Gamma-ray polarization constraints on Planck scale violations of special   relativity
  Using recent polarimetric observations of the Crab Nebula in the hard X-ray band by INTEGRAL, we show that the absence of vacuum birefringence effects constrains O(E/M) Lorentz violation in QED to the level |\xi| < 9x10^{-10} at three sigma CL, tightening by more than three orders of magnitude previous constraints. We show that planned X-ray polarimeters have the potential the potential to probe |\xi|~ 10^{-16} by detecting polarization in active galaxies at red-shift ~1. 
Luca Maccione, Stefano Liberati, Annalisa Celotti, John G. Kirk,   Pietro Ubertini