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A basic tenet of special relativity is that all massless particles travel at a constant, energyindependent velocity. Astrophysical data, including observation of the Crab pulsar at -100 MeV and the recent detection of the pulsar in Hercules X-1 at energies 1 100 TeV, are used to place new experimental constraints on energy-dependent deviations from constant velocity for massless particles. Previous experiments reached energies -10 GeV; this analysis improves the previous constraints by 7 orders of magnitude.