Uncertainty Of The GR's Experiment Inspections And The Upper Limit Of The Photon Rest Mass

Maxwellian electromagnetism is the greatest physical achievement of 19 century, and as the mathematic description of the classical electromagnetic field, it has a basic hypothesis: the photon rest mass equals zero. However the hypothesis's correctness has gotten the attention all the time. By comparing with the massive Klein—Gordon theory, the nonzero photon rest mass can be incorporated into electromagnetic by replacing Maxwell's theory with Proca's electromagnetic one. Based on Proca equations, some effects can be implied from massive photon, such as the frequency dependence of the speed of light, the deviations of electrostatic Coulomb potential—the additional Yukawa potential, the longitudinal electromagnetic radiation et al. Therefore, corresponding experiments can be taken in flat space to make sure these effects'exist, and the upper limit of the photon rest mass can be gotten. Nowadays, although photon rest mass has obtained a stringent upper limit, various independent techniques have been used for analyzing and testing whether the photon rest mass is zero. Here we discuss the massive photon in the case of curved space-time, that is to say, consider the massive photon in the General relativity's experimental inspections, and get the photon rest mass's upper limit.Generally speaking, the study in this paper firstly shows that a nonzero photon rest mass has effect on one of the General relativity's experimental inspections--the radar echo delay. From a detail deduce we get the equation with massive photon. Then we discuss the gravitational redshift, and also get the equation of Doppler redshift with massive photon. Lastly, by summing up and discussing the effects of the General relativity such as: the radar echo delay, the light deflection and the gravitational redshift, the upper limit of the photon rest mass can be gotten.