The physics of the Sagnac-Mashhoon effects

Abstract

We carry out a complete examination of the effects of rotation on the physics of spin-\textonehalf{} particles. The origin of these effects is connected to the fact that the frame of the rotating experiment is Fermi-Walker transported, and is related to the inertia rest frame (with respect to which the apparatus rotates with angular velocity $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}$) by an instantaneous Lorentz boost plus a time-dependent spatial rotation, in that order. Two distinct sets of effects are obtained. The first depends on the spin-rotation interaction, and consists of the Mashhoon effect and a mass split effect due to the Lorentz boost mentioned above. In a neutron interferometer the latter effect produces a phase shift smaller than the Mashhoon phase shift by a factor of order $O(\frac{{v}^{2}}{{c}^{2}})$, where $v$ is the velocity of the particles in the beams of the interferometer. The detection of the Mashhoon effect is crucial to decide if free spin-\textonehalf{} particles actually behave as gyroscopes. The second set appears already in the eikonal approximation and is due to the active boost of the particles by the rotating apparatus; it results in the Sagnac effect. We also discuss a criterion to fix the frame of the experiment among all mathematically admissible frames in the Brill-Wheeler formulation, and show that frames used in the literature to derive the Sagnac-Mashhoon effect cannot be physically realized.