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.

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) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 23rd, December 2014, revised: 2nd, February 2015, accepted: 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