A Note on the Sagnac Effect for Matter Beams

TL;DR

This paper investigates the Sagnac effect for matter beams, showing that the time delay formula is consistent with that for light beams in stationary space-times, and discusses related kinematic corrections and analogies with the Aharonov-Bohm effect.

Contribution

It demonstrates the equivalence of Sagnac time delay formulas for matter and light beams in stationary space-times, extending previous results and analyzing kinematic corrections and analogies.

Findings

The Sagnac time delay formula applies to matter beams under certain conditions.

Kinematic corrections depend on the interferometer's position and size.

An analogy between the Sagnac effect and the Aharonov-Bohm effect is discussed.

Abstract

We study the Sagnac effect for matter beams, in order to estimate the kinematic corrections to the basic formula, deriving from the position and the extent of the interferometer, and discuss the analogy with the Aharonov-Bohm effect. We show that the formula for the Sagnac time delay is the same for matter and light beams in arbitrary stationary space-times, provided that a suitable condition on the speed of the beams is fulfilled. Hence, the same results obtained for light beams apply to matter beams.