Almost everybody knows that light is massless. But where this come from and how it can be proven (experimentally or theoretically)? I actually found this article which explains and calculates the mass of light at rest (which is not 0). So how do we know that light is massless?
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2The 'article' confuses relativistic mass and rest mass. Possible duplicates: http://physics.stackexchange.com/q/4700/2451 and links therein. – Qmechanic Apr 14 '13 at 17:00
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The duplicate link has good answers.
The experimental proof comes from fitting decays where photons are involved. For example the pi_0 decays into two photons. If these had a mass the energies would not balance in the fits.
Pair production would also be problematic, because a "massive photon" disappears into an electron positron pair in the field of a nucleus or an electron. Photons have not been seen to decay in vacuum.
If the photon had a mass,it would have to be twice the mass of the electron in the photon center of mass, not a negligible value , and energy and momentum balances would never work.
All these arguments are encapsulated in the theoretical framework described in the answers to the duplicate question.
