
Searches for Lorentz violation involving photons are among the best tests of relativity. Examples range from modern versions of the classic MichelsonMorley 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 10^{38}. == Minimal Lorentzviolating electrodynamics == The most general framework for studies of relativity violations is an effective field theory called the StandardModel Extension (SME).〔 D. Colladay and V.A. Kostelecky, CPT Violation and the Standard Model, Phys. Rev. D 55, 6760 (1997). 〕〔 D. Colladay and V.A. Kostelecky, LorentzViolating Extension of the Standard Model, Phys. Rev. D 58, 116002 (1998). 〕〔 V.A. Kostelecky, Lorentz Violation, and the Standard Model, Phys. Rev. D 69, 105009 (2004). 〕 Lorentzviolating operators in the SME are classified by their mass dimension $d$. To date, the most widely studied limit of the SME is the minimal SME,〔 V.A. Kostelecky and M. Mewes, Signals for Lorentz violation in electrodynamics, Phys. Rev. D 66, 056005 (2002).〕 which limits attention to operators of renormalizable massdimension, $d=3,4$, in flat spacetime. Within the minimal SME, photons are governed by the lagrangian density $$ \mathcal = \textstyle\,F_F^ +\textstyle\,(k_)^\kappa\,\epsilon_A^\lambda F^ \textstyle\,(k_F)_F^F^. The first term on the righthand side is the conventional Maxwell lagrangian and gives rise to the usual sourcefree Maxwell equations. The next term violates both Lorentz and CPT invariance and is constructed from a dimension $d=3$ operator and a constant coefficient for Lorentz violation $(k\_)^\backslash kappa$.〔 S. Carroll, G. Field, and R. Jackiw, Limits on a Lorentz and Parity Violating Modification of Electrodynamics, Phys.Rev. D 41, 1231 (1990). 〕〔 R. Jackiw and V.A Kostelecky, Radiatively Induced Lorentz and CPT Violation in Electrodynamics, Phys. Rev. Lett. 82, 3572 (1999). 〕 The second term introduces Lorentz violation, but preserves CPT invariance. It consists of a dimension $d=4$ operator contracted with constant coefficients for Lorentz violation $(k\_F)\_$.〔 V.A. Kostelecky and M. Mewes, Cosmological constraints on Lorentz violation in electrodynamics, Phys.Rev.Lett. 87, 251304 (2001).〕 There are a total of four independent $(k\_)^\backslash kappa$ coefficients and nineteen $(k\_F)\_$ coefficients. Both Lorentzviolating terms are invariant under observer Lorentz transformations, implying that the physics in independent of observer or coordinate choice. However, the coefficient tensors $(k\_)^\backslash kappa$ and $(k\_F)\_$ are outside the control of experimenters and can be viewed as constant background fields that fill the entire Universe, introducing directionality to the otherwise isotropic spacetime. Photons interact with these background fields and experience framedependent effects, violating Lorentz invariance. The mathematics describing Lorentz violation in photons is similar to that of conventional electromagnetism in dielectrics. As a result, many of the effects of Lorentz violation are also seen in light passing through transparent materials. These include changes in the speed that can depend on frequency, polarization, and direction of propagation. Consequently, Lorentz violation can introduce dispersion in light propagating in empty space. It can also introduce birefringence, an effect seen in crystals such as calcite. The best constraints on Lorentz violation come from constraints on birefringence in light from astrophysical sources.〔V.A. Kostelecky and M. Mewes, Astrophysical Tests of Lorentz and CPT Violation with Photons, Astrophys. J. Lett. 689, L1 (2008).〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lorentzviolating electrodynamics」の詳細全文を読む スポンサード リンク
