Extended Fizeau experiment and the ether

Abstract

In view of the current interest in constructing ether-like models, a simple analysis is given of how the description of the classic Fizeau experiment becomes modified if the moving dielectric is surrounded by a nonviscous fluid, the ether, having dielectric constant $N$. For analytic tractability we introduce an explicit model in which the change in fluid velocity is slow for an optical wave traveling from the resting ether into the moving medium. We show how the Einstein addition formula for velocities is not modified at all. What is changed, however, is the expression for the wave frequency in the rest inertial frame of the medium. This change is in principle measurable. Worth noticing is the close resemblance between this kind of theory and the covariant electrodynamics for a medium in uniform rectilinear motion. This point is elaborated upon by comparing with the Lorentz-violating electrodynamics studied by Kosteleck\'y and collaborators in several recent papers.