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I've marked this as a follow-up to ones that may answer it. The key is to pay attention to the different uses of the symbol "m", either as rest-mass or as the factor in p=mv.
"How do we know the momentum of a massless particle?" There are several ways. One is to directly measure the momentum by measuring, for example, the force exerted on a mirror by a stream of photons. Here one uses that p is conserved and also that the particle number can be determined using universal quantum relation E=hf, where E is energy, h is Planck's constant, and f is frequency. Another way is to use an argument from Maxwell's equations that requires E=pc if momentum is to be conserved. That gives a momentum density in terms of the electric and magnetic fields. It can be converted to a momentum per particle again using E=hf. Another way is to look for the missing momentum in events involving a few massive particles and a photon or two. Other ways include using the universal quantum relation |p|=h/λ, where λ is the wavelength. λ can be measured with diffraction gratings or other methods.
(published on 06/04/2013)
Inertial mass is a well defined quantity that appears in physical effects, such as momentum conservation and gravity. Those effects show the inertial mass (not rest mass) of light. There's more discussion in the earlier part of the thread in which I've put your question.
I'm not sure what the word "matter" means.
(published on 12/21/2013)
As we have said many times the full equation for energy is E2 = p2 + mc2 where p is the momentum. LeeH
(published on 04/18/2014)