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Quadratic Sagnac effect — the influence of the gravitational potential of the Coriolis force on the phase difference between the arms of a rotating Michelson interferometer (an explanation of D C Miller's experimental results 1921—1926)

 a,  b
a Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
b Institute of Microstructure Physics, Russian Academy of Sciences, ul. Ulyanova 46, Nizhnii Novgorod, 603600, Russian Federation

It is shown that when an equal-arm Michelson interferometer is involved in rotation (for example, Earth's rotation around its axis or around the Sun) and if its arms are oriented differently with respect to the plane of rotation, a phase difference arises between the rays that pass through different arms. This phase difference is due to the fact that the arms experience different values of the Newton (nonrelativistic) scalar gravitation potential of the Coriolis force. It is shown that phase difference is proportional to the interferometer arm length, the square of the angular velocity of the rotation and the square of the distance from the center of rotation — hence the proposal to call this phenomenon quadratic Sagnac effect. In the present paper we consider, as an illustrative example, the results of the once well-known experiments of D C Miller, who claimed to observe the translational motion of the Earth relative to the hypothetical "luminiferous ether". It is shown that this claim can actually be explained by the fact that, because of the orbital motion of the Earth, the time dilations in the orthogonal arms of the Michelson interferometer are influenced differently by the scalar gravitation potential of the Coriolis force.

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Fulltext is also available at DOI: 10.3367/UFNe.0185.201504g.0431
Keywords: Michelson interferometer, Coriolis force, gravitational potential, Earth orbital motion rotation
PACS: 03.30 +p
DOI: 10.3367/UFNe.0185.201504g.0431
URL: https://ufn.ru/en/articles/2015/4/f/
000357718100006
2-s2.0-84936763119
2015PhyU...58..398M
Citation: Malykin G B, Pozdnyakova V I "Quadratic Sagnac effect — the influence of the gravitational potential of the Coriolis force on the phase difference between the arms of a rotating Michelson interferometer (an explanation of D C Miller's experimental results 1921—1926)" Phys. Usp. 58 398–406 (2015)
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Received: 23rd, December 2014, revised: 2nd, February 2015, 3rd, February 2015

Оригинал: Малыкин Г Б, Позднякова В И «Квадратичный эффект Саньяка: влияние гравитационного потенциала силы Кориолиса на разность фаз в плечах вращающегося интерферометра Майкельсона (объяснение результатов экспериментов Д.К. Миллера 1921—1926 гг.)» УФН 185 431–440 (2015); DOI: 10.3367/UFNr.0185.201504g.0431

References (70) Cited by (8) Similar articles (20) ↓

  1. G.B. Malykin “Sagnac effect in ring lasers and ring resonators. How does the refraction index of the optical medium influence the sensitivity to rotation?” 57 714–720 (2014)
  2. G.B. Malykin “Para-Lorentz transformations” 52 263–266 (2009)
  3. G.B. Malykin, V.I. Pozdnyakova “Geometric phases in singlemode fiber lightguides and fiber ring interferometers” 47 289–308 (2004)
  4. B.M. Bolotovskii, G.B. Malykin “Visible shape of moving bodies” 62 1012–1030 (2019)
  5. G.B. Malykin “Application of the modified Duguay method for measuring the Lorentz contraction of a moving body length” 64 1058–1062 (2021)
  6. G.B. Malykin “The Sagnac effect: correct and incorrect explanations” 43 1229 (2000)
  7. A.A. Logunov, Yu.V. Chugreev “Special theory of relativity and the Sagnac effect” 31 861–864 (1988)
  8. E.G. Bessonov “Another route to the Lorentz transformations” 59 475–479 (2016)
  9. B.M. Bolotovskii, S.N. Stolyarov “Reflection of light from a moving mirror and related problems” 32 813–827 (1989)
  10. Ya.B. Zel’dovich, L.P. Grishchuk “Gravitation, the general theory of relativity, and alternative theories” 29 780–787 (1986)
  11. G.B. Malykin “The relation of Thomas precession to Ishlinskii’s theorem as applied to the rotating image of a relativistically moving body” 42 505–509 (1999)
  12. A.A. Logunov “The theory of the classical gravitational field” 38 179–193 (1995)
  13. I.O. Zolotovskii, R.N. Minvaliev, D.I. Sementsov “Dynamics of frequency-modulated wave packets in optical guides with complex-valued material parameters” 56 1245–1256 (2013)
  14. V.A. Aleshkevich “On special relativity teaching using modern experimental data” 55 1214–1231 (2012)
  15. V.I. Ritus “Generalization of the k coefficient method in relativity to an arbitrary angle between the velocity of an observer (source) and the direction of the light ray from (to) a faraway source (observer) at rest” 63 601–610 (2020)
  16. Yu.I. Hovsepyan “Some notes on the relativistic Doppler effect” 41 941–944 (1998)
  17. R.Z. Muratov “Some useful correspondences in classical magnetostatics, and the multipole representations of the magnetic potential of an ellipsoid” 55 919–928 (2012)
  18. V.I. Vysotskii, V.I. Vorontsov et al “The Sagnac experiment with X-radiation” 37 289–302 (1994)
  19. V.Ya. Gavrik “A liquid filled pendulum for demonstration of the diurnal rotation of the Earth” 6 941–944 (1964)
  20. N.N. Rozanov “Superluminal localized structures of electromagnetic radiation” 48 167–171 (2005)

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