through the mirror in one world may interact with the photon that reflected off the mirror in the other world. The photons may continue to interact with each other until an observer from one world measures the photon's state. This produces the incredible but necessarily counterfactual results of the gedanken (thought experiment).
203
ElitzurVaidman bomb tester
Experiments In 1994, Anton Zeilinger, Paul Kwiat, Harald Weinfurter, and Thomas Herzog actually performed an equivalent of the above experiment, proving interaction-free measurements are indeed possible.[2] In 1996, Kwiat et al. devised a method, using a sequence of polarising devices, that efficiently increases the yield rate to a level arbitrarily close to one. The key idea is to split a fraction of the photon beam into a large number of beams of very small amplitude, and reflect all of them off the mirror, recombining them with the original beam afterwards.[7] ( See also http:/ / www. nature. com/ nature/ journal/ v439/ n7079/ full/ nature04523. html#B1 .) It can also be argued that this revised construction is simply equivalent to a resonant cavity and the result looks much less shocking in this language. See Watanabe and Inoue (2000). This experiment is philosophically significant because it determines the answer to a counterfactual question: "What would happen were the photon to pass through the bomb sensor?". The answer is either: "the bomb works, the photon was observed, and the bomb will explode", or "the bomb is a dud, the photon was not observed, and the photon passes through unimpeded". If we were actually to perform the measurement, any bomb would actually explode. But here the answer to the question "what would happen" is determined without the bomb going off. This provides an example of an experimental method to answer a counterfactual question.
References [1] [2] [3] [4] [5] [6] [7]
Elitzur & Vaidman 1993 Paul Kwiat 1994 Seven wonders of the quantum world (http:/ / www. newscientist. com/ special/ seven-wonders-of-the-quantum-world), newscientist.com Can Schrodinger's Cat Collapse the Wavefunction? (http:/ / nonlocal. com/ quantum-d/ v2/ kbowden_03-15-97. html), Keith Bowden 1997 Keith Bowden ([email protected]) David Harrison Kwiat: Tao of Interaction-Free Measurements
Further reading • P. G. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich (1995). "Interaction-free Measurement". Phys. Rev. Lett. 74 (24): 4763. Bibcode 1995PhRvL..74.4763K. doi:10.1103/PhysRevLett.74.4763. PMID 10058593. • Paul G. Kwiat; H. Weinfurter, T. Herzog, A. Zeilinger, and M. Kasevich (1994). "Experimental realization of "interaction-free" measurements" (http://www.univie.ac.at/qfp/publications3/pdffiles/1994-08.pdf) (pdf). Retrieved 2012-05-07. • Paul G. Kwiat. "Tao of Interaction-Free Measurements" (http://web.archive.org/web/19990222174102/www. p23.lanl.gov/Quantum/kwiat/ifm-folder/ifmtext.html). Archived from the original (http://www.p23.lanl. gov/Quantum/kwiat/ifm-folder/ifmtext.html) on 1999-02-21. Retrieved 2007-12-08. • Paul Kwiat. "Current Location of "Tao of Interaction-Free Measurements"" (http://physics.illinois.edu/people/ kwiat/interaction-free-measurements.asp). Retrieved 2009-04-01. • Keith Bowden (1997-03-15). "Can Schrodinger's Cat Collapse the Wavefunction?" (http://nonlocal.com/ quantum-d/v2/kbowden_03-15-97.html). Retrieved 2007-12-08. • David M. Harrison (2005-08-17). "Mach–Zehnder Interferometer" (http://www.upscale.utoronto.ca/ GeneralInterest/Harrison/MachZehnder/MachZehnder.html). Retrieved 2007-12-08. • Elitzur A. C. and Vaidman L. (1993). Quantum mechanical interaction-free measurements. Found. Phys. 23, 987-97. arxiv:hep-th/9305002 (http://arxiv.org/abs/hep-th/9305002) • Penrose, R. (2004). The Road to Reality: A Complete Guide to the Laws of Physics. Jonathan Cape, London. • G.S. Paraoanu (2006). "Interaction-free Measurement". Phys. Rev. Lett. 97 (18): 180406. Bibcode 2006PhRvL..97r0406P. doi:10.1103/PhysRevLett.97.180406. PMID 17155523.
204
ElitzurVaidman bomb tester
205
• Watanabe H. and Inoue S. (2000). Experimental demonstration of two dimensional interaction free measurement. APPC 2000: Proceedings of the 8th Asia-Pacific Physics, pp 148–150. (http://books.google.be/ books?id=yZwtFgiVs74C&lpg=RA1-PA148&ots=j4geYe-fWg&dq=Shuichiro Inoue imaging&hl=en& pg=RA1-PA148#v=onepage&q=Shuichiro Inoue imaging&f=false)
Eötvös experiment The Eötvös experiment was a famous physics experiment that measured the correlation between inertial mass and gravitational mass, demonstrating that the two were one and the same, something that had long been suspected but never demonstrated with the same accuracy. The earliest experiments were done by Isaac Newton (1642–1727) and improved upon by Friedrich Wilhelm Bessel (1784–1846).[1] A much more accurate experiment using a torsion balance was carried out by Loránd Eötvös starting around 1885, with further improvements in a lengthy run between 1906 and 1909. Eötvös' team followed this with a series of similar but more accurate experiments, as well as experiments with different types of materials and in different locations around the Earth, all of which demonstrated the same equivalence in mass. In turn, these experiments led to the modern understanding of the equivalence principle encoded in general relativity, which states that the gravitational and inertial masses are the same. It is sufficient for the inertial mass to be proportional to the gravitational mass. Any multiplicative constant will be absorbed in the definition of the unit of force. [2]
Eötvös' original experiment Eötvös' original experimental device consisted of two masses on opposite ends of a rod, hung from a thin fiber. A mirror attached to the rod, or fiber, reflected light into a small telescope. Even tiny changes in the rotation of the rod would cause the light beam to be deflected, which would in turn cause a noticeable change when magnified by the telescope. As seen from the Earth's frame of reference (or "lab frame", which is not an inertial frame of reference), the primary forces acting on the balanced masses are the string tension, gravity, and the centrifugal force due to the rotation of the Earth. Gravity is calculated by Newton's law of universal gravitation, which depends on gravitational mass. The centrifugal force is calculated by Newton's laws of motion and depends on inertial mass. If the ratio of F to F would differ from the ratio
1 2 The experiment was arranged so that if the two types of masses were of G1 to G2, the rod would rotate. The mirror is different, the two forces will not act in exactly the same way on the used to monitor the rotation. two bodies, and over time the rod will rotate. As seen from the rotating "lab frame", the string tension plus the (much smaller) centrifugal force cancels the weight (as vectors), while as seen from any inertial frame the (vector) sum of the weight and the tension makes the object rotate along with the earth.
For the rod to be at rest in lab frame, the reactions, on the rod, of the tensions acting on each body, must create a zero net torque (the only
Eötvös experiment
206
degree of freedom is rotation on the horizontal plane). Supposing that the system were constantly at rest – this meaning mechanical equilibrium (i.e. net forces and torques zero) – with the two bodies thus hanging also at rest, but having different centrifugal forces upon them and consequently exerting different torques on the rod through the reactions of the tensions, the rod then would spontaneously rotate, in contradiction with our assumption that the system is at rest. So the system cannot exist in this state; any difference between the centrifugal forces on the two bodies will set the rod in rotation. Direction of the centrifugal force in relation to gravity on the surface of earth.
Further improvements Initial experiments around 1885 demonstrated that there was no apparent difference, and he improved the experiment to demonstrate this with more accuracy. In 1889 he used the device with different types of sample materials to see if there was any change in gravitational force due to materials. This experiment proved that no such change could be measured, to a claimed accuracy of 1 in 20 million. In 1890 he published these results, as well as a measurement of the mass of Gellért Hill in Budapest.[3] The next year he started work on a modified version of the device, which he called the "horizontal variometer". This modified the basic layout slightly to place one of the two rest masses hanging from the end of the rod on a fiber of its own, as opposed to being attached directly to the end. This allowed it to measure torsion in two dimensions, and in turn, the local horizontal component of g. It was also much more accurate. Now generally referred to as the Eötvös balance, this device is commonly used today in prospecting by searching for local mass concentrations. Using the new device a series of experiments taking 4000 hours was carried out with Dezsö Pekár (1873–1953) and Jenő Fekete (1880–1943) starting in 1906. These were first presented at the 16th International Geodesic Conference in London in 1909, raising the accuracy to 1 in 100 million.[4] Eötvös died in 1919, and the complete measurements were only published in 1922 by Pekár and Fekete.
Related studies Eötvös also studied similar experiments being carried out by other teams on moving ships, which led to his development of the Eötvös effect to explain the small differences they measured. These were due to the additional accelerative forces due to the motion of the ships in relation to the Earth, an effect that was demonstrated on an additional run carried out on the Black Sea in 1908. In the 1930s a former student of Eötvös, János Renner (1889–1976), further improved the results to between 1 in 2 to 5 billion.[5] Robert H. Dicke with P. G. Roll and R. Krotkov re-ran the experiment much later using improved apparatus and further improved the accuracy to 1 in 100 billion.[6] They also made several observations about the original experiment which suggested that the claimed accuracy was somewhat suspect. Re-examining the data in light of these concerns led to an apparent very slight effect that appeared to suggest that the equivalence principle was not exact, and changed with different types of material. In the 1980s several new physics theories attempting to combine gravitation and quantum physics suggested that matter and anti-matter would be affected slightly differently by gravity. Combined with Dicke's claims there appeared to be a possibility that such a difference could be measured, this led to a new series of Eötvös-type experiments (as well as timed falls in evacuated columns) that eventually demonstrated no such effect. A side-effect
Eötvös experiment
207
of these experiments was a re-examination of the original Eötvös data, including detailed studies of the local stratigraphy, the physical layout of the Physics Institute (which Eötvös had personally designed), and even the weather and other effects. The experiment is therefore well recorded.[7]
References [1] Marco Mamone Capria (2005). Physics Before and After Einstein (http:/ / books. google. com/ books?id=r9C-SCXymPoC& pg=PA167& dq=Einstein+ Eotvos& lr=& as_brr=0& sig=ACfU3U2faCvlcHKJZm3yxT3CASi8Vz6Mdw). Amsterdam: IOS Press. p. 167. ISBN 1-58603-462-6. . [2] Brewer, Jess H. (1998). "The Eötvös Experiment" (http:/ / musr. physics. ubc. ca/ ~jess/ hr/ skept/ Forces/ node2. html). . [3] R. v. Eötvös, Mathematische und Naturwissenschaftliche Berichte aus Ungarn, 8, 65, 1890 [4] R. v. Eötvös, in Verhandlungen der 16 Allgemeinen Konferenz der Internationalen Erdmessung, G. Reiner, Berlin, 319,1910 [5] J. Renner, Matematikai és Természettudományi Értesítõ, 13, 542, 1935, with abstract in German [6] P. G. Roll, R. Krotkov, R. H. Dicke, Annals of Physics, 26, 442, 1964. [7] One Hundred Years of the Eötvös Experiment (http:/ / www. kfki. hu/ eotvos/ onehund. html)
Franck–Hertz experiment The Franck–Hertz experiment was a physics experiment that provided support for the Bohr model of the atom, a precursor to quantum mechanics. In 1914, the German physicists James Franck and Gustav Ludwig Hertz sought to experimentally probe the energy levels of the atom. The now-famous Franck–Hertz experiment elegantly supported Niels Bohr's model of the atom, with electrons orbiting the nucleus with specific, discrete energies. Franck and Hertz were awarded the Nobel Prize in Physics in 1925 for this work. The Franck–Hertz experiment confirmed Bohr's quantized model of the atom by demonstrating that atoms could indeed only absorb (and be excited by) specific amounts of energy (quanta).
The experiment The classic experiment involved a tube containing low pressure gas fitted with three electrodes: an electron-emitting cathode, a mesh grid for acceleration, and an anode. The anode was held at a slightly negative electrical potential relative to the grid (although positive compared to the cathode), so that electrons had to have at least a corresponding amount of kinetic energy to reach it after passing the grid. Instruments were fitted to measure the current passing between the electrodes, and to adjust the potential difference (voltage) between the cathode (negative electrode) and the accelerating grid.
Accelerating voltage versus anode current
• At low potential differences—up to 4.9 volts when the tube contained mercury vapour—the current through the tube increased steadily with increasing potential difference. The higher voltage increased the electric field in the tube and electrons were drawn more forcefully towards and through the accelerating grid.
FranckHertz experiment • At 4.9 volts the current drops sharply, almost back to zero. • The current increases steadily once again if the voltage is increased further, until 9.8 volts is reached (exactly 4.9+4.9 volts). • At 9.8 volts a similar sharp drop is observed. • This series of dips in current at approximately 4.9 volt increments will visibly continue to potentials of at least 100 volts.
Interpretation of results Franck and Hertz were able to explain their experiment in terms of elastic and inelastic collisions. At low potentials, the accelerated electrons acquired only a modest amount of kinetic energy. When they encountered mercury atoms in the tube, they participated in purely elastic collisions. This is due to the prediction of quantum mechanics that an atom can absorb no energy until the collision energy exceeds that required to lift an electron into a higher energy state. With purely elastic collisions, the total amount of kinetic energy in the system remains the same. Since electrons are over one thousand times less massive than even the lightest atoms, this meant that the electrons held on to the vast majority of that kinetic energy. Higher potentials served to drive more electrons through the grid to the anode and increase the observed current, until the accelerating potential reached 4.9 volts. The lowest energy electronic excitation a mercury atom can participate in requires 4.9 electron volts (eV). When the accelerating potential reached 4.9 volts, each free electron possessed exactly 4.9 eV of kinetic energy (above its rest energy at that temperature) when it reached the grid. Consequently, a collision between a mercury atom and a free electron at that point could be inelastic: that is, a free electron's kinetic energy could be converted into potential energy by raising the energy level of an electron bound to a mercury atom: this is called exciting the mercury atom. With the loss of all its acquired kinetic energy in this way, the free electron can no longer overcome the slight negative potential at the ground electrode, and the measured current drops sharply. As the voltage is increased, electrons will participate in one inelastic collision, lose their 4.9 eV, but then continue to be accelerated. In this manner, the current rises again after the accelerating potential exceeds 4.9 V. At 9.8 V, the situation changes again. There, each electron now has just enough energy to participate in two inelastic collisions, excite two mercury atoms, and then be left with no kinetic energy. Once again, the observed current drops. At intervals of 4.9 volts this process will repeat; each time the electrons will undergo one additional inelastic collision. New findings of this experiment have found that the spacing between minima and maxima increase with number of minima and vary with temperature. Refer to DOI: 10.1119/1.2174033 for more information.
Effect in other gases A similar pattern is observed with neon gas, but at intervals of approximately 19 volts. The process is identical, just with a much different threshold. One additional difference is that a glow will appear near the accelerating grid at 19 volts—one of the transitions of relaxing neon atoms emits red-orange light. This glow will move closer to the cathode with increasing accelerating potential, to whatever point in the tube the electrons acquire the 19 eV required to excite a neon atom. At 38 volts two distinct glows will be visible: one between the cathode and grid, and one right at the accelerating grid. Higher potentials, spaced at 19 volt intervals, will result in additional glowing regions in the tube.
208
FranckHertz experiment
References An Interactive Simulation of The Franck-Hertz Experiment [1] The Franck-Hertz Experiment at Hyperphysics [2] Literature on the Franck-Hertz Experiment [3] Up-to-date literature on the Franck-Hertz Experiment [4] J. Franck and G. Hertz (1914). "Über Zusammenstöße zwischen Elektronen und Molekülen des Quecksilberdampfes und die Ionisierungsspannung desselben". Verh. Dtsch. Phys. Ges. 16: 457–467. • G. Rapior, K. Senstock, and V. Baev (2006). "New features of the Franck-Hertz experiment". Amer. J. Phys. 74: 423–428. doi:10.1119/1.2174033. • • • • •
References [1] [2] [3] [4]
http:/ / phys. educ. ksu. edu/ vqm/ free/ FranckHertz. html http:/ / hyperphysics. phy-astr. gsu. edu/ hbase/ FrHz. html http:/ / users. skynet. be/ P. Nicoletopoulos/ references. html http:/ / web. me. com/ peter. nicoletopoulos/ Site/ Literature_on_the_Franck-Hertz_Experiment. html
Quantum eraser experiment In quantum mechanics, the quantum eraser experiment is a double-slit experiment that demonstrates several fundamental aspects of the quantum theory, including quantum entanglement and complementarity. The experiment has two stages: first the experimenter marks through which slit each photon went, without disturbing their movement, and demonstrates that the interference pattern is destroyed. This stage shows that it is the existence of the "which-path" information which causes the destruction of the interference pattern. The second stage goes by erasing the "which-path" information, and demonstrating that the interference pattern is recovered. It does not matter whether the erasure procedure is done before or after the detection of the photons.
Introduction The quantum eraser experiment is a variation of Thomas Young's classic double-slit experiment. It establishes that when a photon is acted upon in a fashion that allows which slit it has passed through to be determined, the photon cannot interfere with itself. When a stream of photons is marked in this way, then the interference fringes characteristic of the Young experiment will not be seen. This experiment displays the capability to create situations in which a photon that has been 'marked' to expose through which slit it has passed can later be 'unmarked'. A photon that has been 'marked' cannot interfere with itself and will not produce fringe patterns, but a photon that has been 'marked' and then 'unmarked' can interfere with itself and will produce the fringes characteristic of Young's experiment. This experiment involves an apparatus with two main sections. After two entangled photons are created, each is directed into its own section of the apparatus. It then becomes clear that anything done to learn the path of the entangled partner of the photon being examined in the double-slit part of the apparatus will influence the second photon, and vice-versa. The experimental apparatus is so constructed that at some point between the double slits and the detection screen (or between a beam splitter that also creates two paths for photon travel and thus the possibility of interference) a change in the apparatus can be made that either maintains separation of the two paths or else runs them together. If the two paths are kept separate, no interference phenomena will be observed. However, if the two paths are reunited then it becomes impossible to determine by which single path a photon might have arrived after the reunion. (Imagine an Interstate highway that takes a northern path around a city, I-1000 North, and a southern path around the city, I-1000 South. While a car is north of the city it is clear that it has traveled by way of I-1000
209
Quantum eraser experiment
210
North, but after its path merges with traffic from I-1000 South neither it nor any other car can be identified as having gone north or south of the city.) The advantage of manipulating the entangled partners of the photons in the double-slit part of the experimental apparatus is that experimenters can destroy or restore the interference pattern in the latter without changing anything in that part of the apparatus. Experimenters do so by manipulating the entangled photon, and they can do so before or after its partner has entered or after it has exited the double-slits and other elements of experimental apparatus between the photon emitter and the detection screen. So, under conditions where the double-slit part of the experiment has been set up to prevent the appearance of interference phenomena (because there is definitive "which path" information present), the quantum eraser can be used to effectively erase that information. In doing so, the experimenter restores interference without altering the double-slit part of the experimental apparatus. An event that is remote in space and in time can restore the readily visible interference pattern that manifests itself through the constructive and destructive wave interference. The apparatus currently under discussion does not have any provision for varying its time parameters, however. A variation of this experiment, delayed choice quantum eraser, allows the decision whether to measure or destroy the "which path" information to be delayed until after the entangled particle partner (the one going through the slits) has either interfered with itself or not. Doing so appears to have the bizarre effect of causing the outcome of an event after the event has already occurred. In other words, something that happens at time t apparently reaches back to some time t - 1 and acts as a determining causal factor at that earlier time.
The experiment First, a photon is shot through a specialized nonlinear optical device: a beta barium borate (BBO) crystal. This action leads to what is known as spontaneous parametric down conversion (SPDC), i.e., it converts the single photon into two entangled photons of lower frequency. From then on these entangled photons follow separate paths. One photon goes directly to a detector, which sends information of the received photon to a coincidence counter, a device that notes the nearly simultaneous reception of a photon in each of two detectors so that it can count how many pairs of entangled photons have made it through the apparatus and exclude the influence of any photons that enter the apparatus without having become entangled. When the coincidence counter is signaled of the arrival of the partner photon it increments its count. A timer is set up so that it signals a stepper motor to move the second detector on a regular basis so that it can scan across the range of positions where interference fringes could be detected. Meanwhile, the second entangled photon is faced with the double-slit, whereupon it proceeds by two paths to the second detector, which sends information of a received photon to the coincidence counter. At this point, the coincidence counter has been
Illustration 1 Crossed polarizations prevent interference fringes
Quantum eraser experiment told that both entangled photons of the original pair have been detected and that fact is added to its record along with the position currently held by the second detector. After a predetermined amount of time has passed, the detector will be moved by the tractor to examine another location. This apparatus will eventually yield the familiar interference pattern, because nothing has interfered with the disturbance that propagates through two paths after meeting the two slits and getting split up. Next, in an attempt to determine which path the photon took through the double slits, a quarter wave plate (QWP) is placed in front of each of the double-slits that the second photon must pass through (see Illustration 1). These crystals will change the polarization of the light, one producing "clockwise" circular polarization and the other producing its contrary, thus "marking" through which slit and polarizer pair the photon has traveled. Subsequently, the newly polarized photon will be measured at the detector. Giving photons that go through one slit a "clockwise" polarization and giving photons that go the other way a "counter- clockwise" polarization will destroy the interference pattern. The next progression in the setup will attempt to bring back the interference pattern by placing a polarizer before the detector of the entangled photons that took the other path out of the beta barium borate crystal (see Illustration 2). Because pairs of photons are entangled, giving one a diagonal polarization (rotating its plane of vibration 45 degrees) will cause a complementary polarization of its entangled pair member. So from this point on, the photons heading down toward the double Illustration 2 Introduction of polarizer in upper path restores interference fringes below slits will meet the two circular polarizers after having been rotated. And when photons enter either circular polarizer "half way off" from their original orientation, the result will be that on each sub-path half will be given one kind of circular polarization and half will receive the other polarization. The end result is that half the photons emerging from each circular polarizer will be "clockwise" and half will be "counter-clockwise." It will then be impossible to look at the polarization of a photon and know by which path it has come. Each component of an original wave-function will interfere with itself. And at this stage the interference fringes will reappear.
External links • A more technical analysis of the quantum eraser experiment [1] • A Scientific American article: A Do-It-Yourself Quantum Eraser - note: SciAm online subscribers only [2] • but here [3] they let you see the images for free. • The original paper on which this article is based. [4] • Demystifying the Delayed Choice Experiments [5]
211
Quantum eraser experiment
References [1] http:/ / grad. physics. sunysb. edu/ ~amarch/ [2] http:/ / www. sciam. com/ article. cfm?chanID=sa006& articleID=DD39218F-E7F2-99DF-39D45DA3DD2602A1& pageNumber=1& catID=2 [3] http:/ / www. sciam. com/ slideshow. cfm?id=a-do-it-yourself-quantum-eraser [4] http:/ / grad. physics. sunysb. edu/ ~amarch/ Walborn. pdf [5] http:/ / arxiv. org/ abs/ 1007. 3977
Stern–Gerlach experiment Important in the field of quantum mechanics, the Stern–Gerlach experiment,[1] named after Otto Stern and Walther Gerlach, is a 1922 experiment on the deflection of particles, often used to illustrate basic principles of quantum mechanics. It can be used to demonstrate that electrons and atoms have intrinsically quantum properties, and how measurement in quantum mechanics affects the system being measured.
Basic theory and description The Stern–Gerlach experiment involves sending a beam of particles through an inhomogeneous magnetic field and observing their deflection. The results show that particles possess an intrinsic angular momentum that is most closely analogous to the angular momentum of a classically spinning object, but that takes only certain quantized values. The experiment is normally conducted using electrically neutral particles or atoms. This avoids the large deflection to the orbit of a Basic elements of the Stern–Gerlach experiment. charged particle moving through a magnetic field and allows spin-dependent effects to dominate. If the particle is treated as a classical spinning dipole, it will precess in a magnetic field because of the torque that the magnetic field exerts on the dipole (see torque-induced precession). If it moves through a homogeneous magnetic field, the forces exerted on opposite ends of the dipole cancel each other out and the trajectory of the particle is unaffected. However, if the magnetic field is inhomogeneous then the force on one end of the dipole will be slightly greater than the opposing force on the other end, so that there is a net force which deflects the particle's trajectory. If the particles were classical spinning objects, one would expect the distribution of their spin angular momentum vectors to be random and continuous. Each particle would be deflected by a different amount, producing some density distribution on the detector screen. Instead, the particles passing through the Stern–Gerlach apparatus are deflected either up or down by a specific amount. This was a measurement of the quantum observable now known as spin, which demonstrated possible outcomes of a measurement where the observable has discrete spectrum. Although some discrete quantum phenomena, such as atomic spectra, were observed much earlier, the Stern–Gerlach experiment allowed scientists to conduct measurements of deliberately superposed quantum states for the first time in the history of science. By now it is known theoretically that angular momentum of any kind has a discrete spectrum, which is sometimes imprecisely expressed as "angular momentum is quantized".
212
SternGerlach experiment
213
If the experiment is conducted using charged particles like electrons, there will be a Lorentz force that tends to bend the trajectory in a circle (see cyclotron motion). This force can be cancelled by an electric field of appropriate magnitude oriented transverse to the charged particle's path.
Spin values for fermions.
Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values measured along any axis, +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. Even if the electron radius were as large as 2.8 fm (the classical electron radius), its surface would have to be rotating at 2.3 × 1011 m/s. The speed of rotation at the surface would be in excess of the speed of light, 2.998 × 108 m/s, and is thus impossible.[2] Instead, the spin angular momentum is a purely quantum mechanical phenomenon. Because its value is always the same, it is regarded as an intrinsic property of electrons, and is sometimes known as "intrinsic angular momentum" (to distinguish it from orbital angular momentum, which can vary and depends on the presence of other particles).
For electrons there are two possible values for spin angular momentum measured along an axis. The same is true for the proton and the neutron, which are composite particles made up of three quarks each (which are themselves spin-1⁄2 particles). Other particles have a different number of possible spin values. Delta baryons (Δ++, Δ+, Δ0, Δ−), for example, are spin +3⁄2 particles and have four possible values for spin angular momentum. Vector mesons, as well as photons, W and Z bosons and gluons are spin +1 particles and have three possible values for spin angular momentum. To describe the experiment with spin +1⁄2 particles mathematically, it is easiest to use Dirac's bra-ket notation. As the particles pass through the Stern–Gerlach device, they are "being observed." The act of observation in quantum mechanics is equivalent to measuring them. Our observation device is the detector and in this case we can observe one of two possible values, either spin up or spin down. These are described by the angular momentum quantum number j, which can take on one of the two possible allowed values, either +ħ/2 or −ħ/2. The act of observing (measuring) the momentum along the z axis corresponds to the operator Jz. In mathematical terms, The constants c1 and c2 are complex numbers. The squares of their absolute values (|c1|2 and |c2|2)determine the probabilities that in the state one of the two possible values of j is found. The constants must also be normalized in order that the probability of finding either one of the values be unity. However, this information is not sufficient to determine the values of c1 and c2, because they may in fact be complex numbers. Therefore the measurement yields only the absolute values of the constants.
SternGerlach experiment
214
Sequential experiments If we link multiple Stern–Gerlach apparatuses, we can clearly see that they do not act as simple selectors, but alter the states observed (as in light polarization), according to quantum mechanical law: [3]
History The Stern–Gerlach experiment was performed in Frankfurt, Germany in 1922 by Otto Stern and Walther Gerlach. At the time, Stern was an assistant to Max Born at the University of Frankfurt's Institute for Theoretical Physics, and Gerlach was an assistant at the same university's Institute for Experimental Physics. At the time of the experiment, the most prevalent model for describing the atom was the Bohr model, which described electrons as going around the positively-charged nucleus only in certain discrete atomic orbitals or energy levels. Since the electron was quantized to be only in certain positions in space, the separation into distinct orbits was referred to as space quantization. The Stern–Gerlach experiment was meant to test the Bohr–Sommerfeld hypothesis that the direction of the angular momentum of a silver atom is quantized.[4]
A plaque at the Frankfurt institute commemorating the experiment
Note that the experiment was performed several years before Uhlenbeck and Goudsmit formulated their hypothesis of the existence of the electron spin. Even though the result of the Stern−Gerlach experiment has later turned out to be in agreement with the predictions of quantum mechanics for a spin-1⁄2 particle, the experiment should be seen as a corroboration of the Bohr-Sommerfeld theory.[5] In 1927, T.E. Phipps and J.B. Taylor reproduced the effect using hydrogen atoms in their ground state, thereby eliminating any doubts that may have been caused by the use of silver atoms.[6] (In 1926 the non-relativistic Schrödinger equation had incorrectly predicted the magnetic moment of hydrogen to be zero in its ground state. To correct this problem Wolfgang Pauli introduced "by hand" so to speak, the 3 spin matrices which now bear his name, but which were then later shown by Paul Dirac in 1928 to be intrinsic in his relativistic equation.)[7]
SternGerlach experiment
Impact The Stern–Gerlach experiment had one of the biggest impacts on modern physics: • In the decade that followed, scientists showed using similar techniques, that the nuclei of some atoms also have quantized angular momentum. It is the interaction of this nuclear angular momentum with the spin of the electron that is responsible for the hyperfine structure of the spectroscopic lines. • In the thirties, using an extended version of the Stern–Gerlach apparatus, Isidor Rabi and colleagues showed that by using a varying magnetic field, one can force the magnetic momentum to go from one state to the other. The series of experiments culminated in 1937 when they discovered that state transitions could be induced using time varying fields or RF fields. The so called Rabi oscillation is the working mechanism for the Magnetic Resonance Imaging equipment found in hospitals. • Norman F. Ramsey later modified the Rabi apparatus to increase the interaction time with the field. The extreme sensitivity due to the frequency of the radiation makes this very useful for keeping accurate time, and it is still used today in atomic clocks. • In the early sixties, Ramsey and Daniel Kleppner used a Stern–Gerlach system to produce a beam of polarized hydrogen as the source of energy for the hydrogen Maser, which is still one of the most popular atomic clocks. • The direct observation of the spin is the most direct evidence of quantization in quantum mechanics. • The Stern–Gerlach experiment has become a paradigm of quantum measurement. In particular, it has been assumed to satisfy von Neumann projection. According to more recent insights, based on a quantum mechanical description of the influence of the inhomogeneous magnetic field,[8] this can be true only in an approximate sense. Von Neumann projection can be rigorously satisfied only if the magnetic field is homogeneous. Hence, von Neumann projection is even incompatible with a proper functioning of the Stern–Gerlach device as an instrument for measuring spin.
References [1] Gerlach, W.; Stern, O. (1922). "Das magnetische Moment des Silberatoms". Zeitschrift für Physik 9: 353–355. Bibcode 1922ZPhy....9..353G. doi:10.1007/BF01326984. [2] Tomonaga, S.-I. (1997). The Story of Spin. University of Chicago Press. p. 35. ISBN 0-226-80794-0. [3] Sakurai, J.-J. (1985). Modern quantum mechanics. Addison-Wesley. ISBN 0-201-53929-2. [4] Stern, O. (1921). "Ein Weg zur experimentellen Pruefung der Richtungsquantelung im Magnetfeld". Zeitschrift für Physik 7: 249–253. Bibcode 1921ZPhy....7..249S. doi:10.1007/BF01332793. [5] Weinert, F. (1995). "Wrong theory—right experiment: The significance of the Stern–Gerlach experiments". Studies in History and Philosophy of Modern Physics 26B: 75−86. doi:10.1016/1355-2198(95)00002-B. [6] Phipps, T.E.; Taylor, J.B. (1927). "The Magnetic Moment of the Hydrogen Atom". Physical Review 29 (2): 309–320. Bibcode 1927PhRv...29..309P. doi:10.1103/PhysRev.29.309. [7] A., Henok (2002). Introduction to Applied Modern Physics. Lulu.com. p. 76. ISBN 1-4357-0521-1. [8] Scully, M.O.; Lamb, W.E.; Barut, A. (1987). "On the theory of the Stern–Gerlach apparatus". Foundations of Physics 17 (6): 575–583. Bibcode 1987FoPh...17..575S. doi:10.1007/BF01882788.
215
SternGerlach experiment
Further reading • Friedrich, B.; Herschbach, D. (2003). "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics". Physics Today 56 (12): 53. Bibcode 2003PhT....56l..53F. doi:10.1063/1.1650229. • Reinisch, G. (1999). "Stern–Gerlach experiment as the pioneer—and probably the simplest—quantum entanglement test?". Physics Letters A 259 (6): 427–430. Bibcode 1999PhLA..259..427R. doi:10.1016/S0375-9601(99)00472-7. • Venugopalan, A. (1997). "Decoherence and Schrödinger-cat states in a Stern−Gerlach-type experiment". Physical Review A 56 (5): 4307–4310. Bibcode 1997PhRvA..56.4307V. doi:10.1103/PhysRevA.56.4307. • Jeremy Bernstein (2010). "The Stern Gerlach Experiment". arXiv:1007.2435v1 [physics.hist-ph]. • Use of ions (http://msc.phys.rug.nl/quantummechanics/stern.htm#Ions)
External links • Stern–Gerlach Experiment Java Applet Animation (http://www.if.ufrgs.br/~betz/quantum/SGPeng.htm) • Stern–Gerlach Experiment Flash Model (http://phet.colorado.edu/simulations/sims. php?sim=SternGerlach_Experiment) • Detailed explanation of the Stern–Gerlach Experiment (http://galileo.phys.virginia.edu/classes/252/ Angular_Momentum/Angular_Momentum.html) • Image of experiment result (http://plato.stanford.edu/entries/physics-experiment/figure13.html) • Stern–Gerlach experiment photo (http://books.google.com/books?id=u-_di7glv9YC&pg=PA432& dq=SternâGerlach+experiment&hl=lt#v=onepage&q=SternâGerlach experiment&f=false) • http://www.kip.uni-heidelberg.de/matterwaveoptics/teaching/archive/ws07-08/SternGerlach.pdf
216
Article Sources and Contributors
Article Sources and Contributors BOOMERanG experiment Source: http://en.wikipedia.org/w/index.php?oldid=490050427 Contributors: Amble, ChrisGualtieri, Cogiati, Gene Nygaard, GregorB, Headbomb, JHG, Jason Quinn, Jpeob, Ketiltrout, Linas, Marek69, Michael Hardy, Mike Peel, Mnmngb, Mtruch, Octahedron80, Pax:Vobiscum, Philip Trueman, Pph, RJHall, S. Korotkiy, Sheliak, Steinsky, Tide rolls, Usp, Wenli, 17 anonymous edits Cosmic Background Explorer Source: http://en.wikipedia.org/w/index.php?oldid=493174349 Contributors: 739ajal22, Aarghdvaark, Ahoerstemeier, Aldebaran66, Alex68677, Aliza250, AllTheseWorlds, Angela, ArielGold, Ashill, Bbbl67, Bkhouser, BlueMoonlet, Bowersj8, CZmarlin, Capn ed, Charles Matthews, ChiZeroOne, Christopher Cooper, Cmichael, Curps, CyberSkull, Daniel.Cardenas, DarthVader, Deglr6328, Diatarn iv, Dinomite, DocWatson42, Dr. Submillimeter, Dravecky, DreamGuy, Duncan.france, Dyfrgi, Earendur, Egil, Egsan Bacon, Fotaun, FrenchIsAwesome, Funandtrvl, GPHemsley, GeeJo, Geekdiva, Gene Nygaard, Headbomb, Hibernian, Hinaen, Hmains, Hydrogen Iodide, IanOsgood, Ifly6, Imroy, JamesMLane, Jlerner, Joke137, Joyous!, Jyril, Katebooty, Keith Edkins, Kurtan, MBK004, Magioladitis, Magnus.de, Mahongue, Michael Hardy, Mike Peel, Mtruch, Murlough23, Narsil, Nasa-verve, Ng.j, Novangelis, Ohms law, Oleg Alexandrov, RandomP, Rentier, Riana, Rich Farmbrough, Rjwilmsi, Rnt20, RodC, Rtfisher, Ryjaz, Sagarsavla, Sam Hocevar, Sardanaphalus, Saxbryn, ScottyBoy900Q, Sheliak, Skeptical scientist, SpaceShuttleSTS6, Steven Luo, Stevenj, Stone, Taejo, Teppic, Theodolite, Torstem, Twang, Van der Hoorn, VanishedUser314159, Whosasking, Wikiheron, WilyD, Wtmitchell, Xosema, Ykliu, Zerpent, Александр Сигачёв, 96 anonymous edits Wilkinson Microwave Anisotropy Probe Source: http://en.wikipedia.org/w/index.php?oldid=490513511 Contributors: 0Zero0, 739ajal22, A2Kafir, Agdewijn, Agge1000, Aldebaran66, Alro, Andre Engels, Andrei Stroe, AndrewHowse, Anonymous799, Argumzio, Bbbl67, Beetstra, Bobblewik, Bobtheowl2, Bogdangiusca, Boud, Brews ohare, Brian0918, Bryan Derksen, Burn, CFLeon, CMD Beaker, CRGreathouse, Chaosdruid, Chrisbrl88, Colonies Chris, ConradPino, CosineKitty, Cosmoedit, Darklilac, DarthVader, Dave Runger, Dchristle, Delpino, Djmckee1, Docjudith, Drbogdan, Emerson7, Emqueuekay, F-j123, FeanorStar7, Friendly Neighbour, Funandtrvl, Gaius Cornelius, Gary King, General Epitaph, Geoffrey.landis, George100, Georgia guy, Glacialfox, Grafen, Gus the mouse, Hairy Dude, Harp, Headbomb, Hoeksas, Hunnjazal, Hypnosifl, Igfm2, Infradig, Int3gr4te, JHG, JabberWok, Jatkins, Jdgilbey, JimR, JoJan, Joke137, Jonverve, Just Another Dan, Keith Edkins, Kerichill, KieferSkunk, Killing Vector, Kurtan, Lainagier, Laplacian, LieAfterLie, Lightmouse, Lizinvt, Looxix, Lumos3, MBlackstone, MER-C, Magioladitis, Mariguld, Mark Krueger, MathEconMajor, Mathewsian, Matthewcieplak, Meaglin, Meier99, Mhvk, Mike Peel, Mlhalpern, Mlsmith10, Modster, Mpatel, MrWikiMiki, Mtruch, Nbarth, NetKismet, Newone, Ng.j, Noisy, Ohconfucius, Ohms law, Olaf Davis, Omegatron, Onsly, Patrick, Perfectblue97, Philip Stevens, Phædrus, Pissant, Prari, Psi-kat, Puzl bustr, Quantumobserver, R'n'B, RJHall, Rich Farmbrough, Rijkbenik, Rjwilmsi, Rnt20, Roadrunner, Scog, Sdsds, Sheliak, Silly rabbit, Spebudmak, Spiffy sperry, Starkiller88, Stone, StradivariusTV, SunCreator, Susvolans, Tempshill, Tesseract2, Toyokuni3, Unyoyega, Van der Hoorn, VanishedUser314159, Viriditas, Vssun, Vyznev Xnebara, WDGraham, Whosasking, WikiLaurent, Wwheaton, Xenonice, Xiaphias, Zoe, Zotel, 131 anonymous edits Fizeau experiment Source: http://en.wikipedia.org/w/index.php?oldid=493651143 Contributors: Army1987, Bender235, Brainybear, Charvest, Czyx, D.H, Dhbradshaw, ErkDemon, Escape Artist Swyer, Hugo999, JCSantos, Jaraalbe, Jaychandra, John of Reading, Jrobinjapan, Martynas Patasius, Michael Hardy, NOrbeck, Negativecharge, Stigmatella aurantiaca, Tokenzero, 12 anonymous edits Fizeau–Foucault apparatus Source: http://en.wikipedia.org/w/index.php?oldid=486613641 Contributors: @lex@ndre, A13ean, Arnero, Brews ohare, Bryan Derksen, Dicklyon, ErkDemon, Fuhghettaboutit, Headbomb, Heron, Hfastedge, Jleedev, Lir, Looxix, Maury Markowitz, Michael Hardy, Myasuda, Pflatau, Pmronchi, Srleffler, Stefan-Xp, Stigmatella aurantiaca, Theresa knott, Vera Cruz, Wricardoh, 6 anonymous edits Hafele–Keating experiment Source: http://en.wikipedia.org/w/index.php?oldid=492214037 Contributors: Ahpook, Ali cheif, Antithanos, Authalic, Ben Standeven, Bender235, Bm gub, Cardamon, Colfer2, Czyx, D.H, DS1000, DVdm, Deb, Dicklyon, Dual Freq, GangofOne, Gbinal, GeorgeMoney, GregVolk, GregorB, Gregory9, Harald88, Headbomb, Hmains, Hugo999, Hypnosifl, Jacobs, Jaraalbe, JimWae, Jok2000, Kbk, Keenan Pepper, Kencf0618, KirkEN, Kovatslala, Maury Markowitz, Maximus Rex, Michael Hardy, Mossig, Mpatel, Nemesis75, Patrick, Pfalstad, Pthag, Railfan2, Rajah, Regent of the Seatopians, Rijkbenik, SlimVirgin, Stanlekub, Tvb, Uknewthat, Velella, XCelam, 117 anonymous edits Hammar experiment Source: http://en.wikipedia.org/w/index.php?oldid=494436915 Contributors: Alynna Kasmira, Ati3414, Bender235, CCavalieri, D-rew, D.H, Esprit15d, Eugene-elgato, Headbomb, HexaChord, HockeyRocksMySocks, IceKarma, Ifnord, Keith D, Mglg, Nemesis75, PirateSmackK, Ragesoss, Rasmus Faber, TheMatty, Tom Pippens, 15 anonymous edits Ives–Stilwell experiment Source: http://en.wikipedia.org/w/index.php?oldid=480176749 Contributors: Ati3414, Bender235, D.H, DS1000, DVdm, Deb, Dicklyon, ErkDemon, Evgeny, Francvs, Graeme Bartlett, Gregory9, Harald88, Headbomb, Hugo999, Jaraalbe, Jeffrey O. Gustafson, JzG, Michael Devore, Monkeynoze, Moroder, Racklever, Rasmus Faber, Rjwilmsi, Shagie, 11 anonymous edits Lunar Laser Ranging experiment Source: http://en.wikipedia.org/w/index.php?oldid=495229127 Contributors: Andy120290, Anigif, Bubba73, Burntsauce, Caltrop, CesarB, Chen, ChiZeroOne, CommonsDelinker, DavidK93, Dcoetzee, Edcolins, Edward, Evil Monkey, Evil-mer0dach, Finn-Zoltan, Gareth E Kegg, Geni, Gparker, GregorB, Gregors, GusFoy, Headbomb, Hillman, Hooperbloob, Hrf, Icairns, Jag123, Jonathunder, Joseph Solis in Australia, Karol Langner, Lasah, Li-sung, LouScheffer, Lriofrio, Lunokhod, Materialscientist, Mlrsutexas, MrLogic, NOrbeck, Nabokov, NickW130, Nimur, Originalwana, Physchim62, Pro crast in a tor, Queenmomcat, R'n'B, RadioFan, Rjwilmsi, Runningonbrains, Ryan Hardy, Salsb, Sardanaphalus, Sdsds, SnappingTurtle, Speaker to wolves, Spiel496, Spitzak, Surajt88, TechnoFaye, Tempshill, TheDJ, Twang, Tyrol5, Whosasking, WolfmanSF, Wongm, Xanzzibar, 49 anonymous edits Kennedy–Thorndike experiment Source: http://en.wikipedia.org/w/index.php?oldid=457847802 Contributors: Algebraist, Arabani, Ati3414, Bender235, BillFlis, D.H, DavidWBrooks, Dicklyon, Dr. Submillimeter, ErkDemon, Giocov, Gregory9, Hairy Dude, Harald88, Headbomb, Hooperbloob, Hugo999, Jaraalbe, Kungfuadam, MakeRocketGoNow, Maury Markowitz, Maximus Rex, Pearle, Poor Yorick, Rasmus Faber, Reddi, Rjwilmsi, Rowan Moore, Splash, Taxman, Teorth, Vicki Rosenzweig, 11 anonymous edits Michelson–Gale–Pearson experiment Source: http://en.wikipedia.org/w/index.php?oldid=485817098 Contributors: CanadianCaesar, Charles Matthews, D.H, Fabometric, Giocov, Hosh1313, Hugo999, JMiall, Jaraalbe, Maury Markowitz, Simon Villeneuve, 5 anonymous edits Michelson–Morley experiment Source: http://en.wikipedia.org/w/index.php?oldid=494174527 Contributors: 1(), A Nobody, A930913, AWX13245, Ajrocke, Amikake3, Andrei Stroe, Animum, Applrpn, Arabani, Arbitrary username, Arjun01, Army1987, Art Carlson, Ati3414, B4hand, Bcrowell, Bdesham, BenRG, Bender235, Berserkerus, Bighead, BlckKnght, BobEnyart, Bobblewik, Brainhell, Brothernight, BrownstoneKnockn, Bryan Derksen, Cabfare123, Carnildo, Caroline Thompson, Charles Matthews, Chas zzz brown, ChrisMiddleton, Cimon Avaro, Cliodule, Complexica, Cronholm144, D.H, DS1000, DVdm, Dabuek, Daniel Case, Danwills, Daralam, Dcoetzee, Deli nk, [email protected], Dhinden, Dicklyon, Dino, Dodiad, DomQ, DonSiano, Dorftrottel, Dr. Submillimeter, Drdonzi, E23, Eeekster, Egg, El C, ElKevbo, Enormousdude, ErkDemon, Evil Monkey, Falcorian, Famspear, Fastfission, Felicity4711, Fibonacci, Frozenport, Giocov, Giro720, Gombang, Gregory9, Gustronico, HCPotter, Hairy Dude, Hakan Kayı, Harald88, Headbomb, Hmains, Hooperbloob, Hughcharlesparker, Hugo999, Ian Pitchford, IceKarma, J.delanoy, JCSantos, Jackehammond, Jaeger5432, Jaraalbe, JerrySteal, Jessemerriman, JohnathanBeef, Jon the Geek, JorisvS, JoshG, Jredmond, Jrincayc, Jrockley, Karl Naylor, Khazar, Kingturtle, Kungfuadam, LKG123, Lacrimosus, Linas, Looxix, Loxley, Magnus Manske, Mahrabu, MakeRocketGoNow, Martin Hogbin, Maury Markowitz, Melchoir, Melongrower, Menchi, Mgiganteus1, Michael C Price, Michael Hardy, Monty845, Mr Stephen, Mxn, NEMT, Nabla, Nedwardmiller, Nemesis75, NewEnglandYankee, Niteowlneils, Notahippie76, Nvf, Odedee, Omegatron, Onedrey, Orangedolphin, Ott2, PJtP, Parameswaranvaliathan, Patrick0Moran, Pethr, Pfuller96, Physchim62, Piano non troppo, Pjacobi, Pjvpjv, RJHall, Ragesoss, Raghith, Rasmus Faber, Reddi, Rememberway, Resolute, Rich Farmbrough, Richard001, Rjwilmsi, Robert K S, Ronz, Rory096, SJRubenstein, STLocutus, Samuelweiss, Sanders muc, Sfahey, Simetrical, Sizarieldor, Smartiger, Smyth, Snowdog, Someone42, Splash, Splintercellguy, Srleffler, Steven Weston, Stevenrl, Stevertigo, Stigmatella aurantiaca, Suruena, Tabletop, Tarquin, Ted87, Tentu, Teorth, The Cunctator, Thegreenj, Theo10011, Thumperward, Tiki God, Tim Shuba, Tim!, Truth seeker, Tuyvan, Unyoyega, Uppland, User2004, Vin-Jang Lee, Vineeth.sukumaran, Wavelength, Will Beback, YanWong, 308 anonymous edits Oil drop experiment Source: http://en.wikipedia.org/w/index.php?oldid=490024173 Contributors: 3mta3, Alansohn, Alison, Am00nz0r5, Andycjp, Asdf1234567890000000000099, Ashcroftgm, Astrogrikor, Auric, Awolf002, AznBurger, Batmanand, Bchcky77, Billzweig, Boffy b, Camw, Charles Matthews, Chhe, Christianjb, CommonsDelinker, Cutler, Cybercobra, D.H, Daniel.Cardenas, DavidCBryant, Discospinster, Dominus, Drbreznjev, Dumbelephants, Eebster the Great, Electrolite, Electron, Elkman, FMCTandP, Fences and windows, Fotoguzzi, GNU, Gaius Cornelius, GcSwRhIc, Gene Nygaard, Gravecat, Guthrie509, Headbomb, Heron, Hon-3s-T, Hooperbloob, Hugo999, Husond, I-hunter, InverseHypercube, Ireas, Itub, J.delanoy, JabberWok, Jaraalbe, JdH, Jerry, Jkeohane, Jll, Kaszeta, Keenan Pepper, Kghose, Kieff, Kkmurray, KnowledgeOfSelf, LachlanA, Levineps, Linas, Lorenj, MECU, Maja3141, Marshman, Mejor Los Indios, Michael Hardy, MisterSheik, Mjmcb1, MrBell, Mulad, Mumby, Nickipedia 008, Nicobn, NuclearWarfare, Pavel Vozenilek, Phantomsteve, Phelonius Friar, Philip Trueman, Pinkadelica, Popefelix, Pretzelpaws, Primalbeing, PrimeHunter, Pt, Puchiko, Ragesoss, Raul654, Reddi, Redit, Rich Farmbrough, Rico402, Robinspw, Sceptre, Schneider anc, Seddon, Shanes, Sixsous, Skittleys, Skoch3, Spiritllama, Stephen.G.McAteer, Stolee, StradivariusTV, Syrthiss, Tevildo, The Hokkaido Crow, The Rambling Man, The Thing That Should Not Be, Thedeathlord, Thedemonhog, Theresa knott, Thumperward, Tom harrison, Tsquared2215, Tttrung, Twbeals31, Vicenarian, Villahj Ideeut, Vivek Verma 38, Waggers, WhiteInk, WikiReviewer.de, Worthawholebean, WurmWoode, Xandi, Yhr, 245 anonymous edits Oxford Electric Bell Source: http://en.wikipedia.org/w/index.php?oldid=485741760 Contributors: Alexey Feldgendler, Axem Titanium, BD2412, Bergsten, Bk0, Cantons-de-l'Est, Chronulator, DV8 2XL, Darkoneko, David Gerard, EEMIV, Eric Shalov, Fitzhugh, GregorB, Headbomb, Infrogmation, Jpbowen, Kelisi, Linas, Martinwguy, Mwongozi, Nicolas1981, OllyH, PKnight, Pm215, Rebrane, Salmanazar, Senra, Spoonriver, Stone, TeaDrinker, Thorwald, Thumperward, Titus III, Wdanwatts, Whosasking, WulfTheSaxon, 24 anonymous edits
217
Article Sources and Contributors Rømer's determination of the speed of light Source: http://en.wikipedia.org/w/index.php?oldid=492466600 Contributors: Alexandrejcosta, Ashmoo, Beetstra, Brian Huffman, Chris the speller, Ettrig, Foobarnix, Hugo999, LilHelpa, Magioladitis, Mykhal, Oerjan, Ospalh, Peter Alberti, Physchim62, RSStockdale, Tabletop, Trevayne08, Ttonyb1, Twang, WikHead, Woohookitty, 9 anonymous edits Sagnac effect Source: http://en.wikipedia.org/w/index.php?oldid=492661343 Contributors: Ahoerstemeier, Almuhammedi, Ati3414, AxelBoldt, Cam, Cleonis, Cmdrjameson, D. mcfadden, D.H, DS1000, Denelson83, Długosz, Edgar v. Hinüber, El C, Electron9, Ems57fcva, Evil saltine, Gregory9, Hamiltondaniel, Harald88, Headbomb, Hess88, Hillman, IVAN3MAN, Incnis Mrsi, Insanity Incarnate, Itnotf, J04n, Jason Quinn, Jeffrey O. Gustafson, Jok2000, Jsbohannon, Julesd, Kurgus, Lantonov, Linas, Luiz.Sauerbronn, Lwalkera, Michael Hardy, Misibacsi, Msablic, Muhandes, NawlinWiki, Ott2, Oxnard27, Patrick, Patrick Berry, Pemmy, Pentasyllabic, Pjacobi, Pwjb, Racharis, Raryel, Rasmus Faber, Reedy, Rjwilmsi, Rracecarr, Russell S Thomas, SEIBasaurus, Saeedbf, Seba5618, Socrunchy, Somnibus, Srleffler, Stcloudstatewang, The Anome, The RedBurn, V1adis1av, Writtenright, Zunaid, 82 anonymous edits Terrella Source: http://en.wikipedia.org/w/index.php?oldid=494104361 Contributors: Aarghdvaark, Caltrop, Changcho, David Eppstein, DavidStern, Deglr6328, G. Warren Grant, Headbomb, Iantresman, Jaraalbe, Krash, Luigi30, Meelar, Mick Knapton, Njál, Pepsidrinka, Ssilvers, TheKMan, XJamRastafire, 10 anonymous edits Trouton–Noble experiment Source: http://en.wikipedia.org/w/index.php?oldid=492883860 Contributors: Ati3414, Chris Roy, Cmdrjameson, D.H, Dicklyon, Dysprosia, Elminster Aumar, FelisSchrödingeris, Gregory9, Headbomb, Hugo999, J.C.Max, Jaraalbe, Joseph Solis in Australia, Karol Langner, Linas, MakeRocketGoNow, Maury Markowitz, Omegatron, Ragesoss, Rasmus Faber, RayTomes, RedWolf, Reddi, Salsb, She Who Must Be Obeyed, Sipsherry, Stevenj, Teorth, The Anome, Tim Starling, TimBentley, 17 anonymous edits Trouton–Rankine experiment Source: http://en.wikipedia.org/w/index.php?oldid=433986378 Contributors: Algebraist, Astrochemist, Ati3414, Bender235, Cmdrjameson, Colonies Chris, D.H, Dicklyon, Dual Freq, GrapeSmuckers, Gregory9, Harald88, Headbomb, HieronymousCrowley, Hugo999, Jaraalbe, Joe Decker, Kingboyk, Mpatel, Netsnipe, Ospalh, Rasmus Faber, TomyDuby, WWStone, 25 anonymous edits Cavendish experiment Source: http://en.wikipedia.org/w/index.php?oldid=493996573 Contributors: Ali Abbasi7, Altenmann, Angela, Astrochemist, BillC, Bobblewik, Boemmels, Chetvorno, Cide Hamete Benengeli, Cometstyles, CommonsDelinker, Coredesat, CronoDAS, Cryptic, Dan East, Dbroadway, DomCleal, Dominus, Dreish, Dzordzm, Eastlaw, Edokter, Elert, Eleusinian, Engineman, Gcfriedman, Headbomb, Hmains, Hooperbloob, Hugo999, Ideal gas equation, James8312201, Jaraalbe, Jbergquist, Jimp, Jthill, KjellG, Kmccoy, Kurosuke88, Leptons, Little1406, Malafaya, Mavrisa, Mcapdevila, Michael Devore, Michael Hardy, Mild Bill Hiccup, Mynameiswill, Naddy, Nightstallion, Omnipaedista, Opelio, Paweł Ziemian, Philip Trueman, Pjedicke, Quiet Silent Bob, Raul654, Rich Farmbrough, Rjwilmsi, Sctfn, Stebbins, Steven Zhang, Tanaats, Tttrung, Unyoyega, Verytallrob, Vinograd19, Wile E. Heresiarch, Zeyn1, 81 anonymous edits De Sitter double star experiment Source: http://en.wikipedia.org/w/index.php?oldid=458681947 Contributors: Ati3414, Charvest, D.H, Donkey7171, Edward, ErkDemon, Fuhghettaboutit, Gaius Cornelius, Gregory9, Hugo999, Jaraalbe, Linas, Martin Hogbin, RobertFritzius, Syndicate, 7 anonymous edits Gravity Probe A Source: http://en.wikipedia.org/w/index.php?oldid=456724770 Contributors: A2Kafir, Awolf002, CarlHewitt, ChiZeroOne, ChrisG, Colonies Chris, Daniel Arteaga, Ems57fcva, Falcorian, Fifteen10e56, Gsl, Headbomb, Herbee, Hooperbloob, Hugo999, Jaraalbe, Keenan Pepper, Michael Hardy, Ms2ger, Reddi, RexNL, Rich Farmbrough, Vatic7, Whosasking, Yath, 13 anonymous edits Gravity Probe B Source: http://en.wikipedia.org/w/index.php?oldid=488582377 Contributors: 1exec1, 84user, 999mal, ABCD, Afshar, Ahoerstemeier, Alexf, Anastrophe, Ancheta Wis, Andres, AussieBoy, Awolf002, AxelBoldt, BentSm, Blaxthos, Bobblewik, BorgQueen, Borhan0, Bowlhover, Brazmyth, Bryan Derksen, Capecodeph, Carlog3, Cburnett, Charles Matthews, ChiZeroOne, Chongruk, Chrislintott, ChronHigherEdReader, Colonies Chris, Crowsnest, D.H, DJTachyon, DMG413, Daniel Arteaga, DarthVader, Deglr6328, Dirkb, Dravecky, Drbreznjev, Dsjvdhbv, Dwpaul, DÅ‚ugosz, Egg, Eleassar, Ems57fcva, Ersatzed, Esirgen, Esradekan, Falcorian, Fieldworld, FienX, Fvincent, Fwappler, GangofOne, Garthbarber, Gene Nygaard, Geoffrey.landis, Giftlite, Gparker, GraviMat, Greg L, Hamiltondaniel, Harley peters, Harris7, Headbomb, Hillman, Iain.mcclatchie, IanOsgood, Inimbrium, JTN, Jacobolus, Jbergquist, Jcmester, Jkasd, Jkl, JoeSmack, Johns1a9, KPlayer, Keenan Pepper, Kieff, Korath, KurtBlueSky, Lambiam, Linas, Loadmaster, LouScheffer, MacsBug, Mario777Zelda, Maximus Rex, Mejor Los Indios, Michael Hardy, Mike s, Mild Bill Hiccup, Minesweeper, Mitsuhirato, Mnmngb, Mortense, Mxn, Nealmcb, NeilUK, Nixer, Noinlair, Onco p53, Originalwana, Ospalh, PabloStraub, PaddyLeahy, Pascal666, Pbroks13, Peter Ellis, Phil Boswell, Planetary, Potatoswatter, REkaxkjdsc, Rapomon, Ravedave, Rich Farmbrough, Rjwilmsi, Robinh, Roidroid, Russell C. Sibley, SECProto, Seth Ilys, Shawn81, Spartaz, Subh83, Taborgate, Tarfu92, TechnoFaye, The Anome, The1physicist, Theshadow27, Tierce, Tom Lougheed, Trojancowboy, TrufflesTheLamb, Tsemii, Varuna, Vinograd19, WDGraham, Whosasking, Wiggles007, Wk muriithi, WolfmanSF, Wolfy9005, Wwheaton, Xosema, Yath, Zero0000, Zumbo, 155 anonymous edits Pound–Rebka experiment Source: http://en.wikipedia.org/w/index.php?oldid=462981891 Contributors: And4e, Ati3414, Basawala, Bender235, ChumpusRex, Conscious, DS1000, Davidhorman, ErkDemon, Fashionslide, Fleem, Gene Nygaard, Graeme Bartlett, Gregory9, Gustronico, Headbomb, Hillman, J.delanoy, JCSantos, Joke137, Kencomer, Kingboyk, Lumidek, Martin Hogbin, Mdd, Michael Devore, Michael Hardy, Mikiwikipikidikipedia, Mpatel, Myasuda, Omnipaedista, PhilKnight, Rasmus Faber, Rijkbenik, Rjwilmsi, Salsb, Seattle Jörg, Sooty85, Suslindisambiguator, T.O. Rainy Day, Varchaswi, Vuo, WWStone, Wesino, 31 anonymous edits Schiehallion experiment Source: http://en.wikipedia.org/w/index.php?oldid=495471132 Contributors: BillC, Engineman, Headbomb, Hmains, Hugo999, Incnis Mrsi, Keith D, Koavf, Kurosuke88, M-le-mot-dit, Mais oui!, Michael Devore, Mouse20080706, Reyk, Rich Farmbrough, Rigadoun, SciberDoc, Spinningspark, Stever Augustus, Tim!, 官 翁, 8 anonymous edits Atwood machine Source: http://en.wikipedia.org/w/index.php?oldid=490569286 Contributors: Abune, Aushulz, Bensabari, CanadianPenguin, Cardamon, Carultch, Charles Matthews, Chmod007, Danski14, Ezelenyv, Femto, Fiveless, Foobaz, Frank823, Gene Nygaard, Headbomb, JForget, JackofOz, Jacobolus, JayC, Karada, Landreoli90, Minored, Mkch, Nick Garvey, NotYouHaha, Phobos, Ret25, Schekinov Alexey Victorovich, Schmloof, Sebastiangarth, Skiasaurus, Tehsi, Theoh, Trevor Johns, Ttiotsw, Uncle Dick, Waitati, 67 anonymous edits Barton's Pendulums Source: http://en.wikipedia.org/w/index.php?oldid=472111545 Contributors: Asrae Johnson, Gmoone94, Headbomb, Jbusenitz, Jpowell, Melongrower, Monty845, ShelfSkewed, Waxigloo, 3 anonymous edits Bedford Level experiment Source: http://en.wikipedia.org/w/index.php?oldid=495317486 Contributors: Allissonn, Anagogist, Benito, Bombaysippin, Chris55, Closedmouth, Dave.Dunford, Doric Loon, Ezriilc, Flyguy649, Fratrep, Good Olfactory, GregorB, Guardimp, Headbomb, Johnuniq, JonHarder, Juansidious, Klilidiplomus, Kosebamse, LilHelpa, Old Moonraker, Ragesoss, Rich Farmbrough, Rjwilmsi, SimonTrew, The Rationalist, Winterstein, ZergZergLOL, 29 anonymous edits Beverly Clock Source: http://en.wikipedia.org/w/index.php?oldid=494614527 Contributors: Annom, Ariel., Axem Titanium, BenRG, Bkell, Bobblewik, CitizenofPanem, DV8 2XL, Danfuzz, Earle Martin, Finn-Zoltan, Gene Nygaard, Headbomb, Hooperbloob, Johnbod, Julesd, Kubiwan, Linas, Mcwatson, Midgley, Moonriddengirl, Nimur, Optics guy07, RJFJR, Rich Farmbrough, Royaume du Maroc, Steevven1, Thumperward, Titus III, Uncle G, WLU, Whosasking, Winston Spencer, XLerate, Zaphod Beeblebrox, 11 anonymous edits Galileo's Leaning Tower of Pisa experiment Source: http://en.wikipedia.org/w/index.php?oldid=488646015 Contributors: (jarbarf), 7, Abecedare, Alansohn, Araignee, BillFlis, Bluefist, Bobo192, Bubba73, DerHexer, Ensparc, Girdag, Headbomb, Hello Control, Johnmarkh, Jpbowen, Juansidious, KConWiki, KGF2009, LittleMissNoisy, Magpie55, Mark Arsten, Materialscientist, Natrajdr, Nsaa, Pavel Vozenilek, Prezbo, Qmwne235, RandomAct, Richwales, Robma, Root2, SorryGuy, Srryan, Theodork, Tommy2010, Utcursch, WikHead, Wildwill2002, 69 anonymous edits Heron's fountain Source: http://en.wikipedia.org/w/index.php?oldid=494212582 Contributors: Ariel., BjKa, Blood sliver, CSWarren, Calibas, Catalographer, Ebraminio, Ed!, EdJogg, Gurps npc, Headbomb, Hmains, Hugh7, Invincecus, Jamelan, Master of Puppets, Mattpickman, MeltBanana, MichaelFrey, Nunh-huh, Pearle, RealGrouchy, Reinyday, RolfBly, Sonett72, The Anome, 27 anonymous edits Magdeburg hemispheres Source: http://en.wikipedia.org/w/index.php?oldid=491782924 Contributors: Aaron D. Ball, Altzinn, Angusmclellan, Bergsten, BillC, Bkmd, Caltrop, Chetvorno, Conscious, Coolhandscot, Darwinius, Deathgleaner, Djmutex, Fastfission, Fconaway, Firien, Fuhghettaboutit, Gaius Cornelius, Gurch, Headbomb, HennessyC, Heron, Jag123, Jeh, Jketola, Lecture Demonstration, Lights, Ligulem, MatthewEHarbowy, Merovingian, Miaow Miaow, Modeha, Nohat, Obersachse, Olessi, Oxymoron83, Pearle, Profoss, R'n'B, Raymondwinn, Rich Farmbrough, Romanm, Sadi Carnot, Salsa Shark, Salsb, Saperaud, Scottfisher, Slashme, Smalljim, Stovetopcookies, Sukratu Barve, That Guy, From That Show!, Thuresson, Topory, Unfortunateoveryield, Vary, XJamRastafire, Ytrottier, 50 anonymous edits Rubens' tube Source: http://en.wikipedia.org/w/index.php?oldid=495067515 Contributors: Alemisstequila, Aricept, Banaticus, Berensflame, BlackPoison78, Bubnicbf, Cantons-de-l'Est, Coffeepusher, Demarchist, ELClinkscale, Frankiwilson, Geekybroad, GregU, Headbomb, High Contrast, JeffyP, Jspacone90, Kvng, Lantonov, Mars216, Nargopolis, Pmsyyz, Prof308, Rich Farmbrough, Rondom, Shawnhath, Y control, ZanderZ, 59 anonymous edits Pitch drop experiment Source: http://en.wikipedia.org/w/index.php?oldid=494660534 Contributors: Ahruman, Alexforcefive, Andjack, Angr, Apalsola, Axem Titanium, Axeman89, Br10ta10, Bryan Derksen, Capi, Cburnett, Common Man, Crowsnest, Dale Arnett, Dominus, Duschi, Epbr123, Fireswordfight, Floaterfluss, Foobar, FrancisGM, Frencheigh, Gene Nygaard, Greeneese, GregorB, Guessing Game, Guy Macon, Headbomb, Heliox00, Heron, Horncomposer, Jeepo, Jehochman, Jibjibjib, John, Katefan0, KathrynLybarger, Keenan Pepper, Kri, LaWa, Leaderofearth, Limulus, Linas, Losahboy, Lowellian, Markus Schmaus, MeekMark, Mercurywoodrose, Mgiganteus1, Mglg, Minglex, Mr Anthem, Mtpaley, Northfox, Okedem, Osarius, P.T. Aufrette, Postlewaight, Rajah, Rich Farmbrough, Robert Brockway, Rror, Rtcpenguin, Rune.welsh, Saibo, Semper discens, Seth Ilys, Sl, Smurfsahoy, Sponge, T0lk, Tanner Lin, Titus III, Tofutwitch11, Twipley, Tylerni7, Undead Herle King, Uqcshann, Verne Equinox, WLU, Wayne Slam, Wdanwatts, Whosasking, Wikipeditor, Zaphod Beeblebrox, Zero1328, ^demon, 55 anonymous edits
218
Article Sources and Contributors Spouting can Source: http://en.wikipedia.org/w/index.php?oldid=470664411 Contributors: Arteyu, Biscuittin, Chowbok, Exdejesus, Headbomb, IRP, Pascal666, Paul Murray, Vanished user 01, ZooFari, 9 anonymous edits Bevatron Source: http://en.wikipedia.org/w/index.php?oldid=490804427 Contributors: Ae77, Allens, Azazello, Backspace, Bender235, Captain panda, Ceraniic, Closedmouth, Conscious, Derdeib, Dhollm, Droll, Egg, Erfa, Falcorian, Glenmark, Headbomb, J.delanoy, KP-Adhikari, Ketme, Lightmouse, LilHelpa, Materialscientist, MrBell, Omeganian, Protron, R'n'B, Radiojon, Regulov, SCZenz, Schmieder, Securiger, Strait, TJJFV, Taupositron, Thunderbird2, Viriditas, Wanderer34, Wwheaton, 16 anonymous edits Chicago Pile-1 Source: http://en.wikipedia.org/w/index.php?oldid=492144918 Contributors: 790, Adamrush, Appraiser, Arniebuteft, Bk0, Blainster, Bomazi, CommonsDelinker, Darsie42, Distantbody, Doncram, DroEsperanto, Dwarfyperson, Ebyabe, Elektrik Shoos, Eluchil404, Eoghanacht, Epolk, Fastfission, Favonian, Funguswhitey, Gertlex, GordonMcD1066, Grandpafootsoldier, GregorB, Headbomb, IvoShandor, Jcaditz, Jcricket4, Jivecat, Jweiss11, KBrown, Kbdank71, KudzuVine, LeeHunter, Lightmouse, Lukejon1995, Markmit, Melchoir, Mwhite66, Myasuda, Neweb, Northwesterner1, Patken4, Petri Krohn, Piano non troppo, Pigsonthewing, RealGrouchy, Rjwilmsi, Sam metal, Sansumaria, Sevilledade, Shaddack, Speciate, Squideshi, Stone, Sylviaelse, Tdadamemd, Tedernst, TheJJJunk, Tom harrison, TonyTheTiger, Treemaster4, UrbanNerd, Vox Rationis, Vsmith, W.andrea, Yoyoyoshia, Zagalejo, Zimage, Zzyzx11, 42 anonymous edits Cowan–Reines neutrino experiment Source: http://en.wikipedia.org/w/index.php?oldid=492103483 Contributors: Bobblewik, ChrisGualtieri, Curb Chain, Eloy, Ettrig, Gene Nygaard, Grimlock, Harp, Headbomb, Jengod, JoshuaZ, Kaspar.jan, Lester Welch, LorenzoB, Maximus Rex, Michael Hardy, Mnmngb, Nickptar, Phr en, Plasticup, Raul654, Rjwilmsi, Salvoaiola, SkyLined, Spike Wilbury, Strait, The Original Wildbear, TimothyRias, Twang, Whatsoevernever, Whosasking, Xeroc, Zagloba, 18 anonymous edits Geiger–Marsden experiment Source: http://en.wikipedia.org/w/index.php?oldid=494801119 Contributors: ABF, Access Denied, Ahoerstemeier, Ainglis, Alansohn, Aldie, Alexbrewer, Alexwarwickvesztrocy, Aristophanes68, Atif.t2, Awolf002, Backslash Forwardslash, BarretB, Benji Stokoe, C.jeynes, CardinalDan, Chris the speller, Christian75, Chrisus93311, Cobaltbluetony, Courcelles, Customcabf100, DHN, Darac, Dcorzine, DeadEyeArrow, Debresser, Deltik, Demonuk, Diannaa, Dirac66, Djr32, Doc glasgow, EdJohnston, Egg, Epbr123, Evil saltine, Excirial, Fastfission, Flipperinu, Fusionmix, Gadfium, Glacialfox, Gopackgo31, GrahamBould, HalfShadow, Hargrimm, Headbomb, Hooperbloob, Hu, Hugo999, Hydeblake, Im.a.lumberjack, Interiot, Inwind, Isgrimnur, Itub, Ixfd64, J.delanoy, JagtarBhogal, Jaraalbe, Jeffrey O. Gustafson, Jhessian Zombie, Jimmy Maxwell Jaffa, Jimp, Jll, Jossi, Juanpdp, Kahkonen, Kelly Martin, Kimchi.sg, Kurzon, La Pianista, LedgendGamer, Linas, MK8, Macy, Malcolm Farmer, Mentifisto, Mercurywoodrose, Mike Christie, Moletrouser, Mooquackwooftweetmeow, Mouchoir le Souris, Mr.98, Nutmegmann, PDH, Paweł Ziemian, Petergans, Pinkadelica, Psbsub, Raul654, Razorflame, Rdsmith4, Registered99, Res2216firestar, Rob625, ST47, SamHB, Sbharris, Sct72, Siddhant, Sjakkalle, Skysmith, Smrozews, SotoCerberus, Stephen e nelson, Techman224, The Evil IP address, The Thing That Should Not Be, Tide rolls, Tomdobb, Tony1, Trusilver, Ttony21, Uopchem252, Viriditas, Voyajer, Vsmith, Waerloeg, Wesolson, Whooooooknows, WikiUserPedia, Wimt, WinterSpw, Zoicon5, 377 anonymous edits Homestake experiment Source: http://en.wikipedia.org/w/index.php?oldid=456735857 Contributors: BatesIsBack, Coronium, Customcabf100, Flying fish, Headbomb, Jaeger5432, JohnCD, Mike Peel, Mnmngb, Mvsrhollywood, Oldelpaso, Scorbatt, Strait, Whosasking, 5 anonymous edits Large Hadron Collider Source: http://en.wikipedia.org/w/index.php?oldid=495302383 Contributors: (jarbarf), -Majestic-, 02millers, 03md, 123smellmyfeet, 1dragon, 2bornot2b, 343GuiltySpark343, 4johnny, 842U, 84user, 99chromehead, A. di M., A.R., A3RO, AMK1211, Abcadi, Abdullais4u, AbhishekSinghRana, AcademyAD, Ace111, Acepectif, Achowat, Acroterion, Adambro, Addw, Adejam, Adhalanay, Adilch, Adj08, Advertiseo, Aetheling1125, Afowler, AgadaUrbanit, Ageekgal, Ahoerstemeier, Ajeetkumar81, Aka042, Aknochel, Al Farnsworth, Alamgir, Alaniaris, Alansohn, Alberto da Calvairate, Alderepas, Aldnonymous, Alexgenaud, Alexius08, [email protected], Amaurea, Amire80, Amorymeltzer, Andefs, AndersFeder, Andre Engels, Andre.holzner, Andrewlp1991, Andrius.v, Andy M. Wang, Anetode, Anna Frodesiak, Anonyfuss, Anonymous Dissident, Anonymous5555, Antimatter Dilbert, Apau98, Apparition11, ArglebargleIV, Army1987, Arnoutf, Arobic, Arpingstone, Arronax50, Art LaPella, Arthena, Arthur Rubin, Ashmoo, AssegaiAli, AstroHurricane001, Atelerix, Atif.t2, Austin512, Autonova, Autumn Fall, AvalonTreman, Axl, AzureFury, Backspace, Baclough, Balcerzak, Bambaiah, Barak Sh, Baryn, Basejumper123, Bastique, Batista619, Batmanand, Beatsbox, Beeblebrox, Beehive101, Beetstra, Beland, Belismakr, Bella Swan, BenRG, Bender235, Benplowman, Bergdohle, Beta Orionis, Bevo, Bhny, Bigbluefish, Bigboy101011, Bigbullhoodboy, Biguana, BillC, BillFlis, Biologicithician, Bjankuloski06en, Black Shadow, Blaxthos, Blehfu, Bm gub, Bmoc2012tms, Bob drobbs, Bobo192, Bodhikun, Boing! said Zebedee, Boodlesthecat, Booyabazooka, Branddobbe, Brandon, BreakerLOLZ, Brickwall04, Brouhaha, Bryan Derksen, Bsadowski1, Bsimmons666, Btcc11, Bubba73, Buckethed, Buddy431, Bugnot, Buridan, Burzmali, CIreland, Caco de vidro, CaelumArisen, Cakedamber, CamB42424, Camronwest, Camw, CanadianLinuxUser, Canthusus, Capricorn42, CaptinJohn, CardinalDan, Cariniabean, Casmiky, Catgut, Cathardic, Cbetan, Cbrown1023, Cellodont, Cenarium, Centrx, Cerebellum, Ceyockey, Cgingold, Cgwaldman, Ch1n4m4n, Chaleur, Chem-MTFC, Chickenweed, Chihuong bk, Chovain, Chris G, Chrisfex, Chrishmt0423, Chrisrus, Chriss789, Christina Silverman, Chronitis, Chrumps, ChuChingadas, Chzz, Citedegg, Clay Juicer, Closedmouth, Cmanser, Coasterlover1994, Colmsherry, Colonel Warden, Connelly, Connormah, Contribut, Courcelles, Crisis, Cristi.falcas, Cstaffa, Ctjf83, Ctmt, Cvet, CyberSkull, Cyclades, DMacks, DMeyering, DMurphy, DVdm, Dacool7, Daelian, Daf, Dailycare, Dalahäst, DanielCD, DanielDeibler, Dante Alighieri, Dark Formal, Darklombax, Darrenhusted, Darsie from german wiki pedia, Darth Mike, DataMatrix, Dauto, Davemck, David Gerard, David Schaich, David.Monniaux, DavidB601, Davodd, Dbutler1986, Deagle AP, Deamon138, Deb, Debresser, Decltype, Deconstructhis, Delusion23, Deon, Der Falke, DewiMorgan, Dirac1933, Dirtygreek, Discospinster, Djinn65, Docjudith, DoctorJoeE, Donfbreed, Doradus, Dormskirk, DoubleBlue, Douchedoom, Download, Dpr101188, Dracoblaze4, DragonFury, Dreadstar, Dreish, Dricherby, Drrngrvy, Dtely, Duncan, Duncan.france, Dux is me, Dycedarg, Długosz, ESkog, EarthRise33, Earthsky, Eastlaw, Ebenonce, EdC, Edderso, Edward, Eeekster, Egil, Ehn, Eintragung ins Nichts, ElationAviation, Electron9, Eliasen, Elipongo, Elliot Lipeles, Elonka, Emily Jensen, EmilyUndead, Entropy, Eothred, Epbr123, Error792, Esb, Estevoaei, Esthurin, EuroWikiWorld, Eurobas, Evans1982, Ever388, Evercat, Everyme, Ewhite2, Ex Everest, Excellt127, Excirial, Eyu100, F Notebook, FT2, Faithlessthewonderboy, Falcon8765, Falcon9x5, Fama Clamosa, Fanatix, Fanman904, Fatpratmatt, Felix Dance, Felixhudson, Final Philosopher, Finnrind, Fl4ian, Fletcher, Florentino floro, Florian Blaschke, Flukas, Fluteflute, FlyingToaster, FrF, Franjesus, Frazzydee, Frecklefoot, Fred Stober, FreddoT, Fredrik, Freerk, Friendly Neighbour, Frikandel, FunkDemon, Funkysapien, Furrykef, GDallimore, Gabbe, Gaming4JC, Gbrandt, Geckon, Ged UK, GeeJo, Geepster, Geljamin, Gene Nygaard, General Epitaph, GetTheShift, Gflashwnox, Giftlite, Gimmetoo, Gimmetrow, Ginsengbomb, Gjtorikian, GlobetrottingAussie, Gmeyerowitz, God=nocioni, GorillaWarfare, Gortu, Goudzovski, Gourra, Gouryella, Govtrust, Gppande, Grahn, GrandDrake, Grayshi, Greatrobo76, GreenGourd, Gregb, GregorB, Griffles, GruBBy, Guoguo12, Gustavoanaya, GuyanaMan, Gwen Gale, Gökhan, H2g2bob, HEL, HalfShadow, HamburgerRadio, Hamiltondaniel, Hans Dunkelberg, Harej, Harp, Haseth, Hashiq, Hazard-SJ, Headbomb, Hechser, Hedgehawk, Heggied, HelloDenyo, Henryodell, Herbee, HexaChord, Hibernian, Hickorybark, Hiflyer, HisNameIsChris, Hj FUN, Hom sepanta, Homocion, Hotswapster, Hqb, Hu, Huddahbuddah, Hurricane Floyd, Hurricanefloyd, Hydrargyrum, Hydrogen Iodide, Hypergeek14, II MusLiM HyBRiD II, ISD, ISGTW, IVAN3MAN, Ice Cold Beer, Iconoclast09, Ifrit, Ihatetoregister, Iloveham, Inferiorjon, Insanity Incarnate, Interchange88, InternetMeme, Iridescent, Islander, Istvan, Itain'tsobad, Ixfd64, J Milburn, J.delanoy, JBsupreme, JCDenton2052, JabberWok, Jac16888, Jacj, Jacob Poon, Jacob2718, Jagged 85, Jamesofur, Jamesooders, Janke, Japo, JarahE, Jdiemer, Jeff G., Jeffakolb, Jeffrey Mall, Jeffrey Solimine, Jemmalouisemay, Jh51681, Jim, Jimbob16314, Jlcoving, Jll, Jmcc150, Jmnbatista, JoanneB, Joeylawn, JohnCD, Jokestress, Jonterry4, Joopercoopers, Joseph Solis in Australia, Josh3580, Joshua Issac, Josiah Rowe, Jredmond, Jtankers, Jtyard, Juhachi, Juhanson, Juliancolton, Jushi, Justinb52, Jóhann Heiðar Árnason, KTo288, Kae1is, Kanags, Kane5187, Karenjc, Kartano, Kavehmz, Keaton, Keenan Pepper, Keilana, Kelvin Case, Kevin Mason Barnard, Khukri, Kilo-Lima, Kingexaldraw, Kittybrewster, Kjkolb, Kludger, Kmchanw, Knowsnothing613, Kocio, Kralizec!, KrazyKelle, Krsont, Kslotte, Ktr101, Kubigula, Kuralyov, Kurtilein, KyleMac, KyleRyanToth, Kylehung, Kyro, Kyurkewicz, Lamikae, Lantrix, Laurascudder, LeadSongDog, LeaveSleaves, Lee Carre, Leeyc0, Lenary, Leon7, Lesdo234, Lethesl, Lets Enjoy Life, Lhshammo, Libriantichi, Lifeboatpres, Lightmouse, Lihaas, Lilac Soul, Linas, Linmhall, Llywelyn2000, Lode, Loliamnot13, LonelyMarble, Loren.wilton, Lotje, Louprado, LovesMacs, Ltlighter, LttS, Lumidek, Lycurgus, MAGZine, MFH, MMS2013, MZMcBride, MacFodder, Maccy69, Mackmgg, MadGeographer, Magog the Ogre, Mahanga, Mako098765, Malinaccier, Managerpants, Mannasoumya, Manu-ve Pro Ski, Marcus Qwertyus, Marek69, Mariekshan, Markhoney, Martinvl, MassKnowledgeLearner, Master michael 90, Maurice Carbonaro, Mavrisa, MaxSem, Maxime.Debosschere, McSly, Mcewan, Mean as custard, Meltonkt, Mentisock, Message From Xenu, Mgambentok, Mhworth, Michael C Price, Michael Farris, Michael Hardy, MichaelMaggs, Michaelmas1957, Michelle Roberts, Mickeyhill, Mike Peel, Mike Rosoft, Mimihitam, Mimzy2011, Mindmatrix, Mineville, Minimac, Minna Sora no Shita, Miquonranger03, Miss Madeline, Mitch Ames, Mix Bouda-Lycaon, Mjspe1, Mkhan-95, Mmenal, Mmovchin, Mononomic, Moravice, Mpatel, Mpwheatley, Mr flea, Mr. Quertee, Mr.Unknown, MrOllie, Mrcoolbp, Mrgalaxy01, Mriya, Mrund, Msablic, Mspraveen, Mtbaldyred, MuZemike, Muad, Muhammedpbuh, Mwvandersteen, My76Strat, Mygerardromance, NORD74, Nacre 10, Nanouniverse, Narutolovehinata5, Natural Cut, NawlinWiki, Nburden, Ndavies2, Ndenison, Nekura, NellieBly, Neo256, NeoTheChosenOne, Nephron, Netanel h, NewEnglandYankee, Newone, Newzebras, Nihiltres, Nineko, Ninjagecko, Nitya Dharma, Nmajmani, Nocarrier813, Noplasma, Northfox, Ntse, NuclearWarfare, Nucleusboy, Nukes4Tots, Num43, Nunocordeiro, Nurg, Oak, Ohconfucius, Ohms law, Ohmyyes, Olaf Davis, Oldnoah, Oldsoul, Olegwiki, OllieFury, Omeganian, Omweb, Onanysunday, Oni Lukos, Ooogly, Orion11M87, Ottawa4ever, Ottre, OverlordQ, Owen214, Oxymoron83, Ozabluda, PL290, PSimeon, Paaulinho, Pac72, Paintman, Palad1n, Paragon12321, Paul Suhler, Pclover, Pdcook, Pedant75, Pedro, Pejman47, PenguiN42, Per piotrr Edman, Perfect Proposal, Persian Poet Gal, Peter johnson4, PeterMcCready, PeterS32, Phancy Physicist, Pharotic, Phasma Felis, Phenylalanine, Phil Boswell, Philc 0780, Philip Trueman, PhilipO, Phlegm Rooster, PhySusie, Physicistjedi, Physicsdavid, Phyte, Piano non troppo, Piggyspider123, Pikematerson, Piksi, Piledhigheranddeeper, Pill, PimRijkee, Pinethicket, Pinkadelica, Pip2andahalf, Pkoppenb, Plasticup, Pleriche, PlumCrumbleAndCustard, PointOfPresence, Pokesausage, Pol098, Polaroids4x5, Polishhill, Ponty Pirate, PooRadley, Possum, Postdlf, Praveen pillay, Prestonmag, Priceman86, Princeb11, Profgregory, Prowikipedians, Pseudoanonymous, PsychoJosh, Ptrslv72, Pundit, Purslane, Puzl bustr, Pwhitwor, Pyfan, Pyrrhus16, QWERTYMASTR, QuadrivialMind, QuantumAmyrillis, QuantumShadow, Quentonamos, Quest for Truth, Quirkie, Ququ, RBPierce, RG2, RJHall, RJaguar3, Rachel Pearce, Radical Mallard, RainbowOfLight, Rainwarrior, Rama, RandomXYZb, Rara bb, Ravedave, Rcw258, Realtruth.co.nr, Recognizance, Red, Red Act, Red Sunset, Reddawnz, Redroach, Redwodka, Reinis, Remnar, Res2216firestar, Resonant.Interval, Retbutler92, RexNL, Reywas92, Rhlozier, Rich Farmbrough, Richard1990, RichardNeill, RickWagnerPhD, Rio, Rjwilmsi, Rls, RoToR, Rob.bastholm, Robert K S, Robfrost, Robma, Rod57, Rodeo90, Rogermw, Romanm, Ronark, Ronhjones, Rossenglish, RotaryAce, Rotiro, RotoSequence, RoyBoy, Rpeh, Rrius, Rsholmes, Rtomas, Rubicon, Rues, Rursus, Rwxrwxrwx, Rygel, Ryulong, SCZenz, SColombo, SPat, SVTCobra, Safetynut, Salamurai, Salsa Shark, Sammy00193, Samsara, Sandeepsuri, Sanders muc, SaveTheWhales, ScAvenger, Scaler1112, Scarecroe, Schapel, Schmitzhugen, Scoops, ScorpO, ScottSteiner, Scottfisher, Scrivener72, Sdedeo, Seddon, Seeleschneider, Semorrison, Seneka, Seniorlimpio, Septuagent, Seraphim, Setanta747 (locked), Sfsupro, ShadowUltra, Shadowjams, ShakataGaNai, ShandraShazam, Shandris, Shanel, Shanmugammpl, Shaunofthefuzz7, Shawnlandden, SheffieldSteel, Sheliak, Sheps999, Shiftyalex1, Shivarudra, Shuipzv3, Siawase, SidKemp, Silas S. Brown, SilkTork, Simesa, Simfish, SimonMenashy, Siriusvector, SkittleJuice, Skizzik, SkyWalker, Sladen, Slaniel, SlaterDeterminant, Slightsmile, Sligocki, SlimVirgin, Smarts53, Smite-Meister, Smitty Mcgee, Snailwalker, Snowmanradio, SoWhy, Sockies, Soler97, Some jerk on the Internet, Someguy1221, Somno, Sp00n, SpaceFlight89, Spaluch1, Spellage, Spinal232, Spinoff, Spitfire, SqueakBox, Sroc, Ssbarker, Ssolbergj, Stack, Staka, Starwed, StaticVision, Stefinho360, Stephen Poppitt, StephenBuxton, Stephenb, Steve2011, Stevertigo, Stew560, Stickee, Stoshmaster, Strait, Stsang, Sumsum2010, Superbeecat, Suruena, Sverdrup, Swatjester, Swedernish, SwordSmurf, Swpb, THC Loadee, THMRK1, TJRC, TSRL, Taco325i, TakuyaMurata, Tanthalas39, Tarret, TarzanASG, Tayste,
219
Article Sources and Contributors Tbhotch, Tbonemalone123, Tcnuk, Teamnumberawesome, Techdawg667, Techman224, TechnoFaye, Tefalstar, Teoryn, Terryblack, Texture, The Anome, The Firewall, The Rogue Penguin, The Thing That Should Not Be, The way, the truth, and the light, The wub, TheBlueFox, TheNeutroniumAlchemist, TheSuave, Theevildoctorodewulfe, Theimmaculatechemist, Themorrissey, Theo Pardilla, Thingg, ThinkBlue, Thiseye, Thomasedavis, Thomasmackat41, Thorenn, Thumperward, Ticklemefugly, Tictac66, Tide rolls, TimProof, Timothylord, Timwi, Tkgd2007, Tmckeage, Tnicol, Toba, Tommyt, Tone, Tony1, Torchwoodwho, Totakeke423, Tourettes1993, Tpbradbury, TravisAF, Trekkie4christ, Trevor Johns, Trickett rocks, Trilobitealive, Trotter, Trusilver, Truthanado, Tuduser, TunaSushi, Tyco.skinner, Tznkai, Uiteoi, Uk554, Uncle Dick, Uni4dfx, Unsuspected, Vanir-sama, Vanished user 47736712, Vanisheduser12345, Veldin963, Velella, Verbal, Verdatum, Versus22, Victorgmartins, Viraz, Visor, Vitalikk, Vivio Testarossa, Voidxor, Voortle, Vsmith, W Nowicki, Wafulz, Wangi, WannabeAmatureHistorian, WaysToEscape, Wbrice83186, Wdfarmer, WebScientist, WeirdEars, WereSpielChequers, WikiLaurent, Wikidokman, Wikidsoup, Wikiviks, Wildthing61476, William Avery, Willking1979, Willknowsalmosteverything, Wiseoldbum, Wk muriithi, Wknight94, Wleizero, Wnt, Wolf1728, Wond3rbread1991, Wonderflash1111, WookieInHeat, Wotnow, Wtmitchell, Wwheaton, XJamRastafire, XP1, Xasdas, Xertoz, YUL89YYZ, Yamamoto Ichiro, Yellowdesk, Yhkhoo, Ylai, Yuefairchild, ZZ9pluralZalpha, Zaak, Zargulon, Zestofalemon, Zidonuke, Zimbabweed, Zomglolwtfzor, Zonk43, Zsinj, Ztbbq, Ztobor, Zucchinidreams, Zykure, Zythe, 1694 anonymous edits Molten-Salt Reactor Experiment Source: http://en.wikipedia.org/w/index.php?oldid=495432848 Contributors: Armistej, Awatral, Bckelleher, Chris the speller, Clicketyclack, Debresser, DexDor, Drpickem, Fivemack, Fru1tbat, GTBacchus, Gene Nygaard, Happyinmotion, Headbomb, Hugo999, Isthisthingworking, JWB, Jaraalbe, KFSorensen, Lcolson, Lightmouse, Limulus, Markos Strofyllas, Materialscientist, Orlady, Petri Krohn, Pstudier, Rich Farmbrough, Robert Hargraves, Rod57, Shaddack, ShotmanMaslo, Thumperward, Ulrich67, Will Beback, William James Croft, Wwoods, Ysangkok, 34 anonymous edits PS210 experiment Source: http://en.wikipedia.org/w/index.php?oldid=467529352 Contributors: Headbomb, Laurascudder, Pak21, Picusanus, Rjwilmsi Trinity Source: http://en.wikipedia.org/w/index.php?oldid=495226692 Contributors: 23skidoo, A876, ACSE, Aardark, Abcdefghijklmnopponmlihbg, Abune, AdemarReis, Aekbal, Aillema, Airosche, Akcarver, Alansohn, Albrozdude, Amazins490, Amber388, Ancheta Wis, Andy Dingley, Andyman1125, Anotherclown, Antandrus, Appraiser, AquaRichy, Aquatics, Aremisasling, Arjun G. Menon, Arniebuteft, Ashujo, Astatine211, Atlant, Authalic, Autopilots, Avt tor, BD2412, Badhotra, Basejumper123, Bcrowell, BeefRendang, Bejnar, BillFlis, BlankVerse, BlueMoonlet, BobM, Bomazi, Bongwarrior, Boris Barowski, Brighterorange, Bryan Derksen, C0N6R355, CMG, CWenger, Cadmium, Caniago, Carnildo, CattleGirl, Centuriono, Chris the speller, Civil Engineer III, Closeapple, CommonsDelinker, ConradPino, Crissov, Crowish, D6, DCGeist, DMCer, DMKTirpitz, DMacks, Dake, Darkangleman, Darrien, DaveJB, Davidcmckee, Daydream believer2, Dead3y3, Deadcode, Decumanus, Deglr6328, Dino, Dinomite, Doltna, Doncram, Donfbreed, Doudja, Dr. Sunglasses, DragonflySixtyseven, Dyingbunny, Dysprosia, Ebear422, Ebyabe, Eclecticos, Ed Poor, Einbierbitte, El C, Ellsworth, Eoghanacht, Epiovesan, Esrever, Eszett, Excirial, FT2, Fastfission, FellGleaming, Figureofnine, Filll, Finlay McWalter, Firipu, Frankie816, FredHayden62, Fredrik, Furrykef, G Clark, Galar71, GarlicBreath, Gczffl, Gene Nygaard, Georgewilliamherbert, Get It, Gigemag76, Give Peace A Chance, Glowimperial, Goodvac, Grand-Duc, GregU, Guliolopez, HarmonicSeries, Hawkeye7, Her042, HereToHelp, Heron, Hmains, Hmmwhatsthisdo, Hodu, Hokanomono, Hoo man, Hooperbloob, HowardMorland, Hrimpurstala, Hugo999, IMiiTH, Ian Rose, Icairns, Igoldste, IndulgentReader, Interlingua, InternetMeme, InverseHypercube, Iridescent, JD79, JHP, JJansen, Jakew, Japanese Searobin, Jcw69, Jean-François Clet, Jef-Infojef, Jeffhos, Jehfes, Jeronimo, Jerzy, Jevansen, Jhbuk, Jllm06, JoeSmack, Johantheghost, John, JohnCub, JohnnyMrNinja, Jtodsen, Junglecat, Jzylstra, K7aay, KDesk, KJRehberg, Karl Andrews, Keenan Pepper, Keilana, Kevin Ryde, Khazar2, Kinkydarkbird, Kiwia, Klilidiplomus, Larryisgood, Leadfingers, Lightmouse, Ligulem, Little guru, Look2See1, LouScheffer, Lugnuts, Lung salad, Lvklock, MArainman, MBK004, MC10, MCTales, Magicmanreborn, Mairi, Manco Capac, Marek69, Mark K. Jensen, Materialscientist, Matt Crypto, MauriceJFox3, McGeddon, Mcclade, Melchoir, Merope, Mgiganteus1, Mike Payne, Milepost53, Miquonranger03, Modest Genius, Moomoomoo, Morshem, Moverton, Mr. Brownstone, Mr.98, MrBook, MrWhipple, Mulad, Mwalcoff, Nehrams2020, NekoDaemon, Nemissimo, Netrapt, NickBush24, Nikthestoned, Ninly, Noroton, Northwesterner1, Nsaum75, NuclearWarfare, Oblivious, Occultations, Odie5533, Ohconfucius, Oldlaptop321, Oleg Alexandrov, Omegatron, Onopearls, Opelio, Ospalh, Ozurbanmusic, PIL1987, PKG2007, Patrick, PatrikR, Pediaguy16, Perceval, Peregrine Fisher, Perkeleperkele, Petebutt, Peterh5322, Pezstar, Phil Boswell, Phlebas, Piano non troppo, Pigsonthewing, Pladask, Plandu, Plazak, Plerdsus, Pluszero, Polargeo, Politicaljunkie6, Postdlf, Ppfk, Procrastinatrix, Pt1234, Q43, Quibik, RODERICKMOLASAR, Raindrift, Rama, Ravedave, Rbj, Rich Farmbrough, Ricky81682, Rillian, Rnt20, RoyBoy, Rrburke, Ryanmalley11, SDC, SEWilco, Sade, Salsa Shark, Senator2029, Sexylui, Sgeppert, Shaddack, Shadiac, Shirt58, Shreevatsa, SilentSmuggler, SilkTork, Smack, Smoo222, Soonercary, Special-T, Spoon!, Stan Shebs, StaticGull, Stevage, Strait, Styrofoam1994, Sunderland06, Supersymetrie, Sverdrup, SweBrainz, Talltanbarbie, Tassedethe, Tedernst, Teraldthecat, The Epopt, The Giant Puffin, The PIPE, The Peacemaker, TheBaron0530, Theseeker4, Thewellman, Tillman, Tiptoety, Tobi, Tommy2010, Trelvis, Trent, Trivialist, Trovatore, Tuckerresearch, TwistOfCain, TwoOneTwo, Uncia, Uncle Dick, Vahn Clark, Vegaswikian, Viriditas, Vsmith, WFinch, Wapcaplet, Waynyo921, Wayward, Wereon, Wikijsmak, Wisden17, Woody Couder, Woohookitty, Wtmitchell, X5dna, Xihr, Xoder, Xtreambar, Yath, Zzyzx11, ²¹², சஞ்சீவி சிவகுமார், 478 anonymous edits Afshar experiment Source: http://en.wikipedia.org/w/index.php?oldid=490414171 Contributors: Aaron Schulz, Ablewisuk, Afshar, Alex Pascual, Andybiddulph, Anonymouser, Art Carlson, Arthur Rubin, Backslash Forwardslash, BenRG, Bethpage89, Bobblewik, Bporopat, Bryan Derksen, CSTAR, CapitalR, Carl A Looper, Charles Matthews, Charlie.liban, Coffee2theorems, Colonies Chris, Cortonin, Cryptic, Danko Georgiev, Darkspots, Dave Kielpinski, Davewild, David Underdown, Dllahr, Dndn1011, Drezet, GangofOne, Geodyde, Gerbrant, Gparker, Grant Gussie, GregorB, HappyCamper, Hdante, Headbomb, Hhanke, Hmonroe, Howardjp, Howcheng, INic, IronDuke, Jonel, Jreferee, Kerotan, L33tminion, LilHelpa, Lilgeopch81, Linas, Lumidek, MIRROR, Mansari, Martin62, Mathrick, Meno25, Michael C Price, Michael Hardy, NotAbel, Paine Ellsworth, Patchouli, Pavel Vozenilek, Peterdjones, Physicsmonk, Pseudospin, Ptgy2003, Rdsmith4, ReyBrujo, Rich Farmbrough, Rjwilmsi, Sam Hocevar, Samboy, Schlafly, Sdedeo, Sdirrim, Seicer, Sfsupro, Sjgooch, SqueakBox, Stifle, Tabish q, Tarotcards, Tassedethe, TeaDrinker, The tooth, TonyMath, TyphoidHippo, Tzarius, VanishedUser314159, Vinograd19, Woohookitty, Wwwwolf, Yevgeny Kats, 201 anonymous edits Davisson–Germer experiment Source: http://en.wikipedia.org/w/index.php?oldid=492375229 Contributors: Bender235, Charles Matthews, Chetvorno, Collstock, DJIndica, Dicklyon, Dirac66, Everyday17, Gershwinrb, Giftlite, Good Olfactory, GregVolk, Grimlock, Headbomb, Hugo999, Imanj11, Jaraalbe, KTC, Lightbound, Linas, Lisatwo, LorenzoB, Mpatel, Mpfiz, Paweł Ziemian, Potatoswatter, Rikimaru, Rjwilmsi, Sheliak, Sibelius42, Siddhant, Silly rabbit, Tarotcards, Thurth, Tone, Wiccan Quagga, Морган, 百 家 姓 之 四, 18 anonymous edits Delayed choice quantum eraser Source: http://en.wikipedia.org/w/index.php?oldid=484100404 Contributors: Alan McBeth, Archelon, Avian, Barraki, Bbbbbbbbba, Bobrayner, Bporopat, Canopus1, Checkguy, Dratman, Drlight11, El C, Elektron, Endogenous -i, Gradatmit, GregorB, Headbomb, Hkyriazi, Hypnosifl, IceWeasel, Iosef, Kpedersen1, Linas, Lostart, Lotu, Michael C Price, Michael9422, Midnight Voice, Mysid, NotAnonymous0, Originalname37, Paine Ellsworth, Patrick0Moran, Plrk, Rich.lewis, Rjwilmsi, Sidb, TASagent, That Guy, From That Show!, Tzepish, Ummonk, UncleDouggie, 55 anonymous edits Double-slit experiment Source: http://en.wikipedia.org/w/index.php?oldid=494628121 Contributors: 1ForTheMoney, 6E656F, ABCD, Abce2, Afiq980, Afshar, Ahoerstemeier, Ajrocke, Amoceann, Amp3030, Ancheta Wis, Andejons, Andy120290, Andycjp, AniRaptor2001, Anomalocaris, Ansell, Anthony, Arkuat, AxelBoldt, Barak Sh, BaxterG4, Bbq332, BenFrantzDale, Bentley4, Bobo192, Bryan Derksen, Bth, C9h13no3hcl, CSTAR, CWenger, Camilo Sanchez, CapitalR, Carbuncle, Carlamichelle, Certes, Charles Matthews, Chas zzz brown, Chetvorno, Clarityfiend, Cleonis, Closedmouth, Complexica, Conversion script, Custos0, Cybercobra, DJIndica, DV8 2XL, DVdm, Dallascloud, Danski14, Danthewhale, Darked, Dauto, Daverocks, Deanlaw, Deb, Deepdreamer, Deepsurvival, Deltaneos, Dicklyon, Dissembly, Djr32, Dna-webmaster, Dndn1011, Dnwq, Dolphin51, Domanix, Donama, Dqbeat, DrBob, DrChinese, Dratman, Drcakes, Drlight11, Eequor, Ekrub-ntyh, Emptymountains, Enormousdude, Ensign beedrill, Epzcaw, Eratosthenes, Etyee, Falcon8765, Fastfission, Favonian, FilippoSidoti, Fredbauder, Gaius Cornelius, Garion96, Gbuchana, George100, Giftlite, Glenn, Gogo Dodo, Gprince007, Gqu, Gradatmit, Graham87, Gutza, Hadal, Haham hanuka, Haikz, Hamedghj, Happyboy2011, Headbomb, Hhanke, Hooperbloob, Ian Pitchford, Ideal gas equation, Intelligentsium, Izehar, J-Wiki, JabberWok, Jakelove, Jakew, Jamesscottbrown, Jayron32, Jeffq, Jeremyzone, Jhayeur, Jim E. Black, Jjreicher, John Broughton, Jonathan Whitehouse, Jonny-mt, Jordgette, Joriki, Jotunn, Jouster, Jpgordon, Julleras, Karol Langner, Kevin Baas, Kimholder, KnowledgeOfSelf, Knshk.iitr, Kornbelt888, Koyaanis Qatsi, Kriak, Kwertii, Kyle Barbour, L33tminion, Larryisgood, Laudaka, Laurascudder, Lemonus', Lightmouse, Linas, Lir, Ljcrabs, Lofor, Lookang, Looxix, Lostart, Lovemuffin333, Lumidek, Lwickstr, Lyght, Mac Davis, Mac Dreamstate, Mars2035, Masoninman, Materialscientist, Maurice Carbonaro, Mbcudmore, Mbell, Megannnn, Michael C Price, Michael Hardy, Milenko.popa, Mophead2002, Mr. Qwert, Mr. Science, Mrwojo, My Flatley, Mårten Berglund, Najoj, Nate Silva, Naumz, Nay01, Nh5h, Nick84, Nwbeeson, Ohanian, Olleicua, Optics guy07, Originalname37, Paine Ellsworth, Patrick0Moran, Pdcook, Peterdjones, Petri Krohn, Pfalstad, Phil Boswell, Plasmageek, Pol098, Pt, Quibik, Radude7, RandomAct, Randyburden, Recurring dreams, Redattore, Reddi, Rfl, Ribashka, Richwil, Rjwilmsi, Rnt20, Roadrunner, Roier, Roundhouse0, SS, Samboy, Sammyzac, SchmuckyTheCat, SchreiberBike, Septegram, Sheliak, Shminux, Shooter468, Siddharth.kulk, Sodium, Someone42, Spikey, Spiral5800, SpookyMulder, Srleffler, Stannered, Stevertigo, StradivariusTV, Sverdrup, Svick, Syrthiss, Tarquin, Tcnuk, The Anome, The Wild West guy, TheNewYork123, TheTerr, Thorwald, Thurth, Timefly, Tom Edwards, Tom.Reding, Tomia, Tonymang, Toyokuni3, Trefork, Ttony21, Tttrung, Ttwaring, UKER, Ugeorge, UncleDouggie, Underdone, Unschool, User A1, Van helsing, Vincenzo.romano, Vinograd19, Voyajer, WMdeMuynck, WestwoodMatt, Whoop whoop pull up, Wikiliki, Wikiregsters, Windyhead, Winston365, Yevgeny Kats, Zazou, Zhen Lin, 391 anonymous edits Elitzur–Vaidman bomb tester Source: http://en.wikipedia.org/w/index.php?oldid=491152774 Contributors: Aaron Rotenberg, Alan McBeth, Avarmaavarma, Bbbbbbbbba, Bboyneko, Blutfink, Brazmyth, Burpen, Cogiati, Danski14, Dchristle, Deviant Paleoart, Dicklyon, Frakkim, Gabbe, Gloumouth1, Gradatmit, GregorB, HACKER1993, Headbomb, Hgkirk, Hugombarreto, Huntingg, InverseHypercube, J S Lundeen, Jason.grossman, Joehubris, Jordgette, Keithbowden, Kuratowski's Ghost, Likebox, Linas, Lionelbrits, Lode Runner, Mejor Los Indios, Miquonranger03, Mporter, Oconnor663, Pfalstad, Prezbo, Quibik, RCSB, Rjwilmsi, SantaBarbarian, Schizobullet, Scottywong, Syamsu, Thoreaulylazy, Tzahy, Wikianon, Xanzzibar, Yonideworst, 39 anonymous edits Eötvös experiment Source: http://en.wikipedia.org/w/index.php?oldid=493225356 Contributors: Brews ohare, DeFaultRyan, Franl, GregorB, Headbomb, InfelixMendax, Ionutzmovie, Lantonov, Maury Markowitz, Mozi17, PSimeon, Pavel Vozenilek, Petteri Aimonen, PleaseStand, Quibik, Vonspringer, WarX, 13 anonymous edits Franck–Hertz experiment Source: http://en.wikipedia.org/w/index.php?oldid=485249369 Contributors: Andrei Stroe, Asoulwhoseintentionsaregood, El C, Epistemenical, Gerry Ashton, Gustronico, Headbomb, Hooperbloob, Hugo999, Icairns, Inshaffer, Jaraalbe, Jnyanydts, Linas, Mac Davis, MarkusHagenlocher, Mnmngb, Nutfortuna, Pareshmalik555, PeterisP, Pnicolet, SlaveToTheWage, SlipperyHippo, Stone, TenOfAllTrades, Thurth, XJamRastafire, 40 anonymous edits
220
Article Sources and Contributors Quantum eraser experiment Source: http://en.wikipedia.org/w/index.php?oldid=487960514 Contributors: Akamad, Alexbender, Asmeurer, CapitalR, Crackerjack, Dave3457, Diza, Dv82matt, Emurphy42, Gautama Buddha, Harald88, Jean-Christophe BENOIST, Jordgette, Keenan Pepper, Linas, Linus M., Lostart, Michael C Price, Nitzans, Occultations, Pace212, Paine Ellsworth, Patrick0Moran, R'n'B, Rjwilmsi, Ryulong, SU Linguist, Shoy, Stanzilla, Tercer, The Anome, UKER, UncleDouggie, Unconventional, Victordk13, Xanthoptica, 24 anonymous edits Stern–Gerlach experiment Source: http://en.wikipedia.org/w/index.php?oldid=488097145 Contributors: Afa86, Alain Michaud, Alpinwolf, Blotwell, Boszzo, C5and19, Calair, Cesco-it, Charles Matthews, Chrismear, Complexica, Contact '97, Covector, Creidieki, DJIndica, Daniel.Cardenas, David Nemati, Dendropithecus, Dr. Universe, Dratman, Dwaipayanc, Eadric, Em3ryguy, Fakeup, Feezo, Flockmeal, Flutefreek, Geremia, Giftlite, Harald88, Headbomb, Hooperbloob, Hugo999, Incnis Mrsi, Ironmandust, JBdV, JFlav, Jaraalbe, Jbergquist, Jeff3000, Jmnbpt, John Vandenberg, Lightmouse, Linas, Lozanorc, Luís Felipe Braga, Marie Poise, Matthead, Mbell, Mct mht, Michael Hardy, Mikhail Klassen, Mushin, Nfu-peng, Owlbuster, Pagw, Palica, Pdpinch, Pmokeefe, PollyPollyPeptide, RJHall, Rajah, Ram einstein, Rich Farmbrough, RobinK, Ruler-of-all, SeventyThree, Sheliak, Simonfairfax, Sonett72, Taborgate, Theresa knott, Tim333, Tommcnabb, Vampx87, Vescovoe, Voyajer, WMdeMuynck, Waleswatcher, WereSpielChequers, Whosasking, Wranadu2, Wricardoh, Zachrey, 60 anonymous edits
221
Image Sources, Licenses and Contributors
Image Sources, Licenses and Contributors Image:Boomerang Telescope.jpeg Source: http://en.wikipedia.org/w/index.php?title=File:Boomerang_Telescope.jpeg License: Public Domain Contributors: Mike Peel, Parkis, Pieter Kuiper Image:Boomerang CMB.jpeg Source: http://en.wikipedia.org/w/index.php?title=File:Boomerang_CMB.jpeg License: Public Domain Contributors: Juiced lemon, Parkis File:020597COBE OV.jpg Source: http://en.wikipedia.org/w/index.php?title=File:020597COBE_OV.jpg License: Public Domain Contributors: Dodo, GDK, Ploum's File:COBELaunch.jpg Source: http://en.wikipedia.org/w/index.php?title=File:COBELaunch.jpg License: Public Domain Contributors: Original uploader was ScottyBoy900Q at en.wikipedia File:COBEDiagram.jpg Source: http://en.wikipedia.org/w/index.php?title=File:COBEDiagram.jpg License: Public Domain Contributors: Original uploader was ScottyBoy900Q at en.wikipedia File:COBE cmb fluctuations.gif Source: http://en.wikipedia.org/w/index.php?title=File:COBE_cmb_fluctuations.gif License: Public Domain Contributors: The COBE datasets were developed by the NASA Goddard Space Flight Center under the guidance of the COBE Science Working Group. File:Cmbr.svg Source: http://en.wikipedia.org/w/index.php?title=File:Cmbr.svg License: Public Domain Contributors: Quantum Doughnut File:COBE DMR Image.PNG Source: http://en.wikipedia.org/w/index.php?title=File:COBE_DMR_Image.PNG License: Public Domain Contributors: The COBE datasets were developed by the NASA Goddard Space Flight Center under the guidance of the COBE Science Working Group. File:COBE galactic disk.PNG Source: http://en.wikipedia.org/w/index.php?title=File:COBE_galactic_disk.PNG License: Public Domain Contributors: Original uploader was Ryjaz at en.wikipedia Image:WMAP collage.jpg Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_collage.jpg License: Public Domain Contributors: NASA / WMAP Science Team Image:CMB Timeline75.jpg Source: http://en.wikipedia.org/w/index.php?title=File:CMB_Timeline75.jpg License: Public Domain Contributors: NASA/WMAP Science Team Image:BigBangNoise.jpg Source: http://en.wikipedia.org/w/index.php?title=File:BigBangNoise.jpg License: Public Domain Contributors: Angeloleithold, Duesentrieb, GDK, Iluvalar, Juiced lemon, Mdd, WikipediaMaster Image:WMAP spacecraft diagram.jpg Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_spacecraft_diagram.jpg License: Public Domain Contributors: Original uploader was Brian0918 at en.wikipedia Image:WMAP receivers.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_receivers.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP trajectory and orbit.jpg Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_trajectory_and_orbit.jpg License: Public Domain Contributors: NASA / WMAP Science Team File:WMAP launch.jpg Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_launch.jpg License: Public Domain Contributors: NASA / Kennedy Space Flight Center Image:WMAP orbit.jpg Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_orbit.jpg License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 23GHz foregrounds.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_23GHz_foregrounds.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 33GHz foregrounds.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_33GHz_foregrounds.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 41GHz foregrounds.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_41GHz_foregrounds.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 61GHz foregrounds.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_61GHz_foregrounds.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 94GHz foregrounds.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_94GHz_foregrounds.png License: Public Domain Contributors: NASA / WMAP Science Team Image:Baby Universe.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Baby_Universe.jpg License: Public Domain Contributors: A7N8X, Angeloleithold, Duesentrieb, GDK, Juiced lemon, Mike Peel, Pieter Kuiper, 1 anonymous edits Image:Microwave Sky polarization.png Source: http://en.wikipedia.org/w/index.php?title=File:Microwave_Sky_polarization.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 TT and TE spectra.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_TT_and_TE_spectra.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 universe content.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_universe_content.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 23GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_23GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 33GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_33GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 41GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_41GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 61GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_61GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2008 94GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2008_94GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2010.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2010.png License: Public Domain Contributors: 0Zero0, Julia W, LobStoR, Raeky, Seleucus, WikipediaMaster, 2 anonymous edits Image:WMAP 2010 23GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2010_23GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2010 33GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2010_33GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2010 41GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2010_41GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2010 61GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2010_61GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:WMAP 2010 94GHz.png Source: http://en.wikipedia.org/w/index.php?title=File:WMAP_2010_94GHz.png License: Public Domain Contributors: NASA / WMAP Science Team Image:Planck satellite.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Planck_satellite.jpg License: Public Domain Contributors: GDK, KGyST, Mike Peel File:Fizeau-Mascart2.png Source: http://en.wikipedia.org/w/index.php?title=File:Fizeau-Mascart2.png License: unknown Contributors: Éleuthère Mascart File:Fizeau-Mascart1.png Source: http://en.wikipedia.org/w/index.php?title=File:Fizeau-Mascart1.png License: unknown Contributors: Éleuthère Mascart File:Foucault apparatus.JPG Source: http://en.wikipedia.org/w/index.php?title=File:Foucault_apparatus.JPG License: Creative Commons Attribution-Sharealike 3.0 Contributors: Brews ohare File:Fizeau.JPG Source: http://en.wikipedia.org/w/index.php?title=File:Fizeau.JPG License: Creative Commons Attribution-Sharealike 3.0 Contributors: Brews ohare Image:Apollo_11_Lunar_Laser_Ranging_Experiment.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Apollo_11_Lunar_Laser_Ranging_Experiment.jpg License: Public Domain Contributors: NASA Image:ALSEP AS15-85-11468.jpg Source: http://en.wikipedia.org/w/index.php?title=File:ALSEP_AS15-85-11468.jpg License: Public Domain Contributors: Original uploader was Andy120290 at en.wikipedia Image:Laser Ranging Retroreflector Apollo 15.svg Source: http://en.wikipedia.org/w/index.php?title=File:Laser_Ranging_Retroreflector_Apollo_15.svg License: Public Domain Contributors: Laser_Ranging_Retroreflector_Apollo_15.gif: Original uploader was Andy120290 at en.wikipedia derivative work: Gregors (talk) 07:45, 23 August 2011 (UTC) Image:ALSEP AS14-67-9386.jpg Source: http://en.wikipedia.org/w/index.php?title=File:ALSEP_AS14-67-9386.jpg License: Public Domain Contributors: Original uploader was Andy120290 at en.wikipedia Image:LunarPhotons.png Source: http://en.wikipedia.org/w/index.php?title=File:LunarPhotons.png License: Creative Commons Attribution 3.0 Contributors: APOLLO Collaboration, found here. Image:Lunokhod hires.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Lunokhod_hires.jpg License: Public Domain Contributors: unknown
222
Image Sources, Licenses and Contributors Image:Wettzell Laser Ranging System.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Wettzell_Laser_Ranging_System.jpg License: Creative Commons Attribution-Sharealike 3.0 Contributors: H. Raab (User:Vesta) Image:Goddard Spaceflight Center Laser Ranging Facility.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Goddard_Spaceflight_Center_Laser_Ranging_Facility.jpg License: Public Domain Contributors: NASA File:On the Relative Motion of the Earth and the Luminiferous Ether - Fig 3.png Source: http://en.wikipedia.org/w/index.php?title=File:On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether_-_Fig_3.png License: Public Domain Contributors: [:en:Albert Abraham Michelson Image:aetherWind.svg Source: http://en.wikipedia.org/w/index.php?title=File:AetherWind.svg License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: User:Cronholm144 File:Michelson1881c.png Source: http://en.wikipedia.org/w/index.php?title=File:Michelson1881c.png License: Public Domain Contributors: Belfer00, D.H, X-romix Image:On the Relative Motion of the Earth and the Luminiferous Ether - Fig 4.png Source: http://en.wikipedia.org/w/index.php?title=File:On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether_-_Fig_4.png License: Public Domain Contributors: [:en:Albert Abraham Michelson File:MichelsonCoinAirLumiereBlanche.JPG Source: http://en.wikipedia.org/w/index.php?title=File:MichelsonCoinAirLumiereBlanche.JPG License: Creative Commons Attribution-Sharealike 2.5 Contributors: Alain Le Rille File:Michelson Morley 1887 Figure 6.png Source: http://en.wikipedia.org/w/index.php?title=File:Michelson_Morley_1887_Figure_6.png License: Public Domain Contributors: Stigmatella aurantiaca File:Illingworth simulation.png Source: http://en.wikipedia.org/w/index.php?title=File:Illingworth_simulation.png License: Creative Commons Attribution 3.0 Contributors: User:Stigmatella aurantiaca File:MMX with optical resonators.svg Source: http://en.wikipedia.org/w/index.php?title=File:MMX_with_optical_resonators.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: User:Stigmatella aurantiaca Image:Millikan's setup for the oil drop experiment.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Millikan's_setup_for_the_oil_drop_experiment.jpg License: Public Domain Contributors: Electron Image:Robert-millikan2.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Robert-millikan2.jpg License: Public Domain Contributors: photograph by Clark Millikan Image:Simplified scheme of Millikan’s oil-drop experiment.png Source: http://en.wikipedia.org/w/index.php?title=File:Simplified_scheme_of_Millikan’s_oil-drop_experiment.png License: GNU Free Documentation License Contributors: Abanima, Divide, Electron, Gregors, Pieter Kuiper Image:Oil-drop-experiment-apparatus.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Oil-drop-experiment-apparatus.jpg License: Creative Commons Attribution-Sharealike 3.0 Contributors: Billzweig Image:Apparatus.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Apparatus.jpg License: Public Domain Contributors: Robert Andrews Millikan Image:Oxford Electric Bell.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Oxford_Electric_Bell.jpg License: Creative Commons Attribution-Sharealike 3.0 Contributors: LeoPanthera Image:Oxford-electric-bell.svg Source: http://en.wikipedia.org/w/index.php?title=File:Oxford-electric-bell.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: Nicolas1981 File:Ole Rømer.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Ole_Rømer.jpg License: Public Domain Contributors: Dbenzhuser, GunnarBach, Jean-Jacques MILAN, Lotse, Physchim62, Quibik, Yann File:Ole Rømer - Obser. Primi Jovialium Parisiis - pp1+4.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Ole_Rømer_-_Obser._Primi_Jovialium_Parisiis_-_pp1+4.jpg License: Public Domain Contributors: Ole Rømer (1644-1710) File:Roemer.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Roemer.jpg License: Public Domain Contributors: Albedo-ukr, Dirk Hünniger, Glj1952, Gregors, Hemmingsen, Jappalang, Mdd, 1 anonymous edits File:sagnac interferometer.png Source: http://en.wikipedia.org/w/index.php?title=File:Sagnac_interferometer.png License: Public domain Contributors: Cleonis at en.wikipedia File:Sagnac shift.svg Source: http://en.wikipedia.org/w/index.php?title=File:Sagnac_shift.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: D. mcfadden File:ring laser interferometer.png Source: http://en.wikipedia.org/w/index.php?title=File:Ring_laser_interferometer.png License: Creative Commons Attribution-Sharealike 2.5 Contributors: User:Cleonis File:Ring laser interferometry shift.png Source: http://en.wikipedia.org/w/index.php?title=File:Ring_laser_interferometry_shift.png License: GNU Free Documentation License Contributors: Cleonis File:Sagnac effect256x128.gif Source: http://en.wikipedia.org/w/index.php?title=File:Sagnac_effect256x128.gif License: Creative Commons Attribution-Sharealike 2.5 Contributors: User:Cleonis Image:Birkeland-terrella-spiral-nebula.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Birkeland-terrella-spiral-nebula.jpg License: Public Domain Contributors: Iantresman, Kelly Image:Terrella3452.png Source: http://en.wikipedia.org/w/index.php?title=File:Terrella3452.png License: Public Domain Contributors: Original uploader was Caltrop at en.wikipedia Image:Birkeland-terrella.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Birkeland-terrella.jpg License: Public Domain Contributors: Gunnernett, JackyR, Kåre-Olav, Quadell, Saperaud, WikipediaMaster File:Lewis3.png Source: http://en.wikipedia.org/w/index.php?title=File:Lewis3.png License: Public Domain Contributors: D.H File:Cavendish Experiment.png Source: http://en.wikipedia.org/w/index.php?title=File:Cavendish_Experiment.png License: Public Domain Contributors: Henry Cavendish File:CavendishSchematic111.jpg Source: http://en.wikipedia.org/w/index.php?title=File:CavendishSchematic111.jpg License: Public Domain Contributors: Original uploader was Zeyn1 at en.wikipedia File:Cavendish Torsion Balance Diagram.svg Source: http://en.wikipedia.org/w/index.php?title=File:Cavendish_Torsion_Balance_Diagram.svg License: Public Domain Contributors: Chris Burks (Chetvorno) File:SitterKonstanz.png Source: http://en.wikipedia.org/w/index.php?title=File:SitterKonstanz.png License: unknown Contributors: D.H File:162567main GPB4.jpg Source: http://en.wikipedia.org/w/index.php?title=File:162567main_GPB4.jpg License: Public Domain Contributors: NASA/MSFC Image:Gravity Probe B.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Gravity_Probe_B.jpg License: Public Domain Contributors: Emesee, GDK, Pline Image:Einstein gyro gravity probe b.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Einstein_gyro_gravity_probe_b.jpg License: Public Domain Contributors: Aavindraa, Amandajm, Docu, GDK, Mattes, Phelipemancheno, Rimshot, Tano4595 Image:Gravity Probe B Confirms the Existence of Gravitomagnetism.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Gravity_Probe_B_Confirms_the_Existence_of_Gravitomagnetism.jpg License: Public Domain Contributors: Gravity Probe B Team, Stanford, NASA Image:Gravity Probe turning axis.gif Source: http://en.wikipedia.org/w/index.php?title=File:Gravity_Probe_turning_axis.gif License: Public Domain Contributors: Original uploader was Beeblebrox19 at de.wikipedia Image:JeffersonLeft.jpg Source: http://en.wikipedia.org/w/index.php?title=File:JeffersonLeft.jpg License: Public Domain Contributors: http://en.wikipedia.org/wiki/User:Lumidek File:Schiehallion 01.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Schiehallion_01.jpg License: Creative Commons Attribution 3.0 Contributors: Original uploader was Andrew2606 at en.wikipedia File:Chimborazo from southwest.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Chimborazo_from_southwest.jpg License: GNU Free Documentation License Contributors: User:Gerd Breitenbach File:Loch Rannoch.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Loch_Rannoch.jpg License: Creative Commons Attribution-Share Alike 2.0 Generic Contributors: Anne Burgess File:Schiehallion angles.svg Source: http://en.wikipedia.org/w/index.php?title=File:Schiehallion_angles.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: BillC File:Edinburgh Arthur Seat dsc06165.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Edinburgh_Arthur_Seat_dsc06165.jpg License: Creative Commons Attribution-Sharealike 2.0 Contributors: David Monniaux
223
Image Sources, Licenses and Contributors File:Schiehallion.svg Source: http://en.wikipedia.org/w/index.php?title=File:Schiehallion.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: BillC Image:Atwoods machine.png Source: http://en.wikipedia.org/w/index.php?title=File:Atwoods_machine.png License: Public Domain Contributors: User:kogo Image:Atwood.svg Source: http://en.wikipedia.org/w/index.php?title=File:Atwood.svg License: Public Domain Contributors: Carultch File:Rowbotham–curvature.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Rowbotham–curvature.jpg License: Public Domain Contributors: Liftarn File:wallace-bedford-level.png Source: http://en.wikipedia.org/w/index.php?title=File:Wallace-bedford-level.png License: Public Domain Contributors: Chris55 Image:Beverly clock.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Beverly_clock.jpg License: Creative Commons Attribution-Sharealike 3.0,2.5,2.0,1.0 Contributors: Mysterious snapper Image:Beverly clock inner.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Beverly_clock_inner.jpg License: Creative Commons Attribution 3.0 Contributors: Mysterious snapper Image:Heron's Fountain.png Source: http://en.wikipedia.org/w/index.php?title=File:Heron's_Fountain.png License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: User:Nunh-huh Image:Heron's fountain.png Source: http://en.wikipedia.org/w/index.php?title=File:Heron's_fountain.png License: Creative Commons Attribution-Sharealike 3.0 Contributors: Hugh Young, artwork by Hugh Young Image:Magdeburg.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Magdeburg.jpg License: Public Domain Contributors: Gaspar Schott Image:Magedurger Halbkugeln Luftpumpe Deutsches Museum.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Magedurger_Halbkugeln_Luftpumpe_Deutsches_Museum.jpg License: Creative Commons Attribution-Sharealike 3.0 Contributors: LepoRello Image:Magdeburg hemispheres small.png Source: http://en.wikipedia.org/w/index.php?title=File:Magdeburg_hemispheres_small.png License: Public Domain Contributors: Adolphe Ganot Image:RubensTube.png Source: http://en.wikipedia.org/w/index.php?title=File:RubensTube.png License: GNU Free Documentation License Contributors: New Zealand Physics Teachers' Resource Bank File:Rubens flame.png Source: http://en.wikipedia.org/w/index.php?title=File:Rubens_flame.png License: Creative Commons Attribution-Sharealike 3.0 Contributors: Prof308 File:Rubens pressure.png Source: http://en.wikipedia.org/w/index.php?title=File:Rubens_pressure.png License: Creative Commons Attribution-Sharealike 3.0 Contributors: Prof308 Image:University of Queensland Pitch drop experiment-6-2.jpg Source: http://en.wikipedia.org/w/index.php?title=File:University_of_Queensland_Pitch_drop_experiment-6-2.jpg License: GNU Free Documentation License Contributors: John Mainstone Image:Pitch drop experiment with John Mainstone.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Pitch_drop_experiment_with_John_Mainstone.jpg License: GNU Free Documentation License Contributors: John Mainstone File:Spouting can jets.svg Source: http://en.wikipedia.org/w/index.php?title=File:Spouting_can_jets.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: ZooFari Image:Liquid hydrogen bubblechamber.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Liquid_hydrogen_bubblechamber.jpg License: Public Domain Contributors: Lamiot, Pieter Kuiper, Saperaud File:Stagg Field reactor.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Stagg_Field_reactor.jpg License: Public Domain Contributors: Melvin A. Miller of the Argonne National Laboratory file:USA Illinois location map.svg Source: http://en.wikipedia.org/w/index.php?title=File:USA_Illinois_location_map.svg License: GNU Free Documentation License Contributors: Alexrk2 File:Red pog.svg Source: http://en.wikipedia.org/w/index.php?title=File:Red_pog.svg License: Public Domain Contributors: Anomie File:Henry_Moore_Nuclear_Energy.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Henry_Moore_Nuclear_Energy.jpg License: Public Domain Contributors: Bluemoose, Catapult, Cuppysfriend, Ebyabe File:Rutherford gold foil experiment results.svg Source: http://en.wikipedia.org/w/index.php?title=File:Rutherford_gold_foil_experiment_results.svg License: Public Domain Contributors: Drawn by User:Fastfission in Illustrator and Inkscape. --Fastfission 15:04, 14 April 2008 (UTC) Image:LHC.svg Source: http://en.wikipedia.org/w/index.php?title=File:LHC.svg License: Creative Commons Attribution-Sharealike 2.5 Contributors: User:Harp File:CMS Higgs-event.jpg Source: http://en.wikipedia.org/w/index.php?title=File:CMS_Higgs-event.jpg License: unknown Contributors: Lucas Taylor File:BosonFusion-Higgs.svg Source: http://en.wikipedia.org/w/index.php?title=File:BosonFusion-Higgs.svg License: GNU Free Documentation License Contributors: derivative work: ~ Booya Bazooka BosonFusion-Higgs.png: User:Harp 12:43, 28 March 2007 File:Location Large Hadron Collider.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Location_Large_Hadron_Collider.PNG License: Creative Commons Attribution-Sharealike 2.0 Contributors: diverse contributors; mashup by User:Zykure File:LHC quadrupole magnets.jpg Source: http://en.wikipedia.org/w/index.php?title=File:LHC_quadrupole_magnets.jpg License: Creative Commons Attribution 2.0 Contributors: Andrius.v File:Construction of LHC at CERN.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Construction_of_LHC_at_CERN.jpg License: GNU Free Documentation License Contributors: Andrius.v, Deadstar, Square87 Image:MSRE Diagram.png Source: http://en.wikipedia.org/w/index.php?title=File:MSRE_Diagram.png License: Public Domain Contributors: Oak Ridge National Laboratory File:MoltenSaltReactor.jpg Source: http://en.wikipedia.org/w/index.php?title=File:MoltenSaltReactor.jpg License: Public Domain Contributors: Oak Ridge National Laboratory Image:MSRE Core.JPG Source: http://en.wikipedia.org/w/index.php?title=File:MSRE_Core.JPG License: Public Domain Contributors: Bomazi, ChNPP, Lcolson, Limulus, Tetris L Image:FLiBe.png Source: http://en.wikipedia.org/w/index.php?title=File:FLiBe.png License: Public Domain Contributors: Bomazi, Limulus Image:MSRE Heat Exchanger.JPG Source: http://en.wikipedia.org/w/index.php?title=File:MSRE_Heat_Exchanger.JPG License: Public Domain Contributors: Bomazi, Lcolson, Limulus, Tetris L Image:ARE Building.JPG Source: http://en.wikipedia.org/w/index.php?title=File:ARE_Building.JPG License: Public Domain Contributors: Bomazi, ChNPP, Fintan264, Lcolson, Limulus, Tetris L, 1 anonymous edits File:Trinity_Test_Fireball_16ms.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_Test_Fireball_16ms.jpg License: Public Domain Contributors: Berlyn Brixner File:Trinity Site Obelisk National Historic Landmark.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_Site_Obelisk_National_Historic_Landmark.jpg License: Creative Commons Attribution-Sharealike 2.0 Contributors: Samat Jain file:USA New Mexico location map.svg Source: http://en.wikipedia.org/w/index.php?title=File:USA_New_Mexico_location_map.svg License: GNU Free Documentation License Contributors: Alexrk2 File:Fission bomb assembly methods.svg Source: http://en.wikipedia.org/w/index.php?title=File:Fission_bomb_assembly_methods.svg License: Public Domain Contributors: Fastfission File:Implosion nuclear weapon design - initiator.svg Source: http://en.wikipedia.org/w/index.php?title=File:Implosion_nuclear_weapon_design_-_initiator.svg License: Public Domain Contributors: User:Fastfission File:Fat Man Detonation.png Source: http://en.wikipedia.org/w/index.php?title=File:Fat_Man_Detonation.png License: Public Domain Contributors: HowardMorland File:TrinitySiteISS008-E-5604.jpg Source: http://en.wikipedia.org/w/index.php?title=File:TrinitySiteISS008-E-5604.jpg License: Public Domain Contributors: Fastfission, It Is Me Here, 1 anonymous edits File:Trinity device readied.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_device_readied.jpg License: Public Domain Contributors: Fastfission, Hawkeye7, Sven Manguard, 1 anonymous edits File:Trinity Test - 100 Ton Test - High Explosive Stack 002.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_Test_-_100_Ton_Test_-_High_Explosive_Stack_002.jpg License: Public Domain Contributors: Federal government of the United States File:Trinity Gadget.png Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_Gadget.png License: Public Domain Contributors: Los Alamos National Laboratory File:Trinity tower.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_tower.jpg License: Public Domain Contributors: Bomazi, Fastfission, Look2See1, 1 anonymous edits File:Trinity shot color.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_shot_color.jpg License: Public Domain Contributors: Jack W. Aeby, July 16, 1945, as a member of the Special Engineering Detachment at Los Alamos laboratory, working under the aegis of the Manhattan Project. File:Trinity-ground-zero-men-in-crater.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity-ground-zero-men-in-crater.jpg License: Public Domain Contributors: Fastfission, Look2See1, 1 anonymous edits File:Trinity crater (annotated) 2.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_crater_(annotated)_2.jpg License: Public Domain Contributors: Trinity_crater.jpg: Federal government of the United States derivative work: Bomazi (talk) File:Trinity fallout.png Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_fallout.png License: GNU Free Documentation License Contributors: Dake, Fastfission, 1 anonymous edits
224
Image Sources, Licenses and Contributors File:Trinity Ground Zero.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_Ground_Zero.jpg License: unknown Contributors: File:TrinitySiteHistoricalMarkerHighwaySign.jpg Source: http://en.wikipedia.org/w/index.php?title=File:TrinitySiteHistoricalMarkerHighwaySign.jpg License: Public Domain Contributors: Df206 File:Trinity Site - Remnants of Jumbo - 2010.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_Site_-_Remnants_of_Jumbo_-_2010.jpg License: Creative Commons Attribution-Sharealike 2.0 Contributors: Samat Jain File:Trinity Site - Tourists at ground zero.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Trinity_Site_-_Tourists_at_ground_zero.jpg License: Public domain Contributors: Talltanbarbie at en.wikipedia Image:Afshar-experiment.png Source: http://en.wikipedia.org/w/index.php?title=File:Afshar-experiment.png License: GNU Free Documentation License Contributors: CSTAR Image:Afshar-experiment-wire.png Source: http://en.wikipedia.org/w/index.php?title=File:Afshar-experiment-wire.png License: GNU Free Documentation License Contributors: CSTAR Image:Afshar-experiment-1.png Source: http://en.wikipedia.org/w/index.php?title=File:Afshar-experiment-1.png License: GNU Free Documentation License Contributors: CSTAR Image:Beam Split and fuse.svg Source: http://en.wikipedia.org/w/index.php?title=File:Beam_Split_and_fuse.svg License: Creative Commons Attribution 3.0 Contributors: Patrick Edwin Moran Image:Kim EtAl Quantum Eraser.svg Source: http://en.wikipedia.org/w/index.php?title=File:Kim_EtAl_Quantum_Eraser.svg License: GNU Free Documentation License Contributors: Patrick Edwin Moran File:Detector0RawResults.svg Source: http://en.wikipedia.org/w/index.php?title=File:Detector0RawResults.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: User:Patrick Edwin Moran File:Dector0ResultsSeparated by counter.svg Source: http://en.wikipedia.org/w/index.php?title=File:Dector0ResultsSeparated_by_counter.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: User:Patrick Edwin Moran Image:Single slit and double slit2.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Single_slit_and_double_slit2.jpg License: Creative Commons Attribution-Sharealike 3.0 Contributors: Jordgette Image:Double-slit experiment results Tanamura 2.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Double-slit_experiment_results_Tanamura_2.jpg License: GNU Free Documentation License Contributors: Belsazar, Glenn, Kdkeller, Pieter Kuiper, Quibik, Tano4595 Image:Double-slit wall sm.jpg Source: http://en.wikipedia.org/w/index.php?title=File:Double-slit_wall_sm.jpg License: GNU Free Documentation License Contributors: Patrick Edwin Moran File:Doubleslit3Dspectrum.gif Source: http://en.wikipedia.org/w/index.php?title=File:Doubleslit3Dspectrum.gif License: Creative Commons Attribution-Sharealike 3.0 Contributors: User:Lookang Image:Doubleslit.svg Source: http://en.wikipedia.org/w/index.php?title=File:Doubleslit.svg License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: Ebohr1.svg: en:User:Lacatosias, User:Stannered derivative work: Epzcaw (talk) Image:Double slit.svg Source: http://en.wikipedia.org/w/index.php?title=File:Double_slit.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: User:Epzcaw Image:Wiener process 3d.png Source: http://en.wikipedia.org/w/index.php?title=File:Wiener_process_3d.png License: GNU Free Documentation License Contributors: Original uploader was Sullivan.t.j at English Wikipedia. File:E-V bomb-testing.svg Source: http://en.wikipedia.org/w/index.php?title=File:E-V_bomb-testing.svg License: Creative Commons Attribution-Sharealike 3.0 Contributors: Burpen File:Original Eotvos experiment.svg Source: http://en.wikipedia.org/w/index.php?title=File:Original_Eotvos_experiment.svg License: Public Domain Contributors: Petteri Aimonen File:Directions of gravity and centrifugal force on earth surface.svg Source: http://en.wikipedia.org/w/index.php?title=File:Directions_of_gravity_and_centrifugal_force_on_earth_surface.svg License: Public Domain Contributors: Petteri Aimonen Image:Franck-Hertz en.svg Source: http://en.wikipedia.org/w/index.php?title=File:Franck-Hertz_en.svg License: Public Domain Contributors: Ahellwig, Pieter Kuiper Image:2SlitApparatus w2 pol.svg Source: http://en.wikipedia.org/w/index.php?title=File:2SlitApparatus_w2_pol.svg License: GNU Free Documentation License Contributors: Patrick Edwin Moran Image:2SlitApparatus w3 pol.svg Source: http://en.wikipedia.org/w/index.php?title=File:2SlitApparatus_w3_pol.svg License: GNU Free Documentation License Contributors: Patrick Edwin Moran File:Stern-Gerlach experiment.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Stern-Gerlach_experiment.PNG License: GNU Free Documentation License Contributors: User:Theresa knott File:Quantum projection of S onto z for spin half particles.PNG Source: http://en.wikipedia.org/w/index.php?title=File:Quantum_projection_of_S_onto_z_for_spin_half_particles.PNG License: GNU Free Documentation License Contributors: Theresa knott File:Sg-seq.svg Source: http://en.wikipedia.org/w/index.php?title=File:Sg-seq.svg License: Public Domain Contributors: Francesco Versaci File:SternGerlach2.jpg Source: http://en.wikipedia.org/w/index.php?title=File:SternGerlach2.jpg License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: Peng 1 July 2005 12:44 (UTC)
225
License
License Creative Commons Attribution-Share Alike 3.0 Unported //creativecommons.org/licenses/by-sa/3.0/
226
