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We derive new bounds on Lorentz violations in the electron sector from existing data on high-energy astrophysical sources. Synchrotron and inverse Compton data give precisely complementary constraints. The best bound on a specific combination of electron Lorentz-violating coefficients is at the 610^-20 level, and independent bounds are available for all the Lorentz-violating c coefficients at the 210^-14 level or better. This represents an improvement in some bounds by 14 orders of magnitude.
Brett Altschul (Fri,) studied this question.