You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more
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 …
And a nice discussion here (and in followups):https://twitter.com/the_happyproton/status/1191107133628207106 …
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).
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 …
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.
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...
... but assuming all that structure begs the question.
Energy is conserved in theories where 1) symmetries give conservation laws and 2) time translation is a symmetry. It's not conserved in the Big Bang cosmology, where 2) fails.
one might argue that energy ought to be that which is conserved (by time evolution) by definition; you can sorta make this precise using noether's theorem, although that might be circular
Noether's theorem is a consequence of Lagrangian mechanics, so it's sorta begging the question. In some sense, though, you can get energy conservation in both GR and NM this way, which I guess is a good point!
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.
