2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/2269High 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 ?Expanded discussion, 9 pages, plain Latex. This essay was selected for an Honorable Mention by the Gravity Research Foundation, 2001Astrophysicstext