Sagnac effect in relativistic and nonrelativistic physics

A simple special-relativistic derivation of the Sagnac effect, which reconciles the earlier general-relativistic and nonrelativistic derivations, is given. A distinction is made between the "classical Sagnac effect" and the "quantum Sagnac effect." A new group-theoretic derivation of these effects is also given. It is pointed out that there must exist a phase shift due to the Thomas precession in the interference of particles with intrinsic spin. The group-theoretic treatment also elucidates the connection between relativistic and nonrelativistic physics, on a classical and quantum level, with and without gravity. A formulation of the principle of equivalence, which is related to the Sagnac effect, is given in relativistic and nonrelativistic physics in terms of the respective invariance groups. New experiments are proposed to test the Sagnac effect in superfluid helium. The possible use of the general-relativistic Sagnac effect to measure the curvature tensor and in particular to detect gravitational waves is suggested.