In this article, the author tried to explain that, Einstein's theory may not valid because he says "photon can decay because it may have minute amount of mass". I'm totally in a conundrum state that how to take this article? Anyone can explain a bit please.
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You can postulate the existence of a photon mass and then use experiments to put an upper bound on it. The mass-modified Lagrangian is called the Proca Lagrangian (see Jackson's Classical Electrodynamics, second edition page 597). In the static case you get a Yukawa type potential. If the photon has nonzero mass, then it should decay. Of course, this would change a lot of what we think we know, but the limits on the mass are very small. Here is a nice overview of mass limits on the photon and graviton. http://arxiv.org/abs/0809.1003
Incidentally, some people like a symmetric form of Maxwell that includes a magnetic "charge density" (monopole). Similar efforts can put bounds on the existance of monopoles.