Olivier,

You probably already read this, but the second paragraph of the Wikipedia entry cited, seems to discuss the experimental issues somewhat:

"Einstein–Cartan theory has been historically overshadowed by its torsion-free counterpart and other alternatives like Brans–Dicke theory because torsion seemed to add little predictive benefit at the expense of the tractability of its equations. In particular, many effects of torsion are hypothesized to be non-propagating[5] so that its direct observation is expected to be difficult; however, the fact that torsion does not propagate ensures that in vacuum there is no torsion, which implies that the Einstein-Sciama-Kibble theory is indistinguishable from the Einstein theory in all experiments performed so far, and therefore the non-propagation of torsion is also the main reason for which the Einstein-Sciama-Kibble theory is still a viable completion of Einstein gravity Experiments apt to detect torsion, or torsional effects, must thus be done in presence of matter with spin, but even then one of the problems torsion had was due to the fact that its effects were expected to be relevant only at the Planck scale; this was due to the fact that the Einstein-Cartan theory is only the most straightforward but not the most general torsional completion of Einstein gravity, which was instead obtained in recent years [6] [7] and where torsional effects manifested as spin-spin contact interactions in the Dirac equation can be relevant at much larger scales. Since the Einstein–Cartan theory is purely classical, it also does not fully address the issue of quantum gravity; this too is a delicate issue, since in the Einstein-Cartan theory the Dirac equation becomes non-linear, and therefore the superposition principle used in usual quantization techniques would not work. Recently, iterest in Einstein–Cartan theory has also been driven toward cosmological implications.[8][9]"

The Wikipedia References section (6-9) provide dynamic links...

References 6 & 7 at least refer to newer, related theories - they might also include earlier references to the Einstein-Cartan theory.

Searching...

http://arxiv.org/abs/gr-qc/0606062 is a Einstein-Cartan theory encyclopedia entry that includes references. Equations 25 confirms the Wikipedia entry.

There's an interesting discussion of prior proposals for tests discussed (with references) here - http://physics.stackexchange.com/questions/27746/experimental-bounds-on-spacetime-torsion

I also find some discussion of the theory as it applies to Eddington experiments in http://www.aias.us/documents/uft/a46thpaper.pdf

They remind me that general relativity's determination of proximal effects (Venus, strong gravitational lensing), seems to me as merely an information systems analyst to represent a proximity 'fudge' factor - the apparently physically ambiguous third term (see http://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity#Effective_radial_potential_energy). I wonder if torsion effects might be a more physical explanation?

Finally I find a reference to "Torsion, an alternative to dark matter?" (http://arxiv.org/pdf/1104.0160.pdf). To the extent that Einstein-Cartan theory might be applicable, galactic rotation might offer some opportunity for verification of results. This is an area of particular interest to me. At a cursory level, it seems that torsional effects might be significant in vast planar distributions of hundreds of billions of discrete objects comprising compound structures like spiral galaxies. If this is of particular interest you might find my brief, informal profile thesis of interest. Also see http://dx.doi.org/10.1007/s10509-011-0854-z.

Perhaps the newer theories might offer better opportunities for experimental testing...

Best wishes,

Jim

Thanks Jim for sharing some interesting links :)

Try this http://inspirehep.net/search?ln=en&as=1&m1=a&p1=Kostelecky+Russell+Tasson&f1=author&op1=a&m2=a&p2=&f2=&op2=a&m3=a&p3=&f3=&action_search=Search&sf=&so=a&rm=&rg=10&sc=0&of=hb and then let me know if this might have been of any help at all.

However, something must be added: while general theories with torsion (torsion as a free field) do not, theories like the Einstein-Cartan-Sciama-Kibble (where torsion is coupled to the spin density of fermions) do have a problem: if this coupling is occurring for actions that are at the least-order derivative, torsion is algebraically coupled to the spin density, which means that torsion vanishes when there is no spin density; worse, if the fermion is the Dirac one, then all field equations reduce to those you would have had in the torsionless case apart from the Dirac field equation itself, where the torsion-spin coupling is manifested as non-linearity of the Dirac field in self-intecation. What all this means is that to detect torsion, or its effects, one must do experiments probing the intrinsic dynamics of Dirac fermions.

Now, if you think this is bad let me finish: in ECSK theories for many Dirac fields there is an additional problem still: all torsionally-induced interactions may be written in the form of 4-fermion interaction, and therefore they may always be mistaken for some effective interaction of a so-far unknown high-energy theory.

So in the case of multiple Dirac fields, the situation is hopeless, unless we were to know for sure there would be no unknown gauge theory from which we could expect such 4-fermion effective interaction as a low-energy limit, while for the single Dirac field, one should be able to see non-linearity of the Dirac fermion, which is quite a difficult task.

Perhaps this may explain why there is so little that has ever been done about experimaental evidence of torsion.

At the other end of the scale, I have to wonder whether the proximal effects of Einstein-Cartan torsional theory might be scaled up or aggregated in some way to apply to spiral galaxy structures - possibly increasing the peripheral gravitational potential, perhaps explaining galactic rotation curves without requiring imaginary elements or empirical scale dependent modifications to gravity...

If torsional gravity seems equivalent to GR, perhaps it is only because GR includes the unexplained empirically derived proximal 'third term'. Torsion within rotating spacetimes may provide a better physical explanation for proximal effects. Again, at large scales, rotating disks might aggregate these torsional effects, where proximity is a 'relative term'.

BTW, thanks for the kindness, Mohammad Ayaz Ahmad, but I must disclose that I'm merely a retired information systems analyst.

Thanks Luca for the link and your comments.

Also a little reply to James Dwyer, if I may: because ECSK theory for Dirac fields is essentially local, in the sense that the effects of torsion are manifested as non-linearities in the dynamics of the Dirac field, and so rather locally, there is little chance that they could have effects on the other hand of the scale; however, your intuition is rather good, especially if it is true that you are not an expert, because torsion can in fact be both "scaled-up" and "aggregated": let me explain.

Torsion can be "aggregated" when Dirac fields happen to form condensates, that is when the see of Dirac particles behave as a single field: the idea is that the torsional effects that would normally be present as locally as a single Dirac particle are now as global as the full condensate: then torsion could in principle strech off to galactic distances since the condensate can (http://inspirehep.net/record/751655 - http://inspirehep.net/record/590853).

In the standard ECSK theory the action is obtained by generalizing the Einstein action given by the Ricci scalar as to include terms with torsion, therefore going from the Ricci purely metric scalar R to the Ricci scalar with metric and torsion G (I call it with another letter to distinguish); now this is only the most straightforward but not the most incusive generalization, since the most complete of such generalization must also consider explicit torsion-square terms in an action of the type G+Q² (where Q is the torsion): the effect of such a generalization, in the case of Dirac matter, for instance, is that nothing changes in the form of the field equations, but the magnitude of the torsion-spin coupling constant does not need to be given by the Newton gravitational constant as it now completely free, a new coupling constant to be determined empirically, and so torsion can be "scaled-up" (http://inspirehep.net/record/923953).

Luca Fabbri,

Thanks for explaining! I am a retired expert information systems analyst, but I have no formal education or background in physics or math. However, in this case my intuition was most likely a combination of brilliant insight and blissful ignorance.

To James Dwyer: hi, so let me go through this:

1. For the 2-body problem, I admit I never worked on it: what you talk about, the fact that there could be tidal forces, is justified by the fact that these tidal forces usually go as an inverse of cubic radial coordinate, so what you say makes sense to me; but again, I do not have much insight on this problem.

2. About the other issue, the preponderance of matter over antimatter, there have been attempts to derive them from torsion: physically, matter and antimatter have opposite helicity states, and so they couple to the same background with slightly different energies. But this is certainly a work-in-progress topic.

If you cannot understand what I write is most probably my fault; so please feel free to ask whatever you like.

I will try my best to reply.

I can’t find any either. I suppose it is a problem with keywords in the search, as an experiment may have bearing on the theory, while not being mentioned explicitly.

In Einstein-Cartan theory torsion also requires fermions to be spatially extended. This is the same approach I used in my models with good results.

The smaller than classical size of the proton was predicted in my book, now out of print, based on a spatially expanded fermion, and the mass of the Up and Down quarks derived from such a model fell within observation and are linked to size of the proton. At the time I my book was printed, I did not think we could make such a fine measurement due to the limits of technology at the time. Things change fast.

My point is that these experimental results, like the size of the proton, might be linked to Einstein-Cartan theory and the limits of technology, but no search on the theory or empirical limits brings up those results. Thus finding a paper with the limited scope you are searching for may pose a challenge.

I see some others have given some links they found, I will have to check them out. Glad I found this discussion.

Dear Charles, would you please tell us the title of your book? That would be interesting to read. Thanks

Simply Logic and Reason was the book title, printed by Virtual Bookworm Publishing. It was two books in one actually Luca Fabbri. As it is out of print now, copies may be hard to find.

One section was on theology, a refute of Modern Creationism, the second part was my basic physics research at the time. I have also written on earthquake engineering and environmental engineering.

Creationists hate science and physics, so I thought if I could get them to read and understand a little physics at the same time. why not. My physics work is on undergraduate educational models.

So for a physicist, it would be a boring read, I spent a chapter just trying to explain the uncertainty principle to readers with no science background.

The successful predictions of Up and Down quark mass, slightly smaller than classical size of the proton, and that plasma produced in particle collisions would behave as a perfect fluid, are not as impressive as they sound.

I don't want to take over this discussion, but if you are interested in the physics behind those predictions of a simple semi-classical educational model, message or email me and I can give you the details easily enough Luca.

Hello,

Perhaps my finding, that for average star luminosity roughly equals it's angular momentum gives some points to Cartan. Space cannot be deformed, however...

Alksnis E. Correcting the false picture of the Universe. GSJ

There is no falsification of ECSK gravity or any fatal theoretical shortcoming. Objections about Torsion being incompatible with U(1) of EM Field are unfounded AS TORSION APPEARS DUE TO THE TRANSLATIONAL GAUGING PART OF THE OVERALL GAUGING OF THE POINCARE GROUP OF LORENTZ TRANSFORMATIONS IN MINKOWSKI SPACE-TIME in this Gauge theory of Gravitation, while U(1), SU(2) and SU(3) are internal Gauge symmetries related to EM, Weak & Strong Force fields. The theory is very unfashionable as it is very difficult due to Torsion etc., but I must submit that it feels much less speculative than string theory.

There is However a startling possibility in this theory that every BH possibly creates a new universes within it and ours too may be within a black hole! Since the new universe is safely tucked away behind an event horizon (which acts as a wormhole to the new internal universe from the one which houses the BH), neither conservation laws nor violation of homogeneity and isotropy of the universe is violated. This is certainly a preferable condition to the current fashion of string theorists whose spatially coexisting multiverses violate homogeneity and isotropy and therefore (by Noether's theorem) also violate conservation of linear and angular momentum.

The difference between ECSK and GR will NOT be observationally discernible until Planck scale energy and lengths are reached where this theory gives very definite radii of leptons etc in terms of L_p (Plank Length) and alpha )(Fine structutre constant) etc and also avoid singularities related to GR or those of QFT, the latter requiring renormalisation. References from Poplawski, Deither, T P Singh on arXiv.org are quite illuminating.

Referencesta on Gauge theories of Gravitation:

Article Gauge Theories of Gravitation

Reprints of the foundational literature are contained in the pricey volume

https://www.worldscientific.com/worldscibooks/10.1142/p781

But the commentaries on the reprinted papers are available for free download at

https://arxiv.org/pdf/1210.3775.pdf