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.
The most general framework for studies of relativity violations is an effective field theory called the Standard-Model Extension (SME).
Within the minimal SME, photons are governed by the Lagrangian density The first term on the right-hand side is the conventional Maxwell Lagrangian and gives rise to the usual source-free Maxwell equations.
The next term violates both Lorentz and CPT invariance and is constructed from a dimension
[5][6] The second term introduces Lorentz violation, but preserves CPT invariance.
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 frame-dependent 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.
[9] It was shown that the more general theory could be written in a form similar to the minimal case, where the constant coefficients are promoted to operators
case, the effects generally grow faster with frequency, due to the additional derivatives.
Vacuum dispersion of light without birefringence is another feature that is found, which does not arise in the minimal SME.
[9] Birefringence of light occurs when the solutions to the modified Lorentz-violating Maxwell equations give rise to polarization-dependent speeds.
, the highest sensitivities are achieved by considering high-energy photons from distant sources, giving large values to the ratio
As a result, maximum sensitivity is achieved by studying the most distant source available, the cosmic microwave background (CMB).
[9] To search for this effect, researchers compare the arrival times of photons from distant sources of pulsed radiation, such as GRB or pulsars.
Sensitivity to Lorentz violation is then increased by considering very distant sources with rapidly changing time profiles.
Consequently, the energy dependence in the light speed from nonbirefringent Lorentz violation can be quadratic
The primary examples are the modern Michelson-Morley experiments based on electromagnetic resonant cavities, which have achieved sensitivities on the order of parts in 1018 to Lorentz violation.
The Lorentz-violating modifications to the Maxwell equations lead to tiny shifts in the resonant frequencies.
Experimenters search for these tiny shifts by comparing two or more cavities at different orientations.
A typical experiment compares the frequencies of two identical cavities oriented at right angles in the laboratory.
The orientation dependence from Lorentz violation would cause the frequency difference to change as the cavities rotate.
Ring resonators provide a complementary class of cavity experiment that can test parity-odd violations.
A number of other searches for Lorentz violation in photons have been performed that do not fall under the above categories.
These include accelerator based experiments,[47][48][36][49] atomic clocks,[50] and threshold analyses.