I shall describe joint work with Oded Kenneth. It concerns a relativistically exact eikonal equation for the propagation of light in moving fibers. We are interested in the phase shift in fibers that may move relativistically while deforming adiabatically. In this case we find an explicit integral expansion for the phase shifts putting under one umbrella two classical formulas for the Sagnac and Fizeau effects. I shall also review the history and applications of the Sagnac and Fizeau interferometers.

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