Whispering Gallery Resonators and Tests of Lorentz Invariance

TL;DR

This paper uses whispering gallery microwave resonators and frequency comparisons of cryogenic sapphire oscillators and hydrogen masers to set new, more stringent limits on potential violations of Lorentz invariance, improving previous constraints significantly.

Contribution

It provides a detailed model of whispering gallery resonators for testing Lorentz invariance and applies these models to derive improved experimental constraints within established theoretical frameworks.

Findings

Set new constraints on Lorentz violation parameters.

Achieved a 70-fold improvement over previous limits.

Validated the effectiveness of whispering gallery resonators in fundamental physics tests.

Abstract

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 give a detailed description of microwave resonators operating in Whispering Gallery modes and then apply it to derive explicit models for Lorentz violating effects in our experiment. Models are calculated in the theoretical framework of Robertson, Mansouri and Sexl and in the standard model extension (SME) of Kostelecky and co-workers. We constrain the parameters of the Mansouri and Sexl test theory to $1/2 - \beta_{MS} + \delta_{MS} = (1.2 \pm 2.2) \times 10^{-9}$ and $\beta_{MS} - \alpha_{MS} - 1 = (1.6 \pm 3.0) \times 10^{-7}$ which is of the same order as the best results from other experiments for the former and represents a 70 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.