Cosmic rays and TeV photons as probes of quantum properties of space-time

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 forms of violation of ordinary Lorentz invariance. In particular, even space-time models leading to the same deformed dispersion relation, the only aspect of Lorentz-invariance violation considered in most recent studies, can lead to very different predictions for the physics of cosmic rays and high-energy gamma rays. This could provide an unexpected window on the (possibly quantum) nature of space-time at very short distances.