I review the main properties of the Gamma Ray Bursts (GRBs) as possible sources of high energy (E>TeV) neutrinos and confirmed sources of high energy (E>GeV) photons.
I discuss the possibility to use the data of neutrino telescopes, such as IceCube and the GeV-photon telescopes, such as Fermi’s LAT, for precision tests of Einstein's Special Relativity as applied to neutrinos and photons. My focus is on possible departures from Special Relativity that can be motivated by models of quantum space-time. I observe that neutrinos which one would not associate to a GRB, when assuming a classical spacetime picture, may well be GRB neutrinos if the possibility that Lorentz invariance is broken at very high energies is taken into account. I outline how future analyses of neutrino data should be done in order to systematically test the Lorentz Invariance Violation possibility. In addition I consider the possibility that Lorentz Invariance Violation might be responsible for the spectral lags that characterize the GeV signal observed for the remarkable GRB130427A.
A comparison of these features for GRBs at different redshifts provides
some encouragement for a redshift dependence of the effects of the type expected for a quantum-spacetime interpretation, but other aspects of the analysis appear to invite the interpretation as intrinsic properties of GRBs.