[Coda]

Originally Posted by Potironette

That's really interesting! And kind of mind boggling. If an object were disassembled into bits of protons, neutrons, and electrons, and whatever parts there are, I wonder if they'd have the same mass XD.

Nope! I mentioned this before: The energy absorbed or released by chemical and nuclear reactions does in fact influence the system's rest mass! And we can use E=mc² to describe just how much.

One example: A hydrogen nucleus (1 proton, 1 neutron) has a mass of 2.01410178 amu. A helium nucleus (2 protons, 2 neutrons) has a mass of 4.002602 amu. But that means two hydrogen nuclei (2 protons, 2 neutrons) have a combined mass of 4.02820356 amu. What's the ~0.0256 amu difference? It's the binding energy in the nucleus holding the protons together!

0.0256 amu is roughly 4.25x10^-29 kg.

E = mc[sup]2[/i]
E = (4.25x10^-29 kg)(3.00x10⁸ m/s)²
E = 3.82x10^-12 J

And so we predict that this would be the energy released by two hydrogen nuclei becoming a helium nucleus in a fusion reaction. It seems like a pretty small number, but then you can go calculate that red light (remember, the LEAST energetic visible light) has a kinetic energy of only 2.84x10[sup]-19[sup] J and you see just how powerful that actually is.

It should be noted that sometimes bond energy can have a negative contribution to mass -- this is usually unstable. Further discussion of the concept starts getting into some chemistry stuff, so I'll defer that.

"But Coda, didn't you just say a couple posts ago that the forces binding objects together DOESN'T have an effect?"

I did indeed. I'll confess that I wasn't being wholly precise before, since this isn't a masters-level physics course here.

The difference is that atomic/molecular binding energy is part of the rest mass. It acts just like any other mass: it has inertia and it participates in gravity. You can measure it just fine using either of those principles, and in fact the only way to measure that as distinct from the "base" mass (if such a thing existed) would be to break all of the bonds and measure the difference.

This is so fundamental that it turns out that around 99% of the mass of a proton is the binding energy holding its constituent quarks together! Only around 1% is the rest mass of the three quarks inside (inasmuch as you can say that quarks have rest mass, because they're unstable in isolation).

So really, what I was saying that we don't know is if there's a contribution to the total E of a system that you can't measure by observing its rest mass or its momentum.