Rotating disk: new physics discovered alongside the Sagnac effect

Abstract

Abstract The description of the rotating disk in special relativity is revisited to find a new property that could help to improve the performance of gyrometers. On a rotating disk, two particles which bounce in opposite directions at the vertices of a regular polygon are considered. On the return to the entry point, a clock measures the time difference. A particle moving in the direction of the rotation of the disc needs more time to make one complete turn. Even if that particle is a photon, as in the original Sagnac experiment. In this paper, the time difference is explained by the difference between clockwise and counter-clockwise trajectories, due to different Coriolis effects. The particular case of the slow disk where the two trajectories are very close and almost polygonal is studied. The theoretical existence of a transition between a classical and a relativistic regime is proved, and an experimental verification with an atomic interferometer is proposed. Although the novel effect discovered and the well-known Sagnac effect seem analogous, in detail, their behavior is quite different.