michael_nielsen

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!

whence the lagrangian with time translation symmetry? (a fair amount of my QFT course was the lecturer writing down a lagrangian and then ¯\_(ツ)_/¯ing)