Ultra-stable cryogenic optical resonators for tests of fundamental physics

We present the design and first measurement results for an ultra-stable cryogenically cooled optical sapphire resonator system with a potential relative frequency stability better than 3x10^-17. This level of oscillator stability allows for more precise tests of Einstein's theories of relativity and thus could help to find first hints of "new physics". We will give some details on a projected experiment to test Lorentz invariance that will utilize these cavities.