An unbinned test for Quantum Gravity effects in high-energy light-curves

Some models of quantum gravity can predict observable effects on the propagation of light: most notably an energy dependent dispersion, where the speed of light is seen to vary with the energy of the photon. As quantum gravity effects should appear at the Planck scale they will be very small and so require very high energy photons to travel large distances before even becoming noticeable. Precisely because this effect is greater for the most energetic photons (dt ~ 10 s/TeV/Gpc), ground-based gamma-ray measurements of large AGN flares are the ideal resource for performing such tests. The modest photon flux combined with the fact that these experiments are capable of recording the photon times with great resolution suggests the use of unbinned algorithms as an optimal solution for testing models of quantum gravity. In this paper we discuss the application of a non-parametric test to such datasets, analysing its limitations and exploring the potential benefits.