General relativistic Sagnac formula revised

TL;DR

This paper revises the general relativistic Sagnac formula by incorporating light deflection effects due to rotational inertial forces, providing a more accurate description of the phase shift in rotating interferometers.

Contribution

It introduces a modified Sagnac formula that accounts for light deflection effects, enhancing the understanding of phase shifts in rotating frames within general relativity.

Findings

Standard Sagnac formula misses light deflection effects.

Modified formula aligns better with physical observations.

Revised interpretation of synchronization and Aharonov-Bohm analogy.

Abstract

The Sagnac effect is a time or phase shift observed between two beams of light traveling in opposite directions in a rotating interferometer. We show that the standard description of this effect within the framework of general relativity misses the effect of deflection of light due to rotational inertial forces. We derive the necessary modification and demonstrate it through a detailed analysis of the square Sagnac interferometer rotating about its symmetry axis in Minkowski space-time. The role of the time shift in a Sagnac interferometer in the synchronization procedure of remote clocks as well as its analogy with the Aharanov-Bohm effect are revised.