Working in the context of a Lorentz-violating extension of the standard model
we show that estimates of Lorentz symmetry violation extracted from ultra-high
energy cosmic rays beyond the Greisen-Kuzmin-Zatsepin (GZK) cutoff allow for
setting bounds on parameters of that extension. Furthermore, we argue that a
correlated measurement of the difference in the arrival time of gamma-ray
photons and neutrinos emitted from active galactic nuclei or gamma-ray bursts
may provide a signature of possible violation of Lorentz symmetry. We have
found that this time delay is energy independent, however it has a dependence
on the chirality of the particles involved. We also briefly discuss the known
settings where the mechanism for spontaneous violation of Lorentz symmetry in
the context of string/M-theory may take place.Comment: Typos corrected. Version to appear in Phys. Rev.
