On the oddly pervasive notion of the conservation of energypic.twitter.com/j0iWw1sbTY
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Regardless of how one actually proves Noether’s Theorem, I think it’s correct to think of energy as something that is conserved because of time-translation invariance. Evidence: with non-time-invariant laws, energy is not conserved!
Nice way of thinking; I like the last point. It still leaves as a puzzle why qm and classical mechanics see this. You can formulate QM as (classical) Hamiltonian evolution on a suitable phase space, but it's sorta artificial...
