Constraining the mass of the photon with gamma-ray bursts

One of the cornerstones of modern physics is Einstein's special relativity, with its constant speed of light and zero photon mass assumptions. Constraint on the rest mass mγmγ of photons is a fundamental way to test Einstein's theory, as well as other essential electromagnetic and particle theories. Since non-zero photon mass can give rise to frequency- (or energy-) dependent dispersions, measuring the time delay of photons with different frequencies emitted from explosive astrophysical events is an important and model-independent method to put such a constraint. The cosmological gamma-ray bursts (GRBs), with short time scales, high redshifts as well as broadband prompt and afterglow emissions, provide an ideal testbed for mγmγ constraints. In this paper we calculate the upper limits of the photon mass with GRB early time radio afterglow observations as well as multi-band radio peaks, thus improve the results of Schaefer (1999) by nearly half an order of magnitude.