  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.
