Tests of Lorentz Invariance Using a Microwave Resonator: An Update

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 $δ- β+ 1/2 \leq 3.4 \times 10^{-9}$ and $β- α- 1 \leq 4.1 \times 10^{-7}$ which is of the same order as the best previous result for the former and represents a 50 fold improvement for the latter. These results correspond to an improvement of our previously published limits [Wolf P. et al., Phys. Rev. Lett. {\bf 90}, 6, 060402, (2003)] by about a factor 2. We describe the changes of the experiment, and show the new data that lead to that improvement.