Cosmic Rays and the Structure of Space-Time

Even a fundamental symmetry like Lorentz Invariance is an experimental fact and must be experimentally verified. We show that the study of the interactions of Cosmic Rays with universal diffuse background radiation can provide very stringent tests of this symmetry. The interactions we consider are the ones characterized by well defined energy thresholds whose energy position can be predicted on the basis of Special Relativity. We argue that the experimental verification of these thresholds can address the physics of supra-Planckian scales.