Neutrinos from gamma-ray bursts as a tool to explore quantum-gravity-induced Lorentz violation

Lorentz-invariance violation (LIV) arises in various quantum-gravity(1,2) theories, but typically at Planck energies that are not accessible on Earth. To test LIV, we must turn to astronomical observations(2-11). Time-of-flight measurements from astronomical sources have set the present limits on the LIV energy scale. According to existing models, gamma-ray bursts (GRBs) are accompanied by very high-energy neutrinos(12,13). At these energies, the background level in neutrino detectors such as IceCube (currently under construction in Antarctica) is extremely low. We show that the detection of even a single neutrino from the same direction as a GRB, months after the burst, would be statistically significant and imply that the neutrino was associated with the burst. The detection of several delayed neutrinos from different bursts with compatible relations between their delay times, energies and distances would enable us to generically determine (or set limits on) LIV at levels that cannot be reached by any other method.