  Experimental observations indicate that gamma-ray bursts (GRB) and
high-energy neutrino bursts may travel at different speeds with a typical delay
measured at the order of hours or days. We consider a potential interpretation
where GRB is slowed down due to dispersion of light in interstellar medium. In
addition to standard media such as electrons and photons, we consider the case
of an axion plasma. We find that none of the considered media are able to
account for the long GRB delays. The GRB delays have occasionally been
interpreted as a sign of Lorentz invariance violation. That interpretation has
its own problems: since the modification of the dispersion relation should not
be dependent on particle type, delays between photons and neutrinos are hard to
explain. We conclude that the two aforementioned interpretations of the GRB
delay can be distinguished observationally due to the different frequency
dependencies of the propagation speed of radiation.
