On the oddly pervasive notion of the conservation of energypic.twitter.com/j0iWw1sbTY
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Well, I goofed. Energy conservation in GR turns out to be subtle, and it's certainly not right to flatly say energy is conserved. Quite a few people pointed this out. Here's a couple of samples, at different levels of explanation:https://twitter.com/johncarlosbaez/status/1191164917597917184 …
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And a nice discussion here (and in followups):https://twitter.com/the_happyproton/status/1191107133628207106 …
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It is, nonetheless, possible to make some sense of the notion of energy conservation in GR. Here's an overview: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html … (also by
@johncarlosbaez and collaborator).Show this thread -
There's also a set of ideas known as the ADM formalism, a so-called Hamiltonian formulation of GR. (The Hamiltonian is a sort of energy function). https://en.wikipedia.org/wiki/ADM_formalism …
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These caveats don't make my original statement correct! But they are useful context, a sense in which the notion of energy (or a Hamiltonian) is correct in general relativity.
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Another topic: some people are replying "Isn't this Noether's theorem?" But that misses the the point. Of course, once you're in Lagrangian mechanics & have time-translation invariance, conservation follows. And there's an analogous quantum argument...
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... but assuming all that structure begs the question.
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