  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 ?
