  One possible feature of quantum gravity may be the violation of Lorentz
invariance. In this paper we consider one particular manifestation of the
violation of Lorentz invariance, namely modified dispersion relations for
massive neutrinos. We show how such modified dispersion relations may affect
atmospheric neutrino oscillations. We then consider how neutrino telescopes,
such as ANTARES, may be able to place bounds on the magnitude of this type of
Lorentz invariance violation.
