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 x 10^(-20) level, and independent bounds are available for all the Lorentz-violating c coefficients at the 2 x 10^(-14) level or better. This represents an improvement in some bounds by fourteen orders of magnitude.