Improved constraints on isotropic shift and anisotropies of the speed of light using rotating cryogenic sapphire oscillators

Abstract

We demonstrate that Michelson-Morley tests, which detect direction-dependent anisotropies in the speed of light, can also be used to place limits upon isotropic deviations of the vacuum speed of light from c, as described by the photon-sector standard model extension parameter tr . A shift in the speed of light that is isotropic in one inertial frame implies anisotropic shifts in others. Using observer Lorentz covariance, we derive the time-dependent variations in the relative resonance frequencies of a pair of electromagnetic resonators that would be generated by such a shift in the rest frame of the Sun. A new analysis of a recent experimental test of relativity using this result constrains tr with a precision of 7:4 Â 10 À9 . This represents the first constraint on tr by a Michelson-Morley experiment and the first analysis of a single experiment to simultaneously set limits on all nine nonbirefringent terms in the photon sector of the minimal standard model extension.

Testing Lorentz invariance using an odd-parity asymmetric optical resonator

“…The value forκ tr determined from this experiment isκ tr = 3.4 ± 6.2 × 10 −9 (1σ error), the tightest published constraint onκ tr to our knowledge. This constraint is more than a factor of 12 better than previous test of LI at optical frequencies [13] and moderately better than the previous best [9]. This exper- iment is the first odd-parity optical resonator experiment and the use of counter propagating modes enables a new constraint onκ tr using a non-rotating resonator without temperature control, vibration isolation or vacuum systems.…”

“…For the scalar parameterκ tr the result is 3.4 ± 6.2 × 10 −9 , a new limit on the constraint. The uncompetitive constraint placed on the odd parameterκ XZ o+ compared to the scalar parameterκ tr is because the current best constraints are derived from experiments with different sensitivities ( [7,8] and [9] respectively) and in this first realization of an asymmetric optical resonator we use a non-rotating experiment, giving reduced sensitivity to the odd parameters [10].…”

“…We further believe that this type of experiment has room for much improvement into the future whereas existing evenparity experiments are near the limit of development and are unlikely to improve by 4 orders of magnitude, limiting the potential for progress in the search for odd-parity and isotropic violations of Lorentz invariance. An analysis of an even-parity rotating microwave resonator experiment designed to test LI [12] has determined κ tr as 15 ± 7.4 × 10 −9 [9]. An alternative means to determineκ tr was obtained using relativistic ion spectroscopy [13] with sensitivity of ±8.4 × 10 −8 .…”

Observational Constraints on Local Lorentz Invariance

“…•Photon Tests [112,113,114,115,116,117,118,119,120,121,122,123,124]: The relevant leading-order terms for the photon sector in the SME are the k AF and k F terms in Eq. (23).…”

One-loop nonbirefringent effects on the electromagnetic vertex in the Standard Model Extension

“…[10], the same authors classified the components of the rank-4 tensor (K F ) µναβ into birefringent and nonbirefrintent. Since those works, this CP T -even, but Lorentz-violating, parametrization has been the subject of diverse works in both the theoretical [20,[22][23][24][25][26][27][28][29][30][31][32] and experimental [33][34][35][36] sides. There is a clear difference concerning the experimental sensitivity reached for each set of parameters, for the constraints established for the birefringent coefficients are more stringent than the current bounds restricting the nonbirefringent components by several orders of magnitude.…”