Gamma ray bursts (GRBs) are short and intense pulses of γ-rays arriving from random directions in the sky. Several years ago Amelino-Camelia et al. [1] (see also [2]) pointed out that a comparison of time of arrival of photons at different energies from a GRB could be used to measure (or obtain a limit on) possible deviations from a constant speed of light at high photons energies. I review here our current understanding of GRBs and reconsider the possibility of performing these observations (see also Norris, Bonnell, Marani, & Scargle [3] for a review of the same topic). I begin (in Sect. 2) with a brief discussion of the motivation to consider an energy dependent variable speed of light. I turn (in Sect. 3) to a general discussion of the detectability of deviations from a constant speed of light via time-lag measurments. I derive constraints on the Energy range, the distance to the sources and the needed temporal resolution of the sources and the detectors. I then turn (in Sect. 4) to a short description of our current understanding of GRBs. This section is included as a background material as for the rest of the discussion GRBs are just cosmological sources of high energy photons and we don't really care how are these photons they produced. In Sect. 5 I return to the subject of the talk and I describe the temporal structure and spectral properties of GRBs. These are the key issues that are relevant for the observations of a variable speed of light. I conclude (in Sect. 6) by confronting the observations needed for determination of (or obtaining a limit on) a variable speed of light with the properties of GRBs. I discuss some recent attempts to obtain limits on Quantum Gravity effects [4, 5, 6, 7] and prospects for future improvements.
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