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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/M₁) or 1 (E/M₂) ^2, using data from supernova explosions and the OPERA long-baseline neutrino experiment. Using the SN1987a neutrino data from the Kamioka II, IMB, and Baksan experiments, we set the limits M₁>2. 7 (2. 5) 10^10 GeV for subluminal (superluminal) propagation and M₂>4. 6 (4. 1) 10^4 GeV at the 95% confidence level. A future galactic supernova at a distance of 10 kpc would have sensitivity to M₁>2 (4) 10^11 GeV for subluminal (superluminal) propagation and M₂>2 (4) 10^5 GeV. With the current CERN neutrinos to Gran Sasso extraction spill length of 10. 5 and with standard clock synchronization techniques, the sensitivity of the OPERA experiment would reach M₁710^5 GeV (M₂810^3 GeV) after 5 years of nominal running. If the time structure of the super proton synchrotron radio frequency bunches within the extracted CERN neutrinos to Gran Sasso spills could be exploited, these figures would be significantly improved to M₁510^7 GeV (M₂410^4 GeV). These results can be improved further if a similar time resolution can be achieved with neutrino events occurring in the rock upstream of the OPERA detector: we find potential sensitivities to M₁410^8 GeV and M₂710^5 GeV.
Ellis et al. (Thu,) studied this question.