New Limit on Signals of Lorentz Violation in Electrodynamics

We describe the results of an experiment to test for spacetime anisotropy terms that might exist from Lorentz violations. The apparatus consists of a pair of cylindrical superconducting cavity-stabilized oscillators operating in the ${\mathrm{T}\mathrm{M}}_{010}$ mode with one axis east-west and the other vertical. Spatial anisotropy is detected by monitoring the beat frequency at the sidereal rate and its first harmonic. We see no anisotropy to a part in ${10}^{13}$. This puts a comparable bound on four linear combinations of parameters in the general standard model extension, and a weaker bound of $<4\times {10}^{-9}$ on three others.