Prospects for constraining quantum gravity dispersion with near term observations

We discuss the prospects for bounding and perhaps even measuring quantum gravity effects on the dispersion of light using the highest-energy photons produced in gamma-ray bursts (GRBs) measured by the Fermi telescope. These prospects are brighter than might have been expected, as in the first ten months of operation, Fermi has so far reported eight events with photons over 100 MeV seen by its Large Area Telescope. We review features of these events which may bear on Planck-scale phenomenology, and we discuss the possible implications for alternative scenarios for in-vacua dispersion coming from breaking or deforming of Poincar\'e invariance. Among these are semiconservative bounds (which rely on some relatively weak assumptions about the sources) on subluminal and superluminal in-vacuo dispersion. We also propose that it may be possible to look for the arrival of still higher-energy photons and neutrinos from GRBs with energies in the range ${10}^{14}\char21{}{10}^{17}\text{ }\text{ }\mathrm{eV}$. In some cases the quantum gravity dispersion effect would predict these arrivals to be delayed or advanced by days to months from the GRB, giving a clean separation of astrophysical source and spacetime propagation effects.