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 $m_{\gamma }$ 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 $m_{\gamma }$ 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.

爱因斯坦的狭义相对论是现代物理学的基石之一，它具有恒定的光速和零光子质量假设。约束剩余质量${米}_{\gamma }$光子探测是测试爱因斯坦理论以及其他必不可少的电磁和粒子理论的基本方法。由于非零光子质量会产生与频率（或能量）有关的色散，因此，测量爆炸性天体事件发射的具有不同频率的光子的时延是一种重要且与模型无关的方法来施加这种约束。具有短时间尺度，高红移以及宽带瞬发和余辉发射的宇宙学伽马射线暴（GRB），为以下情况提供了理想的测试平台${米}_{\gamma }$约束。在本文中，我们通过GRB早期无线电余辉观测以及多波段无线电峰值来计算光子质量的上限，从而将Schaefer（1999）的结果提高了近一个数量级。