Why does a photon have momentum and no mass, yet $p=mv$?

Question

Okay so according to my high-school knowledge I know about inertia and momentum. Now I have a question regarding the photon which my teachers say that is to be learnt in higher classes(and thus not answering my question so).

So the question is, why does a photon have momentum and no mass? I mean $p=mv$, right? If $m=0$ then it shouldn't have any momentum. Considering it to be a 0-dimensional the answer could be yes, it could have momentum without mass but if I had to add more to the question, I would say, what if you've got like a million-billion photons which stacked together very closely and moving as a single thing, then it would have a volume and thus, according to Newton, anything with a volume has a mass. Now photons is energy, you may say, but then there is the mass-energy equivalence, i.e., $E=mc^2$.

I know it's a sort of a childish but a question.

Answer 1

$p=mv$ is not the full equation. Which is to say that it works in most normal events, you have not been mislead.

Photons have momentum derived from their energy rather than their mass. Perhaps you have heard that energy and mass are interchangeable under $E=mc^2$, they also have similar effects.