GEORGES SAGNAC'S EXPERIMENT (REPRODUCTION AND INTERPRETATION)
Georges Sagnac. L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme. // Comptes Rendus, 157: 708-710
Georges Sagnac. Sur la preuve de la réalité de l’éther lumineux par l’expérience de l’interférographe tournant. // Comptes Rendus, 157: 1410-1413. 22 décembre 1913.
It is shown that the Sagnac experiment consistently explained on the basis of the special theory of relativity.
Different explanations for the Sagnac effect are discussed. It is shown that this effect is a consequence of the relativistic law of velocity composition and that it can also be explained adequately within the framework of general relativity. When certain restrictions on the rotational velocity are imposed, the Sagnac effect can be attributed to the difference in the time dilation (or phase change) of material particle wave functions in the scalar (or correspondingly vector) gravitational potential of the inertial forces in a rotating reference system for counterpropagating waves. It is also shown that all the nonrelativistic interpretations of the Sagnac effect, which are unfortunately sometimes found in scientific papers, monographs and textbooks, are wrong in principle, even though the results they yield are accurate up to relativistic corrections in some special cases.
Various explanations of the causes of the Sagnac effect are given. It is shown that the Sagnac effect is a consequence of the relativistic law of addition of velocities. This effect also finds an adequate explanation in the context of general relativity. When some limits are put on rotation speed, the Sagnac effect can be seen as a consequence of differences in time deceleration, or of difference of phase change in material particles’ wave functions, in scalar or vector potential of the gravitational forces of inertia in the rotating reference frame for the incoming waves.
It is also shown that all non-relativistic explanations of the Sagnac effect, which, unfortunately, are found in a number of scientific articles, monographs and lessons, are fundamentally incorrect, although in some particular cases they lead to correct result, with a precision up to the relativistic correction. Most of these ways, despite their obvious incorrectness, lead in some cases to correct results, that to a certain extent, led to a lack of clarity in this matter.
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). (G.B. Malykin, V.I. Pozdnyakova) (2015)
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.
Supplement to the paper "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)". (G.B. Malykin, V.I. Pozdnyakova) (2015)
The paper "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)" (Usp. Fiz. Nauk 185 431 (2015) [Phys. Usp. 58 398 (2015)]) is amended and supplemented by adding information concerning earlier work on the influence of rotation on Michelson-Morley's nonzero results.
On the phase shift in a uniformly rotating Michelson interferometer (comment on "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)" by G B Malykin and V I Pozdnyakova [Phys. Usp. 58 398 (2015); Usp. Fiz. Nauk 185 431 (2015)]). P. Maraner (2016)
It is argued that the "quadratic Sagnac effect" recently put forward by G.B. Malykin and V.I. Pozdnyakova is the consequence of an incorrect estimation of second order relativistic corrections and not a real physical phenomenon. The correct expression for the phase shift induced by rotations in a Michelson interferometer is presented.
On inconsistencies in the work of P Maraner (reply to comment [Usp. Fiz. Nauk 186 793 2016] to the paper "Quadratic Sagnac effect ‑ the influence of gravitational potential of 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)". (Usp. Fiz. Nauk 185 431 (2015) [Phys. Usp. 58 398 (2015)]) (G.B. Malykin, V.I. Pozdnyakova) (2016)
We consider the distributions of the scalar gravitational potential of Coriolis forces in different parts of the shoulder rotating equal-arms Michelson interferometer. It results in view of the very small difference between the phase of light in the shoulders of the Michelson interferometer, in comparison with the phase difference due to the quadratic Sagnac effect. It has been shown that it is there is an effect discussed earlier by P. Maraner, which is higher approximation quadratic Sagnac effect.
The Michelson–Gale–Pearson experiment (1925) is a modified version of the Michelson–Morley experiment and the Sagnac-Interferometer. It measured the Sagnac effect due to Earth's rotation, and thus tests the theories of special relativity and luminiferous ether along the rotating frame of Earth.
According to Michelson/Gale, the results of experiment are compatible with both the idea of a stationary ether and special relativity. As it was already pointed out by Michelson in 1904, a positive result in such experiments contradicts the hypothesis of complete aether drag. On the other hand, the stationary aether concept is in agreement with this result, yet it contradicts (with the exception of Lorentz's ether) the Michelson-Morley experiment. Thus special relativity is the only theory which explains both experiments. The experiment is consistent with relativity for the same reason as all other Sagnac type experiments. Today, Sagnac type effects due to Earth's rotation are routinely incorporated into GPS.
The Effect of the Earth’s Rotation on the Velocity of Light. (A.A. Michelson, H.E. Gale) (1925) (pdf)
In the Philosophical Magazine (6) 1904, an experiment was described, designed to test the effect of the earth’s rotation on the velocity of light.
The observed displacement of the fringes was found to be 0.230±.005, agreeing with the computed value 0.236±.002 within the limits of experimental error. (It coincided with expected fringe shift in accordance with hypothesis of stationary aether and special relativity.)
The result of the experiment conducted in 1925 was that the measured fringe shift was found to be 0.230 +/- 0.005, which was found to agree with the prediction of no ether drag by rotation within the experimental error. What this means is that the speed of light is constant in the non-rotating frame, a result that is consistent with Lorentz Ether Theory. Theories that propose that the Earth Centered Inertial Frame (ECI Frame) is a preferred frame for the speed of light also are consistent with this result, since the speed of light in this experiment is constant in the ECI frame of the earth.
In this way the Michelson-Gale experiment, and Sagnac interferometers in general, give a contradictory result to all other interferometer experiments that take the laboratory frame as an inertial frame and have assumed that light speed is isotropic in that frame.
It is interesting to note that the speed of light in a Sagnac interferometer is only constant with respect to the laboratory frame (on the earth) if its z-axis is pointing E-W and thereby the sensitive axis is perpendicular to all motion. In all other orientations, the device is sensitive to the diurnal rotation of the earth to some degree, and it is even sensitive to the rotation of the earth around the sun, an effect 365 times smaller.
It is sometimes said that the Sagnac interferometer detects rotation with respect to the fixed stars - this is difficult to distinguish from the idea that the Sagnac interferometer detects rotation with respect to the non-rotating gravitational frame of the earth (Earth Centered Inertial, ECI frame) that is considered to be non-rotating with respect to the fixed stars. It has been demonstrated experimentally that Ring Laser gyroscopes, the cousin of the fiber optic gyroscope, detects the sidereal day rotation rather than the 24 hour day rotation. This latter observation is important but is incapable of distinguishing whether the ECI frame or sidereal space is static frame that the Sagnac rotation is measured against.