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)

Abstract

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 its arms are oriented differently with respect to the plane of rotation, a phase difference arises between the light rays that pass through different arms. This phase difference is due to the fact that the arms experience variously the Newtonian (nonrelativistic) scalar gravitational potential of the Coriolis forces. It is shown that the phase difference is proportional to the length of the interferometer arm, 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 the 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 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 revolution of Earth, the time dilations in the orthogonal arms of the Michelson interferometer are influenced differently by the scalar gravitational potential of the Coriolis forces.