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Experimental basis of Special Relativity/Other Experiments

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The Fizeau Experiment

Fizeau measured the speed of light in moving mediums, most notably moving water. Fresnel proposed a “drag coefficient” that putatively described how strongly a moving material medium “dragged” the aether. SR predicts no aether but does predict that the speed of light in a moving medium differs from the speed in the medium at rest, by an amount consistent (to within experimental resolutions) with these experiments and with the Fresnel drag coefficient.

  • Michelson-Morley, Am. J. Sci. 31, 377 (1886).: This is a repetition of Fizeau's experiment, not the original MMX experiment!
  • Zeeman: Proc. Royal Soc. Amsterdam 17, pg 445 (1914); Proc. Royal Soc. Amsterdam 18, pg 398 (1915); Amst. Versl. 23, pg 245 (1914); Amst. Versl. 24, pg 18 (1915).: A critical review of Zeeman's experiments is in: Lerche, American Journal of Physics Vol. 45, pg 1154 (1977).
  • Macek et al., “Measurement of Fresnel Drag with the Ring Laser”, J. Appl. Phys. 35 (1964), pg 2556.: A more accurate, modern repetition. Includes a moving solid, liquid, and gas.
  • Bilger et al., Phys. Rev. A5 (1972) pg 591.: -
  • James and Sternberg, Nature 197 (1963), pg 1192.: Measurements with a glass plate moving perpendicular to the light path. The experiment measures no significant effect, but is not sensitive enough to detect the small effect predicted by SR.

The Sagnac Experiment

Sagnac constructed a ring interferometer and measured its fringe shifts as it is rotated. Contrary to some uninformed claims, this experiment can be fully analyzed using SR, and the results are consistent with SR.

  • Sagnac, C.R.A.S 157 (1913), p708, p1410; J. Phys. Radium, 5th Ser. 4 (1914), pg 177.: The classic papers by Sagnac.
  • Post, “Sagnac Effect”, Rev. Mod. Phys., 39 no. 2, pg 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), pg 975.: A more recent review, and description of a much more accurate ring interferometer.
  • Hasselbach and Nicklaus, Phys. Rev. A 48 no. 1 (1993), pg 143.: The Sagnac effect using electrons.
  • Allan et al., Science, 228 (1985), pg 69.: They observed the Sagnac effect using GPS satellite signals observed simultaneously at multiple locations around the world. See GPS.
  • Anandan, “Sagnac Effect in Relativistic and Nonrelativistic Physics”, Phys. Rev. D24 no. 2 (1981), pg 338.Gron, “Relativistic description of a Rotating Disk”, AJP 43 no. 10 (1975), pg 869.Rizzi and Tartaglia, “Speed of Light on Rotating Platforms”, preprint arxiv:gr-qc/9805089.Mainwaring and Stedman, “Accelerated Clock Principles in Special Relativity”, Phys. Rev. A47 no. 5 (1993), pg 3611.Berenda, “The Problem of the Rotating Disk”, Phys. Rev. 62 (1942), pg 280.: 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), pg 341.: A discussion using GR.
  • The Canterbury Ring Laser, publications: A detailed and varied series of modern measurements using a highly sensitive ring laser. A review paper is: Stedman, Rep. Prog. Phys. 60: pg 615–688 (1997),

The Michelson and Gale Experiment

  • Michelson and Gale, Nature 115 (1925), pg 566; Astrophys. J. 61 (1925), pg 137.: 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 mile by 0.4 mile (about 320 m by 640 m). They did indeed detect the rotation of the Earth.
  • Dunn et al., “Design and Operation of a 367 m2 rectangular ring laser”, Appl. Optics, 41, pg 1685 (2002).: A modern large ring laser.

g−2 Experiments as a Test of Special Relativity

The value g is the gyromagnetic ratio of a particle, and is exactly 2 for a classical particle with charge and spin. So g−2 measures the anomalous magnetic moment of the particle, and can be used (via QED) as a test of SR.

  • Newman et al., Phys. Rev. Lett. 40 no. 21 (1978), pg 1355.: A discussion of the basic technique of using measurements of the anomalous magnetic moment of electrons and muons as a test of SR, and an analysis of some low-energy electron data.
  • F. Combley et al., Physical Review Letters 42 (1979), pg 1383.: Electron and muon measurements.
  • P.S. Cooper et al., Physical Review Letters 42 (1979), pg 1386.: Electron measurements up to 12 GeV.
  • Farley et al., Nuovo Cimento Vol 45, pg 281 (1966).Farley et al., Nature 217, pg 17 (1968).Bailey et al., Nuovo Cimento 9A, pg 369 (1972).Bailey et al., Phys. Lett. 68B no. 2 (1977), pg 191.: Measurements of the anomalous magnetic moment of muons.
  • Bennett et al., “Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm”, Phys. Rev. Lett., 92; 1618102 (2004).: The Brookhaven experiment to measure g−2 for muons,

The Global Positioning System (GPS)

While not really an experiment, and not really any sort of test of SR, the GPS is an interesting and useful system in which relativity plays an important part. In particular it has become the best and most economical method of highly accurate time transfer around the globe.

  • US naval Observatory (USNO) GPS Operations. Includes an overview of the GPS and current details of its operation.
  • A tutorial and general overview of the GPS.
  • A large collection of links to GPS resources, tutorials, and references. More up to date than most other references in this section.
  • Allan et al., IEEE Trans. Inst. and Meas., IM-32 no. 2 (1985), pg 118.: 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), pg 1858.: 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), pg 971.: -
  • Saburi et al., “High-Precision Time Comparison via Satellite and Observed Discrepancy of Synchronization”, IEEE Trans. Inst. Meas. IM-25 no. 4 (1976), pg 473.: The “discrepancy” they mention is merely the Sagnac effect, and observations agree with predictions.

Lunar Laser Ranging

  • Bender et al., Science 182 (1973), pg 229.: 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), pg L101.: -
  • Williams et al., Phys. Rev. Lett. 36 no. 11 (1976), pg 551.Williams et al., Phys. Rev. D53 no. 12 (1996), pg 6730.: -
  • Dickey et al., Science 265 (1994), pg 482.: -

Cosmic Microwave Background Radiation (CMBR)

The CMBR is a diffuse and almost isotropic microwave radiation that apparently suffuses all of space. It is generally thought to be a relic of the big bang. While not really a test of SR, CMBR measurements may be of interest to some readers—there is a unique locally inertial frame near Earth in which its dipole moment is zero; this frame moves with speed ~370 km/s relative to the sun.

  • Smoot et al., Phys. Rev. Lett. 39 no. 14 (1977), pg 898.: 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/s with respect to the Earth.
  • Mather et al., Ap. J. 420 (1994), pg 439.: Measurement of the CMBR by the COBE satellite's FIRAS instrument.
  • Bennett et al., Physics Today (Nov. 1997), pg 32.: 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 with respect to the Earth).
  • Songalla et al., Nature 371 (1994), pg 43.: They present a measurement of the CMBR for a distant object with z = 1.776 (z is the redshift, often used as a measure of distance from Earth).
  • Ge et al., Ap. J. 474 (1997), pg 67.: They present a measurement of the CMBR for a distant object with z = 1.9731.
  • ”The Wilkinson Microwave Anisotropy Probe”, WMAP is a more recent set of satellite measurements of the CMBR. It has considerably better resolution than previous measurements.

The Constancy of Physical Constants

  • Tubbs and Wolfe, “Evidence for large-Scale Uniformity of Physical Laws”, Ap. J. 236 (1980), pg L105.: 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), pg 89.: Quasar spectra with redshifts z ~0.2–3.7 are used to put a limit on the rate of change of alpha of about 4Ч10−14 per year.
  • Fischer et al., “New Limits on the Drift of Fundamental Constants from Laboratory Measurements”, Phys. Rev. Lett., 92, no. 23, 230802 (2004).: New limits from measurements in atomic hydrogen.

The Neutrality of Molecules

  • Dylla and King, Phys. Rev. A7 (1973) pg 1224.: The charge on sulfur hexafluoride is less than 2Ч10−19 times the charge on an electron.

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