Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy–momentum relations of those electrons. They can thus be used to place bounds on the possibility of Lorentz violation in the electron sector. Recent 𝛾 -ray telescope data allow the Lorentz-violating electron 𝑐𝜈𝜇 parameters to be constrained extremely well, so that all bounds are at the level of 7×10−16 or better.
Brett Altschul (Thu,) studied this question.