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 |ξ| < 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 |ξ|~ 10^{-16} by detecting polarization in active galaxies at red-shift ~1.

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