Ultra-High Energy Cosmic Rays and Symmetries of Spacetime
  High energy cosmic rays allow probing phenomena that are inacessible to accelerators. Observation of cosmic rays, presumebly protons, with energies beyond $4 \times 10^{19} eV$, the so-called Greisen-Zatsepin-Kuzmin (GZK) cut-off, give origin to two puzzles: How do particles accelerate to such energies ? Are their sources within $50 - 100 Mpc$ from Earth, or Lorentz invariance is actually a broken symmetry ? 
O. Bertolami