Why is the rest mass of the photon is taken to be zero?
If rest mass of the photon is non zero, then it leads to infinite energy of the photon (by $E=mc^2$ equation) and there is a violation of conservation of energy. Is this a reason?
Also, is there any thing called the relativistic mass of the photon?
closed as unclear what you're asking by John Rennie, Buzz, FGSUZ, ZeroTheHero, Jon Custer Jan 28 at 17:19
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There's no infinite energy. If you substitute $\gamma mc^2$ with v $\to$ c, and m=0 at the same time, $E=0/0$ form which is an undefined quantity. Energy is not either zero or infinity from that expression. Forms like that means the formula breaks down and need some other formula that can evade that mess.
Do you know the expression $E^2 = (mc^2)^2 + (pc)^2$? Here, $m$ is the rest mass. If you use this, $E=pc$, for $m=0$.
Besides, using the concept of relativistic mass is not favorable as it is under a lot of scrutiny. There are questions on this website that answers this part of the question better. Using such a relativistic mass concept works out for a few types of problems, but provides false understanding as they predict "tangential" masses as such.
In response to the OP's comment, photons are responsible for the electromagnetism and is a fundamental force of nature. When we mean fundamental, it means that it cannot really be split into anything else. For example, the masses in protons and neutrons are due to binding energies of smaller particles that constitute them. The assumption here is that photons are elementary particles as such.
why is the rest mass of the photon is taken to be zero
A photon is 'special' in that there is no inertial reference frame (IRF) in which it is at rest. In any IRF, a photon propagates with speed $c$ in vacuo.
Since a photon is not at rest in any IRF, one could reasonably argue that the notion of rest mass, the mass of a particle in the IRF in which is at rest, just isn't meaningful in the case of a photon.
I should point out now that the term of art is invariant mass rather than rest mass.
The relativistic energy-momentum equation for a massive particle with invariant mass $m$ is
$$E^2 = (pc)^2 + (mc^2)^2$$
Importantly, in this equation we can zero the invariant mass and get, for a massless particle,
$$E = pc$$
which says that the energy and momentum are proportional for particles with zero invariant mass. For further reading, start with Does light have mass.
If rest mass of the photon is non zero,then it leads to infinite energy of the photon (by E=mc^2 equation) and there is a violation of conservation of energy.
One cannot stipulate that a particle has a rest frame and that it moves with speed $c$ since $c$ is the invariant speed. If you suppose that a photon has non-zero rest mass, then it has a rest frame and so cannot have speed $c$ in any IRF.
In physics there is a large collection of different particles, with different attributes. Some are massive, some are massless, and both cases are perfectly acceptable. Photons are observed to be massless, and as a consequence moving at the speed of light. To ask why photons are massless is not really in the realm of physics, and the answer is instead of philosophical or religious character.