Sagnac Effect with Gravity Correction

Abstract

Sagnac was an advocate of aether theory. He did experiment to prove the existence of aether. His experiments used two light rays moving in opposite directions along a circular ring that is rotating with angular velocity omega. Theoretically, such rays will take different times to arrive at the end point, and this theoretical fact was demonstrated by Sagnac himself and by many other experimenters. The usual Sagnac effect is only effected by omega; the gravitational field's effect is absent. In this work, we correct the Sagnac time delay by considering the influence of gravity on time. Our formula reduces to the usual one when the Schwarzschild radius is very small.