Abstract: One of the hypotheses of Einstein's special relativity is the constant speed of light, which directly implies that the photon should be massless, and hence experimental tests of its foundations are always of considerable interest. Based on Proca′s equations, some far-reaching implications for nonzero photon mass, for example, the frequency dependence of the speed of light in free space, the deviations of Coulomb′s Law and Ampère′s Law, the existence of longitudinal electromagnetic waves and the additional Yukawa potential of magnetic dipole fields were seriously studied. Through use of a modulated torsion balance our experimental measurements improved the current upper limits on the photon rest mass by at least two orders, and gave mγ≤1.5×10-52g. Experimental investigations of the photon rest mass are an indirect test of the constancy of the speed of light, and any conclusive evidence of a finite mass for the photon will greatly affect the development of all physics.