[Physics FAQ] - [Copyright]
By Tom Roberts, June 2000.
Original by Siegmar Schleif and others, January 1998.

What is the experimental basis of Special Relativity?

1. Introduction

1. It is required that the theory not be refuted by any experiment within the theory's domain of applicability.
2. It is expected that the theory be confirmed by a number of experiments which cover a significant fraction of the theory's domain of applicability.
3. It is expected that the theory be confirmed by a number of experiments which examine a significant fraction of the theory's predictions.

Other than their sheer numbers, the most striking thing about these experimental tests of SR is their remarkable breadth and diversity. An important aspect of SR is its universality - it applies to all known physical phenomena and not just to the electromagnetic phenomena it was originally invented to explain. In these experiments you will find tests using electromagnetic and nuclear measurements (including both strong and weak interactions); gravitational tests are the province of General Relativity, and are not considered here, see Experimental Tests of GR.

There are several useful surveys of the experimental basis of SR:

• Y.Z.Zhang, Special Relativity and its Experimental Foundations, World Scientific (1997).
• G.Holton, "Resource Letter SRT-1 on Special Relativity Theory", Am. J. Phys., 30 (1962), p462.
• D.I.Blotkhintsev, "Basis for Special Relativity Theory Provided by Experiments in High Energy Physics", Sov. Phys. Uspekhi, 9 (1966), p405.
• Newman et al. Phys. Rev. Lett. 40 no. 21 (1978), p1355.

Textbooks which have good summaries of the experimental basis of relativity are:

• M.Born, Einstein's theory of Relativity.
• Bergmann, Introduction to the Theory of Relativity.
• Moller, The Theory of Relativity.
• M. von Laue, Die relativitätstheorie (in German).

Note, however, that SR is not perfect (in agreement with every experiment), and there are some experiments which are in disagreement with its predictions. See Experiments Which Apparently are NOT Consistent with SR where some of these experiments are referenced and discussed. It is clear that most if not all of these experiments have difficulties which are unrelated to SR. Note also that few if any standard references or textbooks even mention the possibility that some experiments might be inconsistent with SR, and there are also aspects of publication bias in the literature. That being said, as of this writing there are no reproducible and generally-accepted experiments which are inconsistent with SR, within its domain of applicability.
 

Domain of Applicability
The domain of applicability of a physical theory is the set of physical situations in which the theory is valid. For SR this is basically measurements of distance, time, momentum, energy, etc. in inertial frames (coordinates); calculus can be used to apply SR in accelerated systems, as can the more advanced mathematics of differential geometry. A more technical definition is that SR is valid only in flat Lorentz manifolds topologically equivalent to R⁴. In particular, any experiment in which the effects of gravitation are important is outside the domain of SR. Because SR is the local limit of General Relativity it is possible to compute how large an error is made when one applies SR to a situation which is approximately but not exactly inertial, such as the common case of experimental apparatus supported against gravity on the earth's surface. In many cases (e.g. most optical and elementary-particle experiments on the rotating earth's surface) these errors are vastly smaller than the experimental resolution, and SR can be accurately applied.
 

Test Theories of SR
A test theory of SR is a generalization of the Lorentz transforms of SR using additional parameters. One can then analyze experiments using the test theory (rather than SR itself) and fit the parameters of the test theory to the experimental results. If the fitted parameter values differ significantly from the values corresponding to SR, then the experiment is inconsistent with SR. But more normally, such fits can show how well a given experiment confirms or disagrees with SR, and what the experimental accuracy is for doing so. This gives a general and tractable method of analysis which can be common to multiple experiments.

Different test theories differ in their assumptions about what form the transform equations could reasonably take. There are at present four test theories of SR:

	Robertson,Rev. of Mod. Phys. 21, p378 (1949).
	Edwards, Am. J. Phys. 31 (1963), p482.
	Mansouri and Sexl, Gen. Rel. Grav. 8 (1977), p497, p515, p809.
	Zhang, Special Relativity and its Experimental Foundations.

Zhang discusses their interrelationships and presents a unified test theory encompasing the other three, but with a better and more interpretable parameterization. His discussion implies that there will be no more test theories of SR which are not reducible to one of the first three.

Robertson showed that one can unambiguously deduce the Lorentz transform of SR to an accuracy of ~0.1% from the following three experiments: Michelson and Morley, Kennedy and Thorndike, Ives and Stilwell. Zhang showed that modern experiments determine the Lorentz transforms to within a few parts per million.

These test theories can also be used to examine potential alternate theories to SR -- such alternate theories predict particular values of the parameters of the test theory, which can easily be compared to values determined by experiments analyzed with the test theory. The existing experiments put rather strong experimental constraints on any alternative theory. In particular, Zhang showed that these experimental limits essentially require that any theory based upon the existence of an ether be experimentally indistinguishable from SR, and have an ether frame which is unobservable (the only alternative is for a theory to "live in the error bars" of the experiments, which is quite difficult given the high accuracies achieved by many of these experiments).

2. Early Experiments (Pre-1905)

When A. Einstein wrote his famous paper: "The Electrodynamics of Moving Bodies" in 1905, he already had experimental support for his new theory:

".... Examples of this sort, together with the unsuccessful attempts to discover any motion of the Earth relatively to the "light medium" suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good..."

3. 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 which will be introduced hereafter, we call it the "stationary system".

-- Ibid.

3.1 Round-Trip Tests of Light-Speed Isotropy

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, pp167-178 (1955), which includes references to each experiment (resolution and the limit on Vaether are from the original sources). The expected fringe shift is what would be expected for a rigid ether at rest with respect to the sun and earth's orbital velocity (~30 km/sec).

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 degree 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.

See also: Hils and Hall.

Modern Laser / Maser Tests of Light-Speed Isotropy

Cedarholm, Havens, and Townes, Phys. Rev. Lett. 1 (1958), p 342.
	They used two ammonia-beam masers back-to-back to put a limit of 30 m/sec on any "ether 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/sec 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/sec (!); in terms of the more usual one-way anisotropy it is 30 m/sec.  Their residual 17 Hz signal (out of ~1015 Hz)  was interpreted as due to the rotation of the earth in: Aspden, Phys. Lett. 8 no. 9 (1981), p411. The experimenters themselves interpreted it as "unknown", and noted it was fixed wrt their laboratory and therefore could not be of cosmic origin.

Hils and Hall, Phys. Rev. Lett. 64 (1990),  p 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 2*10-13. 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).

Other Experiments

Trimmer et al., Phys. Rev. D8, p3321 (1973); Phys. Rev. D9 p2489 (1974).
	A triangle interferometer with one leg in glass. They set an upper limit on the anisotropy of  0.025 m/sec. 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, p81 (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/sec.

Silvertooth, J. O. S. A. 62 (1972), p1330.
	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

 3.3 Tests of Light Speed from Moving Sources

Experiments Using Cosmological Sources

Comstock, Phys. Rev. 10 (1910), p267. DeSitter, Koninklijke Akademie van Wetenschappen, vol 15, part 2, p.1297-1298 (1913); DeSitter, Koninklijke Akademie van Wetenschappen, vol 16, part 1, p.395 - 396 (1913). Zurhellen, Astr. Nachr. 198 (1914), p1.
	Observations of binary stars. k < 10-6.

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 < 2*10-9.

Heckmann, Ann. D'. Astrophys. 23 (1960), p410.
	Differential aberration, galaxies vs stars.

These experiments are all subject to criticism due to extinction effects in the interstellar gas; see for instance J.G. Fox Am. J. Phys. 30, p297 (1962); AJP 33, 1 (1964). The standard reference for optical extinction is Born and Wolf, Principles of Optics.

Experiments Using Terrestrial Sources

Beckmann and Mandies, Radio. Sci. 69D (1965), p623.
	A moving mirror experiment.

Alvaeger F.J.M. Farley, J. Kjellman and I Wallin, Physics Letters 12, 260 (1964).
	Measured the speed of gamma rays from the decay of fast pi0 (~0.99975 c) to be c with a resolution of 400 parts per million.

Sadeh, Phys. Rev. Lett. 10 no. 7 (1963), p271.
	Measured the speed of the gammas emitted from e+e- annihilation (with center-of-mass v/c ~ 0.5) to be c within 10%.

Babcock and Bergmann, Journal Opt. Soc. Amer. Vol. 54, p. 147 (1964).
	-

Filipas and Fox, Phys. Rev. 135 no. 4B (1964), p B1071.
	Measured the speed of gamma rays from the decay of fast pi0 (~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.

Because of the high energies of the gammas in Alvaeger, extinction is not a problem for it; Filipas and Fox specifically designed their experiment to avoid extinction.

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

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), p763.
	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), p355.
	-

Schaefer, Phys. Rev. Lett. 82 no. 25 (1999), p4964.
	For photons of 30 keV and 200keV 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), p567.
	A limit of 2.3*10-15 eV.

Goldhaber and Nieto, "Terrestrial and Extraterrestrial limits on the Photon Mass", Rev. Mod. Phys. 43 no. 3 (1971), p277.
	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), p1402.
	A limit of 6*10-16 eV.

Lakes, "Experimental limits on the Photon Mass and Cosmic Magnetic Vector Potential", Phys. Rev. Lett. 80 no. 9 (1998), p1826.
	An experimental approach using a toroid Cavendish balance.

See also the Particle Data Group's summary on "Gauge and Higgs Bosons".
 

3.5 Tests of the Principle of Relativity and Lorentz Invariance

The Trouton - Noble Experiment

Trouton and Noble, Phil. Trans. 202 (1903), p165.
	This classic experiment looked for a torque induced on a charged capacitor due to its motion through the ether. Its null result is consistent with SR.

Chase, Phys, Rev, 28, p. 378 (1926).
	Set an upper limit on ether drift of 4 km/sec.

Tomaschek, Ann. d Phys. 78 (1926), p743; 80 (1926), p509.
	-

Other Experiments

Coleman and Glashow, "Cosmic ray and Neutrino Tests of Special Relativity", preprint 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 5*10-23 are obtained.

Coleman and Glashow, "High-Energy Tests of Lorentz Invariance", preprint hep-ph/9812418.
	A more general perturbative framework is developed.

3.6 Tests of the Isotropy of Space

See also Brillet and Hall.
 

 4. Tests of Time Dilation and Transverse Doppler Effect

The Ives and Stilwell Experiment

H.E. Ives and G.R. Stilwell, "An Experimental Study of the Rate of a Moving Atomic Clock", J. Opt. Soc. Am. 28 215-226 (1938); JOSA 31 369-374 (1941).
	This classic experiment measured the transverse Doppler effect for moving atoms.

Hasselkamp et al, Z. Physik A289 (1989), p151.
	A measurement which is truly at 90 degrees in the lab. Agreement with SR to an accuracy of a few percent.

Measurements of Particle Lifetimes

Rossi and Hoag, Physical Review 57, p. 461 (1940). Rossi and Hall, Physical Review 59, p. 223 (1941). Rasetti, Physical Review 60, p. 198 (1941). Redei, Phys. Rev. 162 no. 5 (1967), p1299.
	Various measurements of the lifetimes of muons.  See also: Bailey et al.

Durbin, Loar and Havens, Physical Review 88, p. 179 (1952).
	-

D. Frisch and J. Smith, "Measurement of the Relativistic Time Dilation Using Mesons", Am. J. Phys. 31 (1963) 342.
	Measurements of the lifetimes of pions.  An interpretation was given by: Terell, Nuovo Cimento 16 (1960) p. 457.

Greenberg et al, Phys. Rev. Lett. 23 no. 21 (1969), p1267.
	More accurate measurement of pion lifetimes.

Ayres et al, Phys. Rev. D3 no. 5 (1971), p1051.
	Measurements of pion lifetimes, comparison of positive and negative pions, etc.

Burrowes et al, Phys. Rev. Lett. 2 (1959), p117.
	Measurements of Kaon lifetimes.

Doppler Shift Measurements

Kaivola et al, Phys. Rev. Lett. 54 no. 4 (1985), p255. McGowan et al, Phys. Rev. Lett. 70 no. 3 (1993), p251.
	They compared the frequency of two lasers, one locked to fast-beam neon and one locked to the same transition in thermal neon. Kaivola found agreement with SR's Doppler formula is to within 4*10-5; McGowan within 2.3*10-6.

Hay et al, Phys. Rev. Lett. 4 (1960), p165.
	A Moessbauer absorber on a rotor.

Kuendig, Phys. Rev. 129 no. 6 (1963), p2371.
	A Moessbauer absorber on a rotor was used to verify the transverse Doppler effect of SR to 1.1%.

Olin et al, Phys. Rev. D8 no. 6 (1973), p1633.
	A nuclear measurement at 0.05 c, in very good agreement with the prediction of SR.

5. Tests of the "Twin Paradox"

The Clock Hypothesis
The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives. The experiment of Bailey et al referenced above stored muons in a magnetic storage ring and measured their lifetime. While being stored in the ring they were subject to a proper acceleration of approximately 10¹⁸ g (1 g = 9.8 m/sec²). The observed agreement between the lifetime of the stored muons with that of muons with the same energy moving inertially confirms the clock hypothesis for accelerations of that magnitude.
 

Sherwin, "Some Recent Experimental Tests of the 'Clock Paradox'", Phys. Rev. 129 no. 1 (1960), p17.
	He discusses some Moessbauer experiments which show that the rate of a clock is independent of acceleration (~1016 g) and depends only upon velocity.

6. Tests of Relativistic Kinematics

Elastic Scattering

Champion, Proc. R. Soc. A136 (1932), p630.
	Electron-electron elastic scattering

Foley et al, "Experimental Test of the Pion-Nucleon Forward Dispersion Relation at High Energies", Phys. Rev. Lett. 19 no. 4 (1967), p193.
	The dispersion relation basically expresses conservation of probability, and its validity at different energies is related to relativistic kinematics.

Experiments Which Show the Limiting Velocity c

Alspector et al, Phys. Rev. Lett. 36, p.837 (1976).
	A comparison of neutrino and muon velocities, at Fermilab.

Kalbfleisch et al., Physics Review Letters 43, p.1361 (1979).
	A comparison of muon, neutrino, and antineutrino velocities over a range of energies, at Fermilab.

Guiragosian et al, Phys. Rev. Lett. 34 no. 6 (1975), p335.
	Relative velocity measurements of 15 GeV electrons and gammas. No significant difference was observed within ~2 parts in 107. See also Brown et al.

G.L. Greene et al.,"Test of special relativity by a determination of the Lorentz limiting velocity: Does E=mc2?" Physical Review D 44 (1991) R2216.
	An analysis combining the results of several experiments gives the result that the Lorentz limiting velocity must be equal to the speed of light to within 12 parts per million.

Stodolsky, "The Speed of Light and the Speed of Neutrinos", Phys. Lett. B201 no. 3 (1988), p353.
	A comparison of neutrino and photon speeds from supernova SN1987A Puts a limit of about 1 part in 108 on their speed difference.

Electron Relativistic Mass Variations

W Kaufmann, "Uber die Konstitution des Elektrons" Ann. Physik 19 ,495 (1906) ( first historical experiment); W. Kaufmann, "Uber die Konstitution des Elektrons", Sitzungsberichte der preussichen Akademie der Wissenschaften, 1915, Part 2.
	There were several discussions about the conclusions from Kaufmann's experiments and his data analysis. See for instance:  M. Planck, "Die Kaufmannschen Messungen der Ablenkbarkeit der beta-Strahlen in ihrer Bedeutung fur die Dynamik der Electron", Verhandlungen der Deutschen Physikalischen Gesellschaft, 8, 1906. M. Planck, "Nachtrag zu der Besprechung der Kaufmannschen Ablenkungsmessungen", Verhandlungen der Deutschen Physikalischen Gesellschaft, 9, 1907.

A.H. Bucherer, Phyz. Zeitschr. 9 (1908), p. 755; Ber. d. deutschen Phys. Ges. 6 (1908), p. 688. A. Bucherer, "Die experimentelle Bestatigung des Relativitatsprinzips", Annalen der Physik, 28, 1909.
	-

E. Hupka, Ann. Phys. 31 (1910), p. 169.
	-

Cl. Schaefer and G. Neumann, Phys. Zeitschr. 14 (1913), p. 1117.
	-

Ch.E. Guye and Ch. Lavanchy, Comptes rendus 161 (1915), p. 52.
	-

Zahn and Spees, Phys. Rev. 53 (1938), p511.
	-

Rogers et al. Physical Review 57 (1940), p379.
	Measurement of m/e and v for three beta-particles (electrons) from Radium. Supports the Lorentz model over the Abraham model by >10 sigma.

Meyer et al. Helv. Physica Acta 36 , p. 981 (1963).
	-

W. Bertozzi, Am. J. Phys. 32, 551 (1964).
	Measurements of speed vs energy for 0.5 - 15 MeV electrons.

Geller and Kollarits, Am. J. Phys. 40 (1972), p1125.
	-

Proton Relativistic Mass Variations

Zrelov, Tiapkin, Farago Soviet Physics JETP, Vol.34, p.384 (1958)
	-

Calorimetric Test of Special Relativity

D.R. Walz, H.P. Noyes and R.L. Carezani, Physical Review A29 (1984), p. 2110.
	The beam power at SLAC is measured using temperature rise in a calorimeter, for electons of ~17 and 20 GeV/c and beam currents up to ~15 microAmperes. Their results confirm SR with a resolution of about 30%, and are "many orders of magnitude larger than predicted by the theory of autodynamics", of which Carezani is the author (and also member of this experimental group).

7. Other Experiments

The Sagnac Experiment
Sagnac constructed a ring interferometer and measured its fringe shifts as it is rotated.
 

Sagnac, C.R.A.S 157 (1913), p708, p1410; J. Phys. Radium, 5th Ser. 4 (1914), p177.
	The classic papers by Sagnac.

Post, "Sagnac Effect", Rev. Mod. Phys., 39 no. 2, p. 475 (1967).
	A review article. This is probably the most useful reference on ring interferometers and the Sagnac effect.

Anderson et al, Am. J. Phys. 62 no. 11 (1994), p975.
	A more recent review, and description of a much more accurate ring interferometer.

Hasselbach and Nicklaus, Phys. Rev. A 48 no. 1 (1993), p143.
	The Sagnac effect using electrons.

Allan et al, Science, 228 (1985), p69.
	They observed the Sagnac effect using GPS satellite signals observed simultaneously at multiple locations around the world.

Anandan, "Sagnac Effect in Relativistic and Nonrelativistic Physics", Phys. Rev. D24 no. 2 (1981), p338. Gron, "Relativistic description of a Rotating Disk", AJP 43 no. 10 (1975), p869. Rizzi and Tartaglia, "Speed of Light on Rotating Platforms", preprint gr-qc/9805089. Mainwaring and Stedman, "Accelerated Clock Principles in Special Relativity", Phys. Rev. A47 no. 5 (1993), p3611. Berenda, "The Problem of the Rotating Disk", Phys. Rev. 62 (1942), p280.
	Various additional papers on the analysis of rotating systems.

Ashtekar and Magnon, "The Sagnac Effect in General Relativity", J. Math. Phys. 16 no. 2 (1975), p341.
	A discussion using GR.

The Michelson and Gale Experiment

Michelson and Gale, Nature 115 (1925), p566; Astrophys. J. 61 (1925), p137.
	This is essentially the Sagnac experiment, but on a much larger scale. They constructed a ring interferometer fixed on the ground with a size of 0.2 mi by 0.4 mi (about 320 m by 640 m). They did indeed detect the rotation of the earth.

g-2 Experiments as a Test of Special Relativity

Newman et al, Phys. Rev. Lett. 40 no. 21 (1978), p1355.
	A discussion of the basic technique of using measurements of the anamolous magnetic moment of electrons and muons as a test of SR, and an analysis of some low-energy electon data.

F. Combley et al., Physical Review Letters 42 (1979), p. 1383.
	Electron and muon measurements.

P.S. Cooper et al,. Physical Review Letters 42 (1979), p. 1386.
	Elecron measurements up to 12 GeV.

Farley et al, Nuovo Cimento Vol 45, p. 281 (1966). Farley et al, Nature 217, p. 17 (1968). Bailey et al, Nuovo Cimento 9A, p. 369 (1972). Bailey et al, Phys. Lett. 68B no. 2 (1977), p191.
	Measurements of the anomalous magnetic moment of muons.

The Global Positioning System (GPS)

http://tycho.usno.navy.mil/gps.html
	U.S. naval Observatory (USNO) GPS Operations. Includes an overview of the GPS and current details of its operation.

http://www.utexas.edu/depts/grg/gcraft/notes/gps/gps.html http://www.colorado.Edu/geography/gcraft/notes/gps/gps_f.html
	A tutorial and general overview of the GPS.

Allan et al, IEEE Trans. Inst. and Meas., IM-32 no. 2 (1985), p118.
	They discuss in detail how time and frequency comparisons among the various standards organizations of the world can be performed with an accuracy of about 1 part in 1014, using GPS satellites.

Ashby and Allan, "Coordinate time On and Near Earth", Phys. Rev. Lett. 53 no. 19 (1984), p1858.
	They discuss how the GPS coordinate system is used on and near earth. They also describe two different comparisons between USNO and the Paris Observatory.

Petit and Wolf, "Relativistic Theory for Picosecond Time Transfer in the Vicinity of earth", Astron. and Astrophys. 286 (1994), p971.
	-

Saburi et al, "High-Precision Time Comparison via Satellite and Observed Discrepancy of Synchronization", IEEE Trans. Inst. Meas. IM-25 no. 4 (1976), p473.
	The "discrepancy" they mention is merely the Sagnac effect, and observations agree with predictions.

Lunar Laser Ranging

Bender et al, Science 182 (1973), p229.
	The corner reflectors placed on the moon by the Apollo astronauts are used to verify GR with a net accuracy of 15 cm in the telescope-to-reflector distance.

Mueller et al, Ap. J. 382 (1991), p L101.
	-

Williams et al, Phys. Rev. Lett. 36 no. 11 (1976), p551. Williams et al, Phys. Rev. D53 no. 12 (1996), p6730.
	-

Dickey et al, Science 265 (1994), p482.
	-

Cosmic Microwave Background Radiation (CMBR)

Smoot et al, Phys. Rev. Lett. 39 no. 14 (1977), p898.
	Detected an anisotropy in the CMBR, and determined it is primarily a dipole anisotropy which would be zero in a frame moving at 390 +- 60 km/sec wrt the earth.

Mather et al, Ap. J. 420 (1994), p439.
	Measurement of the CMBR by the COBE satellite's FIRAS instrument.

Bennett et al, Physics Today (Nov. 1997), p32.
	Microkelvin variations in the CMBR are described. Note that these are after the dipole is subtracted out (i.e. these variations are measured in the "zero-dipole frame" of the CMBR moving about 370 km/s wrt the earth).

Songalla et al, Nature 371 (1994), p43.
	They present a measurement of the CMBR for a distant object with z=1.776.

Ge et al, Ap. J. 474 (1997), p67.
	They present a measurement of the CMBR for a distant object with z=1.9731.

The Constancy of Physical Constants

Tubbs and Wolfe, "Evidence for large-Scale Uniformity of Physical Laws", Ap. J. 236 (1980), pL105.
	Uniformity to 1 part in 104 is shown, subsequent to an epoch corresponding to less than 5% of the current age of the universe.

Potekhin and Varshalovich, "Non-Variability of the Fine-Structure Constant over cosmological Time Scales", Astron. Astrophys. Suppl. Ser. 104 (1994), p89.
	Quasar spectra with redshifts z ~ 0.2 - 3.7 are used to put a limit on the rate of change of alpha of about 4*10-14 per year.

The Neutrality of Molecules

Dylla and King, Phys. Rev. A7 (1973) p1224.
	The charge on sulfur hexafluoride is less than 2*10-19 times the charge on an electron.

Other experiments which I'm not sure how to classify (and haven't seen)
Otting, Physik. Zeitschr. 40 , 681 (1939).
Mandelberg and Witten, Journal Opt. Soc. Amer. 52, p. 529 (1962).
Zeitschrift fuer Physik A 342, p. 455 (1992).
 

8. Experiments Which Apparently are NOT Consistent with SR/GR

All that being said, I repeat: as of this writing there are no reproducible and generally-accepted experiments which are inconsistent with SR, within its domain of applicability.
 

Esclangon, C.R.A.S. 185 no. 26 (1927), p1593.
	He observed a systematic variation in the position of an optical image, correlated with sidereal time. This result is inconsistent not only with SR, but is also inconsistent with the hypothesis that space is Euclidean and light travels in straight lines (on earth).  His "signal" is actually composed of points which are an average of several thousand measurements each, and the magnitude of the signal is about 100 times smaller than the resolution of the individual measurements. See  Experimenter's Bias below.

Miller, Rev. Mod. Phys. 5 (1933), p203.
	This is a laborious repetition of the Michelson-Morley experiment (MMX), with observations taken over a decade. He reports a net ether drift of about 10 km/sec, and describes the variation in velocity and direction in terms of the motions of the sun and the earth combined with a net ether drift.  This experiment was re-analyzed in: R.S. Shankland, S.W. McCuskey, F.C. Leone and G. Kuerti, "New Analysis of the Interferometric Observations of Dayton C. Miller", Rev. Mod. Phys. 27 167-178 (1955). They re-examined Miller's original data logs and explained his non-null result as partly due to statistical fluctuations and partly due to local temperature conditions. Their re-analysis is consistent with a null result at all epochs during a year. They gave no justification for any correlation with sidereal time such as Miller reported.  Miller's "signal" is actually composed of points which are an average of several hundred measurements each, and the magnitude of the signal is more than 10 times smaller than the resolution with which the measurements were recorded.  See  Experimenter's Bias below.

Kantor, J. O. S. A. 52 (1962),978.
	Criticized in: Burcev, Phys. Lett. 5 no. 1 (1963), p44. Repeated by: Babcock and Bergman, J.O.S.A. 54 (1964), p147. Repeated by: Rotz, Phys. Lett. 7 no. 4 (1963), p252. The consensus is now that Kantor's non-null result was due to his rotating mirrors dragging the air; repetitions in vacuum yield a null result consistent with SR.

Silvertooth and Jacobs, Applied Optics 22 no. 9 (1983), p1274. Silvertooth, Specl. Sci. and Tech. 10 no. 1 (1986), p3. Silvertooth and Whitney, Physics Essays 5 no. 1 (1992), p82.
	This is a series of experiments using variations on a novel interferometer in which Silvertooth claims to have observed the ether. The first paper is simply a description of the special phototube and its usage in measuring Wiener fringes. The second and third present different variations of Silvertooth's basic double-interferometer; both claim to observe the ether.  I believe there have been discussions of this in Physics Essays following the third paper, but I have no access to them.  The experiments are marred by two clear instrumentation effects: there is almost certainly feedback into the laser in at least the first paper (and quite probably in the others), and the multi-mode lasers employed could mimic the effect seen due to the interrelationships among the different modes. Also the analysis presented is downright wrong -- the anisotropy in the speed of light postulated in the 2nd and 3rd papers is completely unable to account for their observations (two different erroneous analyses are presented in the last two papers, making the same elementary mistake both times: not considering the entire light path).

Kolen and Torr, Found. Phys. 12 no. 4 (1982), p401. Torr and Kolen, NBS Special Publication 617 (1984), p675-679.
	This is an experiment using two atomic clocks separated by 500 m which looks for sidereal variations in the phase between them. The first paper is merely a proposal and the second presents results which are reported to show a non-null result (but other reports indicate consistency with a null result). That second paper is not available to me as of this writing. This experiment is quite similar to those of Krisher et al and Cialdea referenced above (both of whom reported null results).

Pearson et al, "Superluminal Expansion of Quasar 3C273". Nature 290 (1981), p365. Mirabel and Rodriguez, "A Superluminal Source in the Galaxy", Nature 371 no. 1 (1994), p46.
	As of this writing it's not clear to me whether or not these observations are consistent with SR, GR and/or current cosmological models.  Note, however, that the simple observation of a visibly-superluminal expansion or motion of a distant object does not necessaily imply that anything actually exceeds c locally. See for instance: Gabuzda, Am. J. Phys. 55 no. 3 (1987), p214. If a high-gamma (subluminal) object is moving at a small angle wrt our line-of-sight it can appear to be going faster than light, but is not. This is different from any uncertainties in distance scales.

Nodland and Ralston, "Indication of Anisotropy in Electromagnetic Propagation over Cosmological Distances", Phys. Rev. Lett. 78 no. 16 (1997), p3043; preprint astro-ph/9704196.
	As of this writing it's not clear to me whether or not this observation is consistent with SR, GR and/or current cosmological models.

Anderson et al, "Indication from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleraition", preprint gr-qc/9808081.
	This has been the subject of an ongoing debate in the recent preprint archives. See also: gr-qc/9809070, gr-qc/9906112, gr-qc/9809075, gr-qc/9810015, gr-qc/9906112, gr-qc/9906113, gr-qc/9907363, gr-qc/9904150.There are probably additional preprints on this subject. While I see no clear consensus, there are prosaic explanations offered (anisotropic heat radiation from the spacecraft).

Experimenter's Bias
Experimenter's bias is a phenomenon caused by the inability of human participants in an experiment to remain completely objective, in which the human experimenter directly influences the experiment's outcome based upon his or her personal desires or expectations. It is most commonly a concern in medical and sociological experiments, in which "single-blind" and "double-blind" protocols are usually required. But some physical experiments in which a human observer is required to round-off measurements can also be subject to it. In the experiments here the conditions for this are basically the combination of a signal smaller than the actual measurement resolution and an over-averaging of the data used to extract the "signal" from the measurements.

In principle, if a measurement has a resolution of R, then if the experimenter averages N independent measurements the average will have a resolution of R/sqrt(N) (this is the central limit theorem of statistics). This is an important experimental technique used to reduce the impact of randomness on an experiment's outcome. But note that this requires that the measurements be statistically independent, and there are several reasons why that may not be true -- if so then the average may not actually be a better measurement but may merely reflect the correlations among the individual measurements and their non-independent nature.

The most common cause of non-independence is systematic errors (errors which affect all measurements equally, causing the different measurements to be highly correlated, so the average is no better than any single measurement). But another cause can be due to the inability of a human observer to round off measurements in a truly random manner. If an experiment is searching for a sidereal variation of some measurement, and if the measurement is rounded-off by a human who knows the sidereal time of the measurement, and if hundreds of measurements are averaged to extract a "signal" which is smaller than the apparatus' actual resolution, then it should be clear that this "signal" can come from the non-random round-off, and not from the apparatus itself. In such cases a single-blind experimental protocol is required; if the human observer does not know the sidereal time of the measurements, then even though the round-off is non-random it cannot introduce a spurious sidereal variation.

Note that modern electronic and/or computerized data acquisition techniques have greatly reduced the likelihood of such bias, but it can still be introduced by a poorly-designed analysis technique. Experimenter's bias was not well recognized until the 1950's and 60's, and then it was primarily in medical experiments and studies. Its effects on experiments in the physical sciences have not always been fully recognized. Several experiments referenced above were clearly affected by it.
 

Publication Bias
There are two very different aspects of publication bias:

1. Unpopular or unexpected results may not be published because either the original experimenters or some journal referees have misgivings or reservations about the results, based on the results themselves and not any independent evaluation of experimental procedures or technique.
2. Expected experimental results may not be published because either the original experimenters or some journal referees do not consider them interesting enough to merit publication.

Note that this does not include papers which are rejected for other reasons, such as: inappropriate subject or style, major internal inconsistencies, or downright incompetence on the part of authors or experimenters. Such rejections are not bias, they are the proper functioning of a peer-reviewed journal.
 

9. Acknowledgments

I wish to thank the previous authors of this FAQ, most notably Siegmar Schleif whose original list of references provided a fertile source of papers for my collection (and also the original source of this page several years ago). While the previous authors may have difficulty finding their original words in this revision, they will note that I have not deleted a single reference while adding many. I also wish to thank Nathan Urban, who as "keeper of the FAQ" has provided invaluable assistance and numerous suggestions.
 

Tom Roberts          tjroberts@lucent.com   [Top]