Spin and torsion of the connection

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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.

kroni
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Hello,

I read in an article that in GR it is possible to use a connection with torsion to model ponctual particle with spin. The connection can be decomposed in a curvatue part and a torsion part. In an other part, we know that the invariance under pointcarré group imply conservation of spin of particle. Can i conclude with a lot of prudence that a particle with spin is a exitation of the connection in GR ?

I say this because boson are quantification of field that is, for yang mills theory, the value of the connection.

Thanks.
 
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If there's spin, there no GR anymore. If there's a torsion, there's no GR anymore. So your first statement is inaccurate. What one needs to read is Hehl's work on Poincare gauge theory, which can be seen as a semi-classical extension of GR.
 
I would propose to start reading a few papers regarding Einstein-Cartan-Gravity, which is the most simple and natural extension of GR in the presence of spin.

The interesting thing is that torsion couples to the spin density but is non-propagating; so there are no torsion-waves (gravitational waves are pure curvature-waves). In vacuum (vanishing energy-momentum / vanishing spin density) there is no torsion and the theory reduces to GR. Inside matter (non-vanishing energy-momentum / non-vanishing spin density) there can be torsion but its effects are highly suppressed.

So in essence GR and Einstein-Cartan-Gravity are different mathematically, but indistinguishable experimentally!
 
I am so sad, because i work with someone who prove that rotational waves in matérials have a fermionic behaviour (standard compression waves are bosonic). So, i was thinking that, may be, fermions appear when a quantification of the torsion of the connection is done. But if torsion is non propagative, it fail. Thanks for your answer, i will read the paper you speak about.

Clément
 
but within the material torsion could propagate b/c the spin current of the material does!

but sorry, I can't say anything regarding effective quasi-particle theories with fermionic d.o.f. + Einstein-Cartan
 
So in essence GR and Einstein-Cartan-Gravity are different mathematically, but indistinguishable experimentally!
Are you sure about that statement? I thought Einstein-Cartan allows violation of conservation of angular momentum and of spin, conserving only the sum of the two. So it is certainly experimentally distinguishable from GR, which conserves angular momentum strictly.
 
haael said:
Are you sure about that statement? I thought Einstein-Cartan allows violation of conservation of angular momentum and of spin, conserving only the sum of the two. So it is certainly experimentally distinguishable from GR, which conserves angular momentum strictly.

Inside matter ... there can be torsion but its effects are highly suppressed ... So in essence GR and Einstein-Cartan-Gravity are different mathematically, but indistinguishable experimentally!

I have to check the calculations but as far as I remember the effects are measurable in principle, not in practice. Either there is isolated spin (e.g. from elementary particles) and therefore GR / ECT effects are not measurable, or there are macroscopic GR / ECT effects due to angular momentum, but then the violations due to spin are suppressed. So as far as I can see there is no known experimental setup which can distinguish between GR and ECT.
 

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