Quadratic Sagnac effect recorded by an observer in the laboratory frame

The quadratic Sagnac effect, recorded by an observer in the laboratory frame of reference (inertial frame), relative to which the Michelson interferometer moves, has been considered. The quadratic Sagnac effect was previously calculated in a rotating frame of reference, where it occurs as a consequence of the influence of the gravitational potential of the Coriolis force in the rotating frame of reference and leads to a phase difference in the rotating Michelson interferometer. It has been shown that the quadratic Sagnac effect values calculated in the inertial frame and rotating frame of reference are practically the same. It has also been shown that, in various cases, the calculation of the quadratic Sagnac effect is most rational to carry out either in the inertial frame or in the rotating frame of reference. The numerical estimates performed have shown that the experiments on recording the quadratic Sagnac effect are quite possible. The concept of effective lengths of the arms of a Michelson interferometer moving relative to a stationary observer: the light paths lengths during its propagation in the forward and backward directions, has been introduced. These effective arm lengths coincide with neither Michelson interferometer proper arm length $L$ nor its relativistic length $L/\gamma$. The introduction of this concept is due to the fact that the moving Michelson interferometer mirrors move during the light propagation. In some calculations, it is advisable to take into account the Michelson interferometer effective arm lengths.