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 observ ations of cosmic rays above the GZK cutoff and the observations of 20-TeV g amma rays from Markarian 501. We show here that different pictures of the s hort-distance structure of space-time would lead to different forms of viol ation of ordinary Lorentz invariance. In particular, even space-time models leading to the same deformed dispersion relation, the only aspect of Loren tz-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) na ture of space-time at very short distances. (C) 2001 Elsevier Science B.V. All rights reserved.