Tests of Lorentz Invariance using a Microwave Resonator

The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are compared to set new constraints on a possible violation of Lorentz invariance. We determine the variation of the oscillator frequency as a function of its orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike test) with respect to a preferred frame candidate. We constrain the corresponding parameters of the Mansouri and Sexl test theory to $\delta -\beta +1/2=(1.5\pm 4.2)\times {10}^{-9}$ and $\beta -\alpha -1=(-3.1\pm 6.9)\times {10}^{-7}$ which is of the same order as the best previous result for the former and represents a 30-fold improvement for the latter.