The Universe of Discourse
           
Fri, 06 Feb 2009

Maybe energy is really real
About a year ago I dared to write down my crackpottish musings about whether energy is a real thing, or whether it is just a mistaken reification. I made what I thought was a good analogy with the center of gravity, a useful mathematical abstraction that nobody claims is actually real.

I call it crackpottish, but I do think I made a reasonable case, and of the many replies I got to that article, I don't think anyone said conclusively that I was a complete jackass. (Of course, it might be that none of the people who really know wanted to argue with a crackpot.) I have thought about it a lot before and since; it continues to bother me.

But I few months ago I did remember an argument that energy is a real thing. Specifically, I remembered Noether's theorem. Noether's theorem, if I understand correctly, claims that for every symmetry in the physical universe, there is a corresponding conservation law, and vice versa.

For example, let's suppose that space itself is uniform. That is, let's suppose that the laws of physics are invariant under a change of position that is a translation. In this special case, Noether's theorem says that the laws must include conservation of momentum: conservation of momentum is mathematically equivalent to the claim that physics is invariant unter a translation transformation.

Perhaps this is a good time to add that I do not (yet) understand Noether's theorem, that I am only parroting stuff that I have read elsewhere, and that my usual physics-related disclaimer applies: I understand just barely enough physics to spin a plausible-sounding line of bullshit.

Anyway, going on with my plausible-sounding bullshit about Noether's theorem, invariance of the laws under a spatial rotation is equivalent to the law of conservation of angular momentum. Actually I think I might have remembered that one wrong. But the crucial one for me I am sure I am not remembering wrong: invariance of physical law under a translation in time rather than in space is equivalent to conservation of energy. Aha.

If this is right, then perhaps there is a good basis for the concept of energy after all, because any physics that is time-invariant must have an equivalent concept of energy. Time-invariance might not be true, but I have no philosophical objection to it, nor do I claim that the notion is incoherent.

So it seems that if I am to understand this properly, I need to understand Noether's theorem. Maybe I'll make that a resolution for 2009. First stop, Wikipedia, to find out what the prerequisites are.


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