system
Given the following post, respond as if you're commenting on Reddit:
human
"Why" does a two-photon system have mass?

I've asked a few of my professors (I'm a physics grad student), and while they aren't completely blown away by the idea (nor am I), they can't really give a good reason for why a two photon system has mass:

Take the equation (with c=1): m^2 = E^2 - P^2

For one photon, |E| = |P| so m = 0.

However, for two (identical) photons travelling in opposite directions, the sum of P is zero, yet E is the sum of the two energies, so the mass of that system is nonzero.  Does this have any real significance?  Does it "mean" anything?
gpt
This has a *ton* of significance. Hugely significant. Consider an atom. electrons are about 1/2000 the mass of the proton. So nearly all the atom's mass is in the protons and neutrons that make it up, no?

A proton or neutron has about 940 MeV/c^2 in mass, and they're made up of 3 valence quarks. But the valence quarks aren't ~300 MeV/c^2 in mass... they're closer to 3 MeV/c^2 ! So where does all the mass of the proton come from? It comes from... the gluons. Massless particles, like the photon is massless, acting as a whole system of particles that impart mass to the proton. By extension, most of the mass of the nucleus, the atom, molecules, every bit of normal matter in the universe... All gluons. All massless particles in a system that has a mass.