A direct kinematical derivation of the relativistic Sagnac effect for light or matter beams

TL;DR

This paper presents a purely kinematical derivation of the relativistic Sagnac effect for light and matter beams in rotating systems, explaining its universality regardless of the beams' physical nature.

Contribution

It introduces a direct relativistic kinematic method to derive the Sagnac effect, emphasizing its independence from the beams' physical properties.

Findings

The Sagnac time delay is universal for light and matter beams.

The effect depends only on the beams' velocities relative to local inertial frames.

The derivation clarifies the fundamental kinematic origin of the Sagnac effect.

Abstract

The Sagnac time delay and the corresponding Sagnac phase shift, for relativistic matter and electromagnetic beams counter-propagating in a rotating interferometer, are deduced on the ground of relativistic kinematics. This purely kinematical approach allows to explain the ''universality'' of the effect, namely the fact that the Sagnac time difference does not depend on the physical nature of the interfering beams. The only prime requirement is that the counter-propagating beams have the same velocity with respect to any Einstein synchronized local co-moving inertial frame.