Theoretical Analysis of Generalized Sagnac Effect in the Standard Synchronization

TL;DR

This paper provides a theoretical analysis of the generalized Sagnac effect within the standard synchronization framework, showing how light speed measurements vary with synchronization and motion, aligning with experimental results.

Contribution

It introduces a comprehensive framework using Mansouri and Sexl's approach to analyze the Sagnac effect under standard synchronization, accounting for arbitrary fiber shapes and relative motion.

Findings

One-way light speed differs from c under standard synchronization.

Two-way light speed remains c with respect to proper time.

The analysis aligns with experimental observations of the Sagnac effect.

Abstract

The Sagnac effect has been shown in inertial frames as well as rotating frames. We solve the problem of the generalized Sagnac effect in the standard synchronization of clocks. The speed of a light beam that traverses an optical fiber loop is measured with respect to the proper time of the light detector, and is shown to be other than the constant c, though it appears to be c if measured by the time standard-synchronized. The fiber loop, which can have an arbitrary shape, is described by an infinite number of straight lines such that it can be handled by the general framework of Mansouri and Sexl (MS). For a complete analysis of the Sagnac effect, the motion of the laboratory should be taken into account. The MS framework is introduced to deal with its motion relative to a preferred reference frame. Though the one-way speed of light is other than c, its two-way speed is shown to be c with respect to the proper time. The theoretical analysis of the generalized Sagnac effect corresponds to the experimental results, and shows the usefulness of the standard synchronization. The introduction of the standard synchrony can make mathematical manipulation easy and can allow us to deal with relative motions between inertial frames without information on their velocities relative to the preferred frame.