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.