Limits on Lorentz Violation from Synchrotron and Inverse Compton Sources

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 $6\times {10}^{-20}$ level, and independent bounds are available for all the Lorentz-violating $c$ coefficients at the $2\times {10}^{-14}$ level or better. This represents an improvement in some bounds by 14 orders of magnitude.