Test of Lorentz Invariance in Electrodynamics Using Rotating Cryogenic Sapphire Microwave Oscillators

We present the first results from a rotating Michelson-Morley experiment that uses two orthogonally orientated cryogenic sapphire resonator-oscillators operating in whispering gallery modes near 10 GHz. The experiment is used to test for violations of Lorentz Invariance in the frame-work of the photon sector of the Standard Model Extension (SME), as well as the isotropy term of the Robertson-Mansouri-Sexl (RMS) framework. In the SME we set a new bound on the previously unmeasured $\tilde{\kappa}_{e-}^{ZZ}$ component of $2.1(5.7)\times10^{-14}$, and set more stringent bounds by up to a factor of 7 on seven other components. In the RMS a more stringent bound of $-0.9(2.0)\times 10^{-10}$ on the isotropy parameter, $P_{MM}=\delta - \beta + {1/2}$ is set, which is more than a factor of 7 improvement. More detailed description of the experiment and calculations can be found in: hep-ph/0506200