Ultra-high energy cosmic rays and symmetries of spacetime

High energy cosmic rays allow probing phenomena that are inaccessible to accelerators. Observation of cosmic rays, presumably protons, with energies beyond 4 x 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? We suggest an astrophysical test to verify the latter alternative and explore a possible connection with an alternative theory of gravity that exhibits preferred-frame effects.