- #1

julian

Gold Member

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## Main Question or Discussion Point

We know that the reason enery and momentum are conserved is b/c of Noether's theorem...time translational invariance implies energy conservation and space translational invariance implies momentum conservation.

Now in a curved spacetime you can still form conserved quantities - energy and momentum if the spacetime has Killing's vector fields.

However, GR is invariant under active diffeomorphisms (Einstein's Hole argument) and general active diffeomorphisms will destroy any Killing vector field. And hence energy and momentum are no longer physically meaningfull quantities? In Rovelli's book "Qunatum Gravity" he emphasizes this. For example he talks about the problem of defing the vacuum state when energy is not meanifull.

Anyway, so GR states that gravity is determined by mass or energy...but energy doesn't have physical meaning anymore?

Now in a curved spacetime you can still form conserved quantities - energy and momentum if the spacetime has Killing's vector fields.

However, GR is invariant under active diffeomorphisms (Einstein's Hole argument) and general active diffeomorphisms will destroy any Killing vector field. And hence energy and momentum are no longer physically meaningfull quantities? In Rovelli's book "Qunatum Gravity" he emphasizes this. For example he talks about the problem of defing the vacuum state when energy is not meanifull.

Anyway, so GR states that gravity is determined by mass or energy...but energy doesn't have physical meaning anymore?