Discussion Overview
The discussion revolves around the relationship between spin, torsion, and general relativity (GR), particularly in the context of modeling particles with spin using connections that include torsion. Participants explore theoretical frameworks such as Einstein-Cartan gravity and Poincaré gauge theory, and their implications for the conservation of angular momentum and the propagation of torsion.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant suggests that a connection with torsion could model particles with spin in GR, proposing that spin may be an excitation of the connection.
- Another participant argues that the presence of spin or torsion negates the applicability of GR, referencing Hehl's work on Poincaré gauge theory as a relevant framework.
- A different viewpoint introduces Einstein-Cartan gravity as a natural extension of GR that incorporates spin, noting that torsion couples to spin density but does not propagate, thus not affecting gravitational waves.
- A participant expresses concern about the implications of torsion being non-propagating, questioning the connection between torsion and fermionic behavior in materials.
- One participant posits that within materials, torsion could propagate due to spin currents, although they refrain from making definitive statements about effective quasi-particle theories involving fermions and Einstein-Cartan theory.
- There is a contention regarding the distinguishability of GR and Einstein-Cartan gravity, with one participant asserting that they are mathematically different but experimentally indistinguishable, while another challenges this by suggesting that Einstein-Cartan allows for violations of angular momentum conservation.
- Further discussion highlights that while effects of torsion may be measurable in principle, they are suppressed in practice, leading to uncertainty about experimental setups that could differentiate between GR and Einstein-Cartan gravity.
Areas of Agreement / Disagreement
Participants express multiple competing views regarding the implications of torsion and spin in the context of GR and Einstein-Cartan gravity. There is no consensus on whether these theories are experimentally distinguishable or on the nature of the relationship between torsion and particle behavior.
Contextual Notes
Participants note limitations in the discussion, such as the dependence on specific definitions of torsion and spin, and the unresolved nature of certain mathematical steps related to the effects of torsion in practical scenarios.