I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establi

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 Poincaré 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 ${10}^{14}–{10}^{17}\mathrm{eV}$. 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.

We investigate the implications of energy dependence of the speed of photons, one of the candidate effects of quantum-gravity theories that has been most studied recently, from the perspective of observations in different reference frames. We examine how a simultaneous burst of photons would be measured by two observers with a relative velocity, establishing some associated conditions for the consistency of theories. For scenarios where the Lorentz transformations remain valid, these consistency conditions allow us to characterize the violations of Lorentz symmetry through an explicit description of the modification of the quantum-gravity scale in boosted frames with respect to its definition in a preferred frame. When applied to relativistic scenarios with a deformation of Lorentz invariance that preserves the equivalence of inertial observers, we find an insightful characterization of the necessity to adopt in such frameworks nonclassical features of spacetime geometry, e.g. events that are at the same spacetime point for one observer cannot be considered at the same spacetime point for other observers. Our findings also suggest that, at least in principle (and perhaps one day even in practice), measurements of the dispersion of photons in relatively boosted frames can be particularly valuable for the purpose of testing these scenarios.