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If photons have no mass, how can they have momentum?

I'm sure this question has been asked here before but I wasn't able to find it clearly answered in one q/a session. I'm a newb, yes.

In the standard model (which I understand is well experimentally supported except for the absent Higgs Boson), all the elementary particles must carry some mass, correct?

For E=MC2 to be true, you can't have energy without mass. And energy has been carried away in collisions of sub-atomic particles that can't be accounted for (the Higgs). So EVERY elementary particle in the Standard Model must have mass, correct?

dvanaria
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