Abstract

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 \(L{\text{/}}\gamma \). 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.

中文翻译：

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观察者在实验室框架中记录的二次Sagnac效应

摘要

已经考虑了由观察者在实验室参考系（惯性系）中记录的二次Sagnac效应，迈克尔逊干涉仪相对于该参考系移动。二次Sagnac效应是事先在旋转参考系中计算得到的，在此，它是由于旋转参考系中科里奥利力的引力的影响而产生的，并导致旋转迈克尔逊干涉仪的相位差。已经表明，在惯性系和旋转参考系中计算出的二次Sagnac效应值实际上是相同的。还已经表明，在各种情况下，二次Sagnac效应的计算是最合理的，无论是在惯性系还是在旋转参考系中进行。进行的数值估计表明，记录二次Sagnac效应的实验是完全可能的。引入了迈克尔逊干涉仪的臂的相对于静止的观察者移动的有效长度的概念：在其向前和向后传播期间的光路长度。这些有效臂长与迈克尔逊干涉仪的正确臂长都不重合\（L \）或相对论长度\（L {\ text {/}} \ gamma \）。该概念的引入是由于在光传播过程中移动的迈克尔逊干涉仪镜在移动。在某些计算中，建议考虑迈克尔逊干涉仪的有效臂长。