[Coda]

If my son's classes are any indication, they're not completely replacing it. He still knows how to do subtraction with borrowing.

Yes, Trisphee's admin control panel. You'll see.

As for momentum and energy... that goes back to E² = p²c² + (mc²)². This is saying that momentum and mass are related in an interchangeable way.

But what if there WERE something else that contributed to that total energy figure? Some internal force inside the object? Then you'd have to add another term to the equation.

You suggested temperature. Well, that one we actually DO know the answer to -- it doesn't, because temperature measures the average kinetic energy of the particles inside the object relative to each other. The same argument concerning Newton's first and third laws applies here -- any motion inside the system would have to be countered by an opposite motion. If it WASN'T countered by an opposite motion, then that would be contributing to the momentum of the system, which is contrary to the definition of temperature measuring motion internal to the system.

BUT!

Given that the object isn't exploding, there must be some force holding it together. It could be atomic bonds, it could be gravity, it could be magnetism, whatever. So does this force contribute energy that's equivalent to momentum and mass?

That's what we don't know. We can't prove it doesn't, but if it does then it's such a small contribution that we haven't detected it yet.

But there could be some other force that we don't know about with a very weak effect that operates over very large scales, so an Earth-based experiment would have a very hard time doing anything with it. If there is, then this might be an explanation for why the universe isn't expanding faster than it is, and finding a way to measure how much of it there is could give us a clue as to the far-future fate of the universe.