Detecting Lorentz Invariance Violations in the 10 -20 Range

In recent years the possibility has been raised of Lorentz invariance violations arising from physics beyond the Standard Model. Some of these effects manifest themselves as small anisotropies in the velocity of light, c. By comparing the resonant frequencies of cavity modes with different spatial alignments, limits on the order δ c/c < 10-15 have been set and some further improvement can be expected. However, the largest Lorentz violations originating at the Planck scale are expected to manifest themselves as a fractional frequency variation at the 10-17 level in the absence of suppression factors. Space experiments have been proposed to approach the 10-18 level. Here we explore the possibilities for pushing further and show that it is possible in principle to reach well into the 10-20 range with existing technology. This could be done in a very quiet cryogenic environment, such as the drag-free orbiter being developed for the Satellite Test of the Equivalence Principle (STEP).