Testability of Torsion in Teleparallel Gravity - V.C. de Andrade et al

[bcrowell]

Mentz114 posted this interesting link: http://arxiv.org/abs/gr-qc/0011087
Teleparallel Gravity: An Overview
Authors: V. C. de Andrade, L. C. T. Guillen, J. G. Pereira
Abstract: The fundamentals of the teleparallel equivalent of general relativity are presented, and its main properties described. In particular, the field equations, the definition of an energy--momentum density for the gravitational field, the teleparallel version of the equivalence principle, and the dynamical role played by torsion as compared to the corresponding role played by curvature in general relativity, are discussed in some details.

This confuses me, because it makes it clear that empirically observable phenomena can be attributed to either curvature or torsion, and yet there are also people, e.g., at UW, doing experimental searches for torsion, which is usually assumed to have spin as its source:
http://www.npl.washington.edu/eotwash/publications/pdf/lowfrontier2.pdf
This type of thing is discussed here:
http://math.ucr.edu/home/baez/gr/torsion.html
MTW has a discussion on p. 250 where they say that torsion would violate the e.p. E.g., if the UW Eot-Wash group got a non-null result from their spin-polarized torsion pendulum, it would clearly be a violation of the e.p., since it would be a composition-dependent motion in a gravitational field.

So are there some types of torsion that are empirically testable, violate the e.p., and are inconsistent with GR, while other types of torsion are just a different way of describing the same physics of GR?

 

[yenchin]

Mentz114 posted this interesting link: http://arxiv.org/abs/gr-qc/0011087
Teleparallel Gravity: An Overview
Authors: V. C. de Andrade, L. C. T. Guillen, J. G. Pereira
Abstract: The fundamentals of the teleparallel equivalent of general relativity are presented, and its main properties described. In particular, the field equations, the definition of an energy--momentum density for the gravitational field, the teleparallel version of the equivalence principle, and the dynamical role played by torsion as compared to the corresponding role played by curvature in general relativity, are discussed in some details.

This confuses me, because it makes it clear that empirically observable phenomena can be attributed to either curvature or torsion, and yet there are also people, e.g., at UW, doing experimental searches for torsion, which is usually assumed to have spin as its source:
http://www.npl.washington.edu/eotwash/publications/pdf/lowfrontier2.pdf
This type of thing is discussed here:
http://math.ucr.edu/home/baez/gr/torsion.html
MTW has a discussion on p. 250 where they say that torsion would violate the e.p. E.g., if the UW Eot-Wash group got a non-null result from their spin-polarized torsion pendulum, it would clearly be a violation of the e.p., since it would be a composition-dependent motion in a gravitational field.

So are there some types of torsion that are empirically testable, violate the e.p., and are inconsistent with GR, while other types of torsion are just a different way of describing the same physics of GR?

As far as my understanding go, in teleparallel gravity, torsion is used as a mathematical formulation of gravity, but in more well known Einstein-Cartan where the metric has both curvature and torsion, torsion is used to model the effect of spin as you mentioned (with curvature still plays it traditional role). So it seems to me that it is the same mathematics used in different models to describe different physics.

 

[Mentz114]

Someone else posted that link, in fact. I've just skimmed it and it looks excellent.

From the abstract of 'Aspects of Gauge Gravity' (arXiv:gr-qc/9602013 v1)

The Einsteinian teleparallelism theory which emerges is shown to be equivalent, for spinless matter and for electromagnetism, to general relativity.

So, for spinning matter it appears that GR and TP gravity don't make the same predictions (?).

 

[yenchin]

Someone else posted that link, in fact. I've just skimmed it and it looks excellent.

From the abstract of 'Aspects of Gauge Gravity' (arXiv:gr-qc/9602013 v1)



So, for spinning matter it appears that GR and TP gravity don't make the same predictions (?).

I am also quite confused. From http://arxiv.org/PS_cache/gr-qc/pdf/0612/0612062v1.pdf, it says, without much details,

"It has been alleged that TEGR has serious source coupling limitations, e.g. it has been said that only scalar matter fields or gauge fields are allowed as sources, whereas matter carrying spin cannot be consistently coupled; some argue that torsion does not couple to electromagnetism, others have a different opinion. For the special case of GR and TEGR we can use an argument similar to that used long ago to establish the effective equivalence of GR and the Einstein-Cartan (EC) theory. As in that case, we find that the TEGR effective equivalent field equations and action also do not require an extra field. Nevertheless we get a complete equivalence for all sources, including,
in particular, spinors."

I really like to understand TEGR and teleparallel gravity in general (there are other teleparallel gravity which are not equivalent to GR, they all have flat geometry but nonzero torsion. An early attempt of modify gravity, if you wish...)

As you might know recently the works in f(T) theory is somewhat popular [see e.g. http://arxiv.org/abs/1005.3039" ]. They do what f(R) people do, but instead of promoting Ricci scalar to function of Ricci scalar, they promote so-called torsion scalar of TEGR to f(T). So the idea of torsion gravity is still pretty much around and active.