But that would take us too far. The main lesson here is that general relativity is not a theory that requires physical objects or fields to propagate in a pre-existing translationally invariant spacetime. That’s why the corresponding energy conservation law justified by Noether’s argument either fails, or becomes approximate, or becomes vacuous, or survives exclusively in spacetimes that preserve their “special relativistic” structure at infinity. At any rate, the status of energy conservation changes when you switch from special relativity to general relativity.

— Lubos Motl

2011.01.11 Tuesday ACHK