Improved Constraints on Isotropic Shift and Anisotropies of the Speed of Light Using Rotating Cryogenic Sapphire Oscillators

Abstract

We demonstrate that Michelson-Morley tests, which detect direction-dependent anisotropies in the speed of light, can also be used to place limits upon isotropic deviations of the vacuum speed of light from \(c\), as described by the photon-sector standard model extension parameter \(\tilde\kappa_{tr}\). A shift in the speed of light that is isotropic in one inertial frame implies anisotropic shifts in others. Using observer Lorentz covariance, we derive the time-dependent variations in the relative resonance frequencies of a pair of electromagnetic resonators that would be generated by such a shift in the rest frame of the Sun. A new analysis of a recent experimental test of relativity using this result constrains \(\tilde\kappa_{tr}\) with a precision of \(7.4 \times 10^{-9}\). This represents the first constraint on \(\tilde\kappa_{tr}\) by a Michelson-Morley experiment and the first analysis of a single experiment to simultaneously set limits on all nine nonbirefringent terms in the photon sector of the minimal standard model extension.