Abstract: It has been recently observed that small violations of Lorentz invariance, of a type which may arise in quantum gravity, could explain both the observations of cosmic rays above the GZK cutoff and the observations of 20-TeV gamma rays from Markarian 501. We show here that different pictures of the short-distance structure of space-time would lead to different manifestations of Lorentz-invariance violation. Specifically, the deformation of Lorentz invariance needed to resolve these observational paradoxes can only arise within commutative short-...
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