Precision Test of Special Relativity Using Gamma Ray Bursts

Gamma ray bursts (GRBs) have energies ranging from 20 - 200 kev per photon, with burst durations dt as short as 1 ms. Several GRBs are now known to come from cosmological distances. Observations of these events can be used to set a limit on possible violations of special relativity (SR). The velocity of light c' with respect to an observer could depend almost arbitrarily on the source velocity v. Here we assume (or use a Taylor series expansion) that c' = c + kv, where k is a constant to be determined: k = 0 in SR, k = 1 in the Ritz ballistic theory of light (where the source velocity adds to the velocity of light). If the SR second postulate is invalid, photons emitted simultaneously towards an observer from a source at distance L, characterized by internal velocities v (both towards and away from the observer), will arrive at the observer as a pulse of finite width dt, implying a value of k = (c^2/2v)(dt/L). The burst mechanism of GRBs is not yet known. Still, whether the photons are emitted by thermal or nonthermal processes, the emitting particles must have velocities v &gt; 0.1 c. For a Hubble constant of 60 km/sec/Mpc, L ~= 10^28 cm. Using these parameters, one finds k &lt; 10<SUP>-20</SUP>. This represents, by a factor of about 10^9, the most precise test of the second postulate of special relativity to date.