Experimental basis of Special Relativity/Tests of Einstein's two Postulates

1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.
2. Any ray of light moves in the “stationary” system of coordinates with determined velocity c, whether the ray be emitted by a stationary or by a moving body.

—Einstein, Ann. d. Physik 17 (1905); translated by Perrett and Jeffery; reprinted in: Einstein, Lorentz, Weyl, Minkowski, The Principle of Relativity, Dover 1952.

“Stationary” was defined in the first paragraph of this section: Let us take a system of coordinates in which the equations of newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of coordinates verbally from others that will be introduced hereafter, we call it the “stationary system”.::::::::::: —Ibid. It is clear that the word “stationary” is used merely as a label, and implies no “absolute” aspects at all.

3.1 Round-Trip Tests of Light-Speed Isotropy

The speed of light is said to be isotropic if it has the same value when measured in any/every direction.

The Michelson-Morley Experiment (the MMX)

The Michelson-Morley experiment (MMX) was intended to measure the velocity of the Earth relative to the “lumeniferous aether” which was at the time presumed to carry electromagnetic phenomena. The failure of it and the other early experiments to actually observe the Earth's motion through the aether became significant in promoting the acceptance of Einstein's theory of Special Relativity, as it was appreciated from early on that Einstein's approach (via symmetry) was more elegant and parsimonious of assumptions than were other approaches (e.g. those of Maxwell, Hertz, Stokes, Fresnel, Lorentz, Ritz, and Abraham).

The following table comes from R.S. Shankland et al., Rev. Mod. Phys. 27 no. 2, pg 167–178 (1955), which includes references to each experiment (resolution and the limit on v_aether are from the original sources). The expected fringe shift is what would be expected for a rigid aether at rest with respect to the sun and Earth's orbital velocity (~30 km/s).

Name	Year	Arm length (meters)	Fringe shift		Experimental Resolution(see note)	Upper Limit on vaether
			expected	measured
Michelson	1881	1.2	0.04	0.02
Michelson + Morley	1887	11.0	0.4	<0.01		8 km/s
Morley + Morley	1902–04	32.2	1.13	0.015
Miller	1921	32.0	1.12	0.08
Miller	1923–24	32.0	1.12	0.03
Miller (Sunlight)	1924	32.0	1.12	0.014
Tomascheck (Starlight)	1924	8.6	0.3	0.02
Miller	1925–26	32.0	1.12	0.088
Miller (re-analysis in 2006, see note)	1925-29	32.0	1.12	0.000	0.015	6 km/s
Kennedy (Mt Wilson)	1926	2.0	0.07	0.002
Illingworth	1927	2.0	0.07	0.0002	0.0006	1 km/s
Piccard + Stahel (Mt Rigi)	1927	2.8	0.13	0.006
Michelson et al.	1929	25.9	0.9	0.01
Joos	1930	21.0	0.75	0.002

Note: before about 1950 it was common to not perform a detailed error analysis, and to not report error bars or resolutions.

Note: the re-analysis of Miller's 1925–29 results is: T. J. Roberts, “An Explanation of Dayton Miller's Anomalous ‘Ether Drift' Results”, arXiv:physics/0608238. There is more discussion of this below.

• A.A. Michelson and E.W. Morley, “On the Relative Motion of the Earth and the Luminiferous Ether”, Am. J. Sci. (3rd series) 34 333–345 (1887).http://www.aip.org/history/gap/PDF/michelson.pdf.: This is the classic paper describing this famous experiment. Contrary to popular myth, their result is not actually “null”—in their words “the relative velocity of the Earth and the aether is probably less than one sixth the Earth's orbital velocity, and certainly less than one-forth”. While some people claim to see a “signal” in their plots, an elementary error analysis shows it is not statistically significant (see Appendix I of arXiv:physics/0608238). So this experiment is certainly consistent with SR.
• Shankland, “Michelson-Morley Experiment”, American Journal of Physics 1964, pg 16.: This is a general review article.
• G. Joos, Ann. Phys. 7 385 (1930).: An excellent repetition of the MMX, in vacuum.
• K.K. Illingworth, Phys. Rev. 30 (1927), pg 692.: Used a clever technique with a tiny step in one mirror to obtain significantly improved resolution.
• Shamir and Fox, N. Cim. 62B no. 2 (1969), pg 258.: A repetition of the MMX with the optical paths in perspex (n = 1.49), and a laser-based optics sensitive to ~0.00003 fringe. They report a null result with an upper limit on v_aether of 6.64 km/s.

See also: Brillet and Hall.

The Kennedy-Thorndike Experiment

• R.J. Kennedy and E.M. Thorndike, “Experimental Establishment of the Relativity of Time”, Phys. Rev. 42 400–418 (1932).: This uses an interferometer similar to Michelson's, except that its arms are of different length, and are not at right angles to each other. They used a spectacular technique to keep the apparatus temperature constant to 0.001°C, which gave them sufficient stability to permit observations during several seasons. They also used photographs of their fringes (rather than observing them in real time as in most other interferometer experiments). Their apparatus was fixed to the Earth and could only rotate with it. Their null result is consistent with SR.
• Mьller and Soffel, “A Kennedy-Thorndike experiment using LLR data”, Phys. Lett. A 198, p71 (1995).: Using lunar laser ranging data they put a limit on Lorentz violating terms in the test theory of Mansouri and Sexl only a factor of two or so worse than modern laser techniques in the laboratory.

See also: Hils and Hall.

Modern Laser / Maser Tests of Light-Speed Isotropy

• Cedarholm, Havens, and Townes, Phys. Rev. Lett. 1(1958), pg 342.: They used two ammonia-beam masers back-to-back to put a limit of 30 m/s on any “aether drift”.
• T.S. Jaseja, A. Javan, J. Murray and C.H. Townes, “Test of Special Relativity or of the Isotropy of Space by Use of Infrared Masers”, Phys. Rev. 133A 1221–1225 (1964): They mounted two He-Ne microwave masers perpendicularly on a shock-mounted table and observed the beat frequency between them as the table was rotated. They put a limit of 30 m/s on the anisotropy.
• A. Brillet and J.L. Hall, “Improved Laser Test of the Isotropy of Space”, Phys. Rev. Lett. 42 549–552 (1979).: This is one of the most accurate limits on any anisotropy in the round-trip speed of light in a laboratory. They measured the beat-frequency between a single-mode laser on a rotating table and a single-mode laser fixed to the Earth to put a limit on such an anisotropy of 3 parts in 10¹⁵. Due to the construction of their rotating laser, this can also be interpreted as a limit on any anisotropy of space. This is a round-trip experiment because of their use of a Fabry-Perot etalon to determine the frequency of the rotating laser. Note that their limit on the round-trip anisotropy corresponds to a round-trip speed of less than 0.000001 m/s (!); in terms of the more usual one-way anisotropy it is 30 m/s.

Their residual 17 Hz signal (out of ~10¹⁵ Hz) was described as “unknown”; it was fixed with respect to their laboratory and therefore could not be of cosmic origin. A. Brillet has indicated privately that this is most likely due to the rotation axis being slightly off-vertical by a few microradians.

• Hils and Hall, Phys. Rev. Lett. 64 (1990), pg 1697.: This is similar to Brillet and Hall (above), but the lasers are fixed to the Earth for better stability. No variations were found at the level of 2Ч10⁻¹³. As they made observations over a year, this is not merely a limit on anisotropy, but also a limit on variations in different inertial frames. Brillet and Hall corresponds roughly to the Michelson-Morley experiment (no variations of the round-trip speed of light in different directions, with a time-scale of minutes or seconds); Hils and Hall corresponds roughly to the Kennedy-Thorndike experiment (no variations of the round-trip speed of light in different directions or for the different inertial frames occupied by the Earth during a year or so).
• Antonini, P., Okhapkin, M., Goklu, E., and Schiller, S., “Test of constancy of speed of light with rotating cryogenic optical resonators”, Phys. Rev. A 71, 050101(R) (2005). arXiv:gr-qc/0504109.: Commented on by Tobar et al., Phys. Rev. A72, 066101 (2005). Reply by the authors Phys. Rev. A72, 066102 (2005).
• Herrmann et al., “Test of the Isotropy of the Speed of light using a Continuously Rotating Optical Resonator”, Phys. Rev. Lett. 95, 150401 (2005) arXiv:physics/0508097.: Improved limits at a level of a few parts in 10⁻¹⁶.
• Mueller et al., “Modern Michelson-Morley Experiment using Cryogenic Optical Resonators”, Phys. Rev. Lett. 91, no. 2, 020401 (2003).: Anisotropy of c < (2.6 ±1.7)Ч10⁻¹⁵.
• Chen et al., “Experimental Test of the Isotropy of Two-way Light Speed”, A.S.N.U. Peking, 33, no. 5, pg 595 (1997).: An experiment similar to Brillet and Hall, with a limit of 1Ч10⁻¹⁸ in the anisotropy of c.

Other Experiments

• Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg 2489 (1974).: A triangle interferometer with one leg in glass. They set an upper limit on the anisotropy of 0.025 m/s. This is about one-millionth of the Earth's orbital velocity and about 1/10,000 of its rotational velocity.
• Riis et al., Phys. Rev. Lett. 60, pg 81 (1988).: This novel experiment uses a two-photon transition in a neon atomic beam to set an upper limit on any anisotropy of 0.3 m/s.
• Wolf and Petit, “Satellite test of special relativity using the global positioning system”, Phys. Rev. A 56, p4405 (1997).: Using GPS satellites to test for anisotropy in the speed of light, they find δc/c < 5Ч10⁻⁹.
• Silvertooth, J. O. S. A. 62 (1972), pg 1330.: This innovative experiment uses an interferometer with frequency-doubling crystals, so the fundamental's fringes are due to signals going all the way around, but the doubled-frequency fringes are due to signals going only half the way around (converging from opposite directions onto the detector). Its null result is consistent with SR.

3.2 One-Way Tests of Light-Speed Isotropy

Note that while these experiments clearly use a one-way light path and find isotropy, they are inherently unable to rule out a large class of theories in which the one-way speed of light is anisotropic. These theories share the property that the round-trip speed of light is isotropic in any inertial frame, but the one-way speed is isotropic only in an aether frame. In all of these theories the effects of slow clock transport exactly offset the effects of the anisotropic one-way speed of light (in any inertial frame), and all are experimentally indistinguishable from SR. All of these theories predict null results for these experiments. See Test Theories above, especially Zhang (in which these theories are called “Edwards frames”).

• Cialdea, Lett. Nuovo Cimento 4 (1972), pg 821.: Uses two multi-mode lasers mounted on a rotating table to look for variations in their interference pattern as the table is rotated. Places an upper limit on any one-way anisotropy of 0.9 m/s.
• Krisher et al., Phys. Rev. D, 42, No. 2, pg 731–734, (1990).: Uses two hydrogen masers fixed to the Earth and separated by a 21-km fiber-optic link to look for variations in the phase between them. They put an upper limit on the one-way linear anisotropy of 100 m/s.
• Champeny et al., Phys. Lett. 7 (1963), pg 241.Champeney, Isaak and Khan, Proc. Physical Soc. 85, pg 583 (1965).Isaak et al., Phys. Bull. 21 (1970), pg 255.: Uses a rotating Mцssbauer absorber and fixed detector to place an upper limit on any one-way anisotropy of 3 m/s.
• Turner and Hill, Phys. Rev. 134 (1964), B252.: Uses a rotating source and fixed Mцssbauer detector to place an upper limit on any one-way anisotropy of 10 m/s.
• Gagnon, Torr, Kolen, and Chang, Phys. Rev. A38 no. 4 (1988), pg 1767.: A guided-wave test of isotropy. Their null result is consistent with SR.
• T.W. Cole, “Astronomical Tests for the Presence of an Ether”, Mon. Not. R. Astr. Soc. (1976), 175 93P-96P.: Several VLBI tests sensitive to first-order effects of an aether are described. No aether is detected, with a sensitivity of 70 m/s.
• Ragulsky, “Determination of light velocity dependence on direction of propagation”, Phys. Lett. A, 235 (1997), pg 125.: A “one-way” test that is bidirectional with the outgoing ray in glass and the return ray in air. The interferometer is by design particularly robust against mechanical perturbations, and temperature controlled. The limit on the anisotropy of c is 0.13 m/s.

3.3 Tests of Light Speed from Moving Sources

If the light emitted from a source moving with velocity v toward the observer has a speed c+kv in the observer's frame, then these experiments place a limit on k. Many but not all of these experiments are subject to criticism due to Optical Extinction.

Experiments Using Cosmological Sources

• Comstock, Phys. Rev. 10 (1910), pg 267.DeSitter, Koninklijke Akademie van Wetenschappen, vol 15, part 2, pg 1297–1298 (1913).DeSitter, Koninklijke Akademie van Wetenschappen, vol 16, part 1, pg 395–396 (1913).DeSitter, Physik. Zeitschr. 14, 429, (1913) http://www.datasync.com/~rsf1/desitter.htm.DeSitter, Physik. Zeitschr. 14, 1267, (1913) http://www.datasync.com/~rsf1/desitter.htm.Zurhellen, Astr. Nachr. 198 (1914), pg 1.: Observations of binary stars. k < 10⁻⁶. These are all subject to criticism due to Optical Extinction.
• K. Brecher, “Is the Speed of Light Independent of the Velocity of the Source?”, Phys. Rev. Lett. 39 1051–1054, 1236(E) (1977).: Uses observations of binary pulsars to put a limit on the source-velocity dependence of the speed of light. k < 2Ч10⁻⁹. Optical Extinction is not a problem here, because the high-energy X-rays used have an extinction length considerably longer than the distance to the sources.
• Heckmann, Ann. d. Astrophys. 23 (1960), pg 410.: Differential aberration, galaxies versus stars. This experiment is subject to criticism due to Optical Extinction.
• Observations of Supernovae: A supernova explosion sends debris out in all directions with speeds of 10,000 km/s or more (known from Doppler broadening of spectral lines). If the speed of light depended on the source velocity, its arrival at Earth would be spread out in time due to the spread of source velocities. Such a time spread is not observed, and observations of distant supernovae give k < 5Ч10⁻⁹. These observations could be subject to criticism due to Optical Extinction, but some observations are for supernovas considerably closer than the extinction length of the X-ray wavelengths used.

Experiments Using Terrestrial Sources

• Alvaeger F.J.M. Farley, J. Kjellman and I Wallin, Physics Letters 12, 260 (1964).Arkiv foer Fysik, Vol 31, pg 145 (1965).: Measured the speed of gamma rays from the decay of fast π⁰ (~0.99975 c) to be c with a resolution of 400 parts per million. Optical extinction is not a problem for such high-energy gamma rays. The speed of the π⁰ is not measured, but is assumed to be similar to that measured for π⁺ and π⁻.
• Sadeh, Phys. Rev. Lett. 10 no. 7 (1963), pg 271.: Measured the speed of the gammas emitted from e⁺e⁻ annihilation (with center of mass v/c ~0.5) to be c within 10%.

This experiment was criticized in Lo Savio, Phys. Lett. A, 1988, Vol 133, pg 176. It is certainly true that at the instant of annihilation the e⁺ need not be traveling in the same direction it had initially, or have the same speed (most annihilations occur at very low energy as the positrons stop). This experiment is inconclusive at best.

• Babcock and Bergmann, Journal Opt. Soc. Amer. Vol. 54, pg 147 (1964).: This repeat of Kantor's experiment in vacuum shows no significant variation in the speed of light affected by moving glass plates. Optical Extinction is not a problem. k < 0.02.
• Filipas and Fox, Phys. Rev. 135 no. 4B (1964), pg B1071.: Measured the speed of gamma rays from the decay of fast π⁰ (~0.2 c) in an experiment specifically designed to avoid extinction effects. Their results are in complete disagreement with the assumption c+v, and are consistent with SR. k < 0.5 with a confidence level of 99.9%.
• Beckmann and Mandics, “Test of the Constancy of the Velocity of Electromagnetic Radiation in High Vacuum”, Radio Science, 69D, no. 4, pg 623 (1965).: A direct experiment with coherent light reflected from a moving mirror was performed in vacuum better than 10⁻⁶ torr. Its result is consistent with the constant velocity of light. This experiment is notable because Beckmann was a perennial critic of SR. Optical Extinction is not a problem.
• Operation of FLASH, a free-electron laser, http://vuv-fel.desy.de/.: A free-electron laser generates highly collimated X-rays parallel to the relativistic electron beam that is their source. If the region that generates the X-rays is L meters long, and the speed of light emitted from the moving electrons is c+kv (here v is essentially c), then at the downstream end of that region the minimum pulse width is k(L/c)/(1+k), because light emitted at the beginning arrives before light emitted at the downstream end. For FLASH, L=30 meters, v=0.9999997 c (700 MeV), and the observed X-ray pulse width is as short as 25 fs. This puts an upper limit on k of 2.5Ч10⁻⁷. Optical extinction is not present, as the entire process occurs in very high vacuum.

3.4 Measurements of the Speed of Light, and Other Limits on it

In 1983 the international standard for the meter was redefined in terms of the definition of the second and a defined value for the speed of light. The defined value was chosen to be as consistent as possible with the earlier metrological definitions of the meter and the second. Since then it is not possible to measure the speed of light using the current metrological standards, but one can still measure any anisotropy in its speed, or use an earlier definition of the meter if necessary.

• Mulligan, Am. J. Phys. 44 no. 10 (1976), pg 960.: A report on measurements by the NBS.
• Rowley et al., Opt. and Quantum Elect. 8 (1976), pg 1.: A review article on the set of precision frequency and wavelength measurements that became the basis for the 1973 value of c. This is the best single reference for this.
• Woods et al., Appl. Optics 17 (1978), pg 1048; Rowley, Opt. Comm. 34 (1980), pg 429.Baird and Whitford, Opt. Comm. 31 (1979), pg 363, pg 367.: Measured c = 299792458.8 ± 0.2 meter/s, with 1.2 meter uncertainty due to realization of the Kr meter standard used. The fact that the Kr standard for the meter became the limit on accuracy was a major reason for the 1983 redefinition of the meter in terms of the definition of c and the definition of the second.
• Goldman, J. O. S. A. 70 (1980), 1640.: Discussion of three proposals for a new definition of the meter (pre-1983).
• Jennings et al., J. Res. N.B.S. 92 (1982), pg 11.: Review of methods to relate c to the meter, and results for further measurements checking the 1973 determination of c leading to the 1983 adoption of the new meter standard in terms of the definition of c and the definition of the second.
• Giacomo, “The New Definition of the Meter”, Am. J. Phys. 52 no. 7 (1984), pg 607.: An overview of past definitions of the meter with emphasis on the guidelines that governed the choice of the new definition in 1983 in terms of the definition of the second and the definition of the speed of light.
• Petley, “New Definition of the Metre”, Nature 303 (1983), pg 373.: A review article discussing the reasons for the re-definition of the meter in 1983 in terms of the definition of the second and the definition of the speed of light.
• Bates, Am. J. Phys. 56 (1986), pg 682.Bates, Am. J. Phys. 51 (1983), pg 1003.: A summary of measurements of c. The second paper describes measuring c by measuring frequency and wavelength and describes a college-level lab experiment.

Limits on Velocity Variations with Frequency

• Essen and Froome, The Velocity of Light and Radio Waves (1969).: For frequencies between 10⁸ and 10¹⁵ Hz the speed of light is constant within 1 part in 10⁵.
• Brown et al., Phys. Rev. Lett. 30 no. 16 (1973), pg 763.: For visible light and 7 GeV gammas the speed of light differs by at most 6 parts in 10⁶. The speed of 11 GeV electrons is within 3 parts in 10⁶ of the speed of visible light.
• Florman, J. Res. N.B.S. 54 (1955), pg 355.: -
• Schaefer, Phys. Rev. Lett. 82 no. 25 (1999), pg 4964.: For photons of 30 keV and 200 keV the speed of light is the same within a few parts in 10²¹.

Limits on the Photon Mass

• Goldhaber and Nieto, “New Geomagnetic Limit on the Mass of the Photon”, Phys. Rev. Lett. 21 no. 8 (1968), pg 567.: A limit of 2.3Ч10⁻¹⁵ eV/c².
• Goldhaber and Nieto, “Terrestrial and Extraterrestrial limits on the Photon Mass”, Rev. Mod. Phys. 43 no. 3 (1971), pg 277.: A review article discussion about various experimental limits.
• Davis et al., “Limit on the Photon Mass Deduced from Pioneer-10 Observations of Jupiter's magnetic Fields”, Phys. Rev. Lett. 35 no. 21 (1975), pg 1402.: A limit of 6Ч10⁻¹⁶ eV/c².
• Lakes, “Experimental limits on the Photon Mass and Cosmic Magnetic Vector Potential”, Phys. Rev. Lett. 80 no. 9 (1998), pg 1826.: An experimental approach using a toroid Cavendish balance.
• Luo et al., “New Experimental Limit on the Photon Rest Mass with a Rotating Torsion Balance”, Phys. Rev. Lett, 90, no. 8, 081801 (2003).: A limit of 1.2Ч10⁻⁵¹ g (6Ч10⁻¹⁹ eV/c²).

See also the Particle Data Group's summary on “Gauge and Higgs Bosons”. As of July 2007, their reported limit on the photon mass is 6Ч10⁻¹⁷ eV/c².

3.5 Tests of the Principle of Relativity and Lorentz Invariance

Einstein's first postulate, the principle of Relativity (PoR), essentially states that the laws of physics do not vary for different inertial frames. Most if not all of the tests of his second postulate (the isotropy experiments above) could also be placed in this section, as could those in the following section on the isotropy of space.

The Trouton-Noble Experiment

• F.T. Trouton, Trans. Royal Soc. Dublin, 76, pg 379 (1902).Trouton and Noble, Phil. Trans. Royal Soc. London, A 202 (1903), pg 165.: This classic experiment looked for a torque induced on a charged capacitor due to its motion through the aether. Its null result is consistent with SR.
• Trouton and Rankine, “On the electrical resistance of moving matter”, Proc. Royal Soc. London, 80, pg 420 (1908).: Measurements of the resistance of a coil fixed in the lab, for various orientations relative to the motion of the Earth. Its null result is consistent with SR.
• Chase, Phys, Rev, 28, pg 378 (1926); 30 pg 516 (1927).: Set an upper limit on aether drift of 4 km/s.
• Tomaschek, Ann. d Phys. 78 (1926), p743; 80 (1926), pg 509.: Tomaschek performed the Trouton-Noble experiment at three different altitudes; all results are consistent with the SR predictions.

Other Experiments

• Coleman and Glashow, “Cosmic ray and Neutrino Tests of Special Relativity”, preprint arxiv:hep-ph/9703240.: Simple observations of the existence of cosmic rays lead to extremely tight limits on Lorentz non-invariance. These are model dependent, and depending on choice of model and other assumptions limits as good as 5Ч10⁻²³ are obtained.
• Coleman and Glashow, “High-Energy Tests of Lorentz Invariance”, preprint arxiv:hep-ph/9812418.: A more general perturbative framework is developed.

3.6 Tests of the Isotropy of Space

• Hughes et al., Phys. Rev. lett. 4 no. 1 (1960), pg 342.Drever, Philosophical Mag. 6, 683.: This extremely accurate experiment looked for any anisotropy in nuclear magnetic resonance. Hughes placed an upper limit on such anisotropy of 10⁻²⁰.
• Prestage et al., Physics Review Letters 54, 2387 (1985).Lamoreaux et al., Physics Review Letters 57, 3125 (1986).Chupp et al., Phys. Rev. Lett. 63, 1541 (1989).: Variations on the Hughes-Drever experiment.
• Phillips, Phys. Rev. Lett. 59 no. 15 (1987), pg 1784.: A test using a cryogenic torsion pendulum carrying a transversely polarized magnet. No significant anisotropy was observed.
• Hou, L.-S., Ni, W.-T., and Li, Y.-C.M., “Test of Cosmic Spatial Isotropy for Polarized Electrons Using a Rotatable Torsion Balance”, Phys. Rev. Lett., 90, 201101, (2003).: -
• Heckel et al., Phys. Rev. Lett. 97 (2006) 021603. arXiv:hep-ph/0606218: This uses a very clever spin-aligned torsion pendulum with a net spin but zero magnetization.

See also Brillet and Hall.

Recent High-Resolution Tests using Cavities

• Mьller, H., “Testing Lorentz invariance by use of vacuum and matter filled cavity resonators”, (2004). arXiv:hep-ph/0412385.: A general review.
• Braxmaier, C., Mьller, H., Pradl, O., Mlynek, J., Peters, A., and Schiller, S., “Tests of Relativity Using a Cryogenic Optical Resonator”, Phys. Rev. Lett., 88, 010401, (2002).: -
• Mьller, H., Herrmann, S., Saenz, A., Peters, A., and Lдmmerzahl, C., “Optical cavity tests of Lorentz invariance for the electron”, Phys. Rev. D, 68, 116006-1-17, (2003). arXiv:hep-ph/0401016.Mьller, H., Braxmaier, C., Hermann, S., Peters, A., and Lдmmerzahl, C., “Electromagnetic cavities and Lorentz invariance violation”, Phys. Rev. D67, 056006 (2003).: -
• Wolf, P., Bize, S., Clairon, A., Santarelli, G., Tobar, M.E., and Luiten, A.N., “Improved test of Lorentz invariance in electrodynamics”, Phys. Rev. D, 70, 051902-1-4, (2004). arxiv:hep-ph/0407232.Wolf et al., “Tests of Lorentz Invariance using a Microwave Resonator”, Phys. Rev. Lett., 90, no. 6, 060402 (2003).: -
• Lipa, J.A., Nissen, J.A., Wang, S., Stricker, D.A., and Avaloff, D., “A New Limit on Signals of Lorentz Violation in Electrodynamics”, Phys. Rev. Lett., 90, 060403, (2003).arXiv:physics/0302093.: Superconducting cylindrical cavities oriented vertically and East-West. No anisotropy to 1 part in 10¹³.
• Stanwix, P.L., Tobar, M.E., Wolf, P., Susli, M., Locke, C.R., Ivanov, E.N., Winterflood, J., and van Kann, F., “Test of Lorentz Invariance in Electrodynamics Using Rotating Cryogenic Sapphire Microwave Oscillators”, Phys. Rev. Lett., 95, 040404, (2005). arXiv:hep-ph/0506074.: