Isotropy of the velocity of light and the Sagnac effect

TL;DR

This paper demonstrates that the velocity of light remains isotropic in a rotating frame within Minkowski space-time and shows this is consistent with the Sagnac effect, using a geometric approach involving geodesic triangles.

Contribution

It introduces a geometric method to analyze light velocity isotropy in rotating frames and connects it with the Sagnac effect through Minkowskian geometry.

Findings

Light velocity is isotropic in rotating frames.

The Sagnac effect is compatible with isotropic light speed.

Geodesic triangles in Minkowskian cylinders model the problem.

Abstract

In this paper, it is shown, using a geometrical approach, the isotropy of the velocity of light measured in a rotating frame in Minkowski space-time, and it is verified that this result is compatible with the Sagnac effect. Furthermore, we find that this problem can be reduced to the solution of geodesic triangles in a Minkowskian cylinder. A relationship between the problems established on the cylinder and on the Minkowskian plane is obtained through a local isometry.