Good job on the article. Maybe you could help clarify a point for me.
You said,
"The invariant mass of a particle is defined as the total energy of the particle measured in the particle’s rest frame divided by the speed of light squared."
In a recent PF thread, (
https://www.physicsforums.com/threads/mass-of-an-electron.826015/#post-5187800) I learned that an atom with electrons in an excited state has (slightly) more rest mass than the same atom in the ground state. From that, I leap to the conclusion that a hot object has more mass than when it was cold, a spring gains mass as it is stretched, a molecule has different mass than its consituents, any chemical reaction must absorb or release energy and therefore does not conserve mass, and any solid structure has different mass than its constituents. The unifying principle is that the rest mass energy is any energy (regardless of type), that remains with the object when momentum is zero.
I recognize that the mass differences I'm talking about are tiny; almost too small to measure.
Thermal energy is tricky because it has to do with motion. But thinking of F=ma, if I accelerate a hot object i must accelerate its thermal energy with it.
I guess my question is this. Is there any difference between what you called "total energy of the particle measured in the particle’s rest frame" and what the others called "internal energy" in the other thread?
A second related question. For purposes of gravitation, all forms of energy gravitate equally, correct? That includes kinetic energy and the energy of massless particles. If the mass of a black hole was converted to massless energy in the singularity, we wouldn't be able to tell in terms of the external gravitational field, correct? F=mMG/R*R should be more properly written in terms of energies.