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.\ud \u
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