Are we observing Lorentz violation in gamma ray bursts?

From recent observations of gamma-ray bursts (GRBs), it appears that spectral time lags between higher-energy gamma rays photons and lower-energy photons vary with energy difference and time (distance) traveled. These lags appear to be smaller for the most luminous (close) bursts but larger for the fainter (farther away) bursts. From this observation, it has been suggested that it might be possible to determine the distance (L) these bursts have traveled from these time lags alone, without performing any red-shift measurements. These observed spreads (dispersion) of high-energy electromagnetic pulses of different energies with time contradict the special theory of relativity (STR). However, extended theories (ET) of the STR have been developed that contain a dispersive term, predicting the above observations. An example of such an ET is presented, allowing us to derive a relationship between time lags of gamma rays of different energies and distance L traveled from their origin. In addition, this theory predicts the origin of X-ray flashes.