Searches for Lorentz violation involving photons provide one possible test of relativity. Examples range from modern versions of the classic Michelson–Morley experiment that utilize highly stable electromagnetic resonant cavities to searches for tiny deviations from c in the speed of light emitted by distant astrophysical sources. Due to the extreme distances involved, astrophysical studies have achieved sensitivities on the order of parts in 1038.
Minimal Lorentz-violating electrodynamics The most general framework for studies of relativity violations is an effective field theory called the Standard-Model Extension (SME). Lorentz-violating operators in the SME are classified by their mass dimension d {\displaystyle d} . To date, the most widely studied limit of the SME is the minimal SME, which limits attention to operators of renormalizable mass-dimension, d = 3 , 4 {\displaystyle d=3,4} , in flat spacetime. Within the minimal SME, photons are governed by the Lagrangian density
L = − 1 4 F μ ν F μ ν + 1 2 ( k A F ) κ ϵ κ λ μ ν A λ F μ ν − 1 4 ( k F ) κ λ μ ν F κ λ F μ ν . {\displaystyle {\mathcal {L}}=-\textstyle {{1} \over {4}}\,F_{\mu \nu }F^{\mu \nu }+\textstyle {{1} \over {2}}\,(k_{\mathrm {AF} })^{\kappa }\,\epsilon _{\kappa \lambda \mu \nu }A^{\lambda }F^{\mu \nu }-\textstyle {{1} \over {4}}\,(k_{\mathrm {F} })_{\kappa \lambda \mu \nu }F^{\kappa \lambda }F^{\mu \nu }.}
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