Exploration of Possible Quantum Gravity Effects with Neutrinos II: Lorentz Violation in Neutrino Propagation

It has been suggested that the interactions of energetic particles with the foamy structure of space-time thought to be generated by quantum-gravitational (QG) effects might violate Lorentz invariance, so that they do not propagate at a universal speed of light. We consider the limits that may be set on a linear or quadratic violation of Lorentz invariance in the propagation of energetic neutrinos, v/c=[1 +- (E/M_\nuQG1)] or [1 +- (E/M_\nu QG2}^2], using data from supernova explosions and the OPERA long-baseline neutrino experiment.