Discussion Overview
The discussion centers on the implications of General Relativity (GR) for the conservation of energy and momentum, particularly in the context of curved spacetime and the role of Killing vector fields. Participants explore theoretical aspects, challenges in defining energy in GR, and the consequences of diffeomorphism invariance.
Discussion Character
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- Some participants assert that Noether's theorem connects energy conservation to time translational invariance and momentum conservation to space translational invariance, but question how this applies in curved spacetime.
- There is a discussion on the existence of Killing vector fields in curved spacetime and their importance for defining conserved quantities like energy and momentum.
- One participant argues that active diffeomorphisms can destroy Killing vector fields, leading to the conclusion that energy and momentum may lose their physical meaning in certain spacetimes.
- Another participant counters that the presence of a Killing vector field is independent of the coordinate chart used, suggesting that diffeomorphism invariance does not negate the existence of conserved quantities.
- Concerns are raised about the implications of GR's diffeomorphism invariance for traditional physics, with references to Rovelli's work emphasizing the need for a new understanding of these concepts.
- Participants discuss the challenge of defining energy in the context of black holes, noting that the stress-energy tensor (SET) describes local energy due to non-gravitational matter, but there is no local interpretation for gravitational energy itself.
Areas of Agreement / Disagreement
Participants express differing views on the implications of diffeomorphism invariance and the physical meaning of energy and momentum in GR. There is no consensus on how these concepts should be interpreted or whether they retain their traditional meanings in the framework of GR.
Contextual Notes
Limitations include the dependence on the presence of Killing vector fields for defining conserved quantities and the unresolved nature of energy interpretation in various spacetimes, particularly in relation to black holes.