Lightknight said:
Wait, the law persists at quantum levels? I was pretty sure this one broke down and was inconsistent in quantum mechanics. Is that not the case?
Even at the quantum level energy is conserved... ultimately. It at least has to be conserved "on average" at the quantum level, otherwise it wouldn't be true for the rest of physics right?
Hm, I don't think I'm smart enough to explain quantum field theory to a non-physicist without writing a book about it... err.. but the basics structure one would motivate it from is classical field theory, which knows an energy-momentum tensor that is a scalar (gives number at every space-time point). Examples of a classical field theory are electromagnetism and hydrodynamics. In such theories the energy-momentum tensor comes from "translational symmetry", which is just a complicated way of saying "we think the laws of physics should be the same everywhere". Through some cute maths this results in a conserved current which we call the energy momentum tensor.
Now, in a quantum field theory one can do the same (because it's formulated in the same way as classical field theory), but the "fields" are now "operators", which act on particle and vacuum "states" (vacuum = "there is no particle", "particle"="something is there with momentum p and mass m" etc.). One would thus have an energy-momentum "operator". This is basically the reason why you would get confused about the energy-momentum tensor in the first place - it's now tied to some weird operator which can only measured through his statistical properties.
I'm not sure how interested you are in the fine print, but quantum field theory (QFT) is actually rather complex when you try to entangle it and I've already deleted quite a bit of half-true junk I had written down... err... well the gist of it is:
If we look to deeply we will probably trip over our own feet. At large times (for example at scattering experiments) we will always find energy to be conserved. I've actually seen a talk (http://pirsa.org/11010111/ warning: super advanced) about a group of physicists working on a "unifying" theory with the idea that all QFT needs to do is give "large time results" (scattering amplitudes), so we should be happy with that statement... I guess
edit: Seems like it ended up being longish and nonsensical regardless. I can only attribute this to my inadequacy. I have only taught physics students so far and it doesn't seem to translate well to a more general audience. Sorry.