QuantumPion said:
So essentially you are saying that since an electron and a positron have mass, and they can annihilate to create two photons, those two photons have mass? I'm pretty sure this is entirely incorrect. Photons are massless.
This is entirely correct, individual photons are massless.
|(.511, .511,0,0) MeV/c|/c = 0 MeV/c²
|(.511,-.511,0,0) MeV/c|/c = 0 MeV/c²
But a system of photons can have mass if the photons are not traveling in the same direction.
(.511,.511,0,0) MeV/c + (.511,-.511,0,0) MeV/c = (1.022,0,0,0) MeV/c
|(1.022,0,0,0) MeV/c|/c = 1.022 MeV/c²
In general a system of particles will have a different mass than the sum of the masses of its constituent particles.
QuantumPion said:
many bosons can occupy the same space. That space isn't necessarily zero. For example, a Bose-Einstein condensate of helium atoms.
You are correct. I was thinking only of elementary particles where elementary bosons do not take up space due to not obeying the Pauli exclusion principle.
I guess I would tentatively also say that any composite particle containing fermions is matter, even if the composite particle as a whole is a boson. Unfortunately, I haven't thought about it enough to catch any potential contradiction.
QuantumPion said:
I think you are a bit confused. This is exactly what I am arguing AGAINST, and what you have been arguing in favor of until your last paragraph! I specifically stated that a hot gas does NOT have more matter then a cold gas. I stated "matter is anything that has mass".
If matter is anything that has mass and a hot gas has more mass than a cold gas then I don't see how you can consistently claim that a hot gas does not have more matter than a cold one.
QuantumPion said:
When you posited that a hot gas has greater "mass" then a cold gas as an example to disprove my definition, I pointed out that your argument was flawed because the "relativistic mass" of a hot gas is not the same as rest mass.
I am using the usual definition of mass as being the invariant norm of the four-momentum, aka rest mass. I am certainly not talking about relativistic mass. The invariant rest mass of the hot gas is higher than that of the cold gas. A hot gas has more energy in its rest frame, it has more inertia as measured in its rest frame, and according to GR it has more gravity.