Discussion Overview
The discussion revolves around the energy of a closed universe, particularly in the context of Hamiltonian formulations and the use of pseudotensors. Participants explore theoretical implications, the physical meaning of energy concepts, and references to relevant literature, including works by Alexander Vilenkin and Tryon.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants assert that the energy of a spacetime is represented by its Hamiltonian, which is zero in a closed universe under certain conditions, referencing Wald E.2.
- Others argue that this leads to abandoning the concepts of positive or negative energy, as used by Vilenkin, which they claim may not be physically meaningful.
- A participant questions the validity of pseudotensors in general relativity, suggesting that their arbitrary nature complicates the definition of energy.
- There is a discussion about whether the Hamiltonian formulation suffers from similar issues regarding physical meaning, with some asserting that the Hamiltonian's zero value has a clear interpretation.
- Concerns are raised about the dependence of energy values on coordinate choices, with some asserting that the Hamiltonian being zero is invariant, while the integral of the stress-energy tensor may vary.
- A participant mentions that the total energy in a closed universe, under certain conditions, is expected to be positive and constant, although they have not verified this mathematically.
- References to Tryon's original paper on quantum fluctuations are made, with some noting that it does not adequately address the use of pseudotensors.
- One participant highlights issues with Tryon's model, including assumptions about conserved quantities and the applicability of gravitational potential energy in non-stationary spacetimes.
Areas of Agreement / Disagreement
Participants express multiple competing views regarding the physical meaning of energy in a closed universe and the role of pseudotensors, indicating that the discussion remains unresolved.
Contextual Notes
Limitations include unresolved mathematical steps regarding the Hamiltonian formulation and the implications of pseudotensors in non-stationary spacetimes. The applicability of Tryon's model to our universe's characteristics is also questioned.
As I noted before, two of the people you would need to convince are Vilenkin and Guth.