On the spontaneous breaking of Lorentz invariance

We show that estimates of the Lorentz symmetry violation extracted from ult ra-high energy cosmic rays beyond the GZK cut-off set bounds on the paramet ers of a Lorentz-violating extension of the Standard Model. Moreover, we ar gue that correlated measurements of the difference in the arrival time of g amma-ray photons and neutrinos emitted from Active Galactic Nuclei or Gamma -Ray Bursts may provide a signature for a possible violation of the Lorentz symmetry. We find that this time delay is energy independent, but that it has a dependence on the chirality of the particles involved.