Einstein or Einstein–Cartan?

[Dmitry67]

Could anyone explain:
http://en.wikipedia.org/wiki/Einstein-Cartan_theory

1 As the master theory of classical physics general relativity has one known flaw: it cannot describe "spin-orbit coupling", i.e., exchange of intrinsic angular momentum (spin) and orbital angular momentum.

2 There is a qualitative proof showing that general relativity must be extended to Einstein-Cartan theory when matter with spin is present.

3 Experimental effects are too small to be observed at the present time because the spin tensor of typical macroscopic objects is often small and torsion is nonpropagating which means that torsion will only appear within a massive body. In addition, only spinning objects couple to torsion.

I don't understand why if #3 (Experimental effects are too small to be observed) there is a 'proof' #2? What is a 'flaw' if there are no observed effects?

 

[Mentz114]

I think #2 and #3 are independent of each other. In order to accommodate spin-orbit coupling a theory must have an asymmetric affine connection. This is not true of GR but is the case for Einstein-Cartan theory. That is a fact and does not depend on the fact that the effects of SO coupling are very small in weak field and small spin regimes.

I think the article is saying that with our present data, it isn't possible to separate the two theories.

 

[Entropia]

Einstein-Cartan theory is an extension of general relativity that takes into account the spin of matter. In general relativity, the curvature of spacetime is described by the metric tensor, which is a symmetric tensor. However, in Einstein-Cartan theory, an additional term is added to the equations to account for the spin of matter, which is described by an antisymmetric tensor called torsion.

The "flaw" in general relativity refers to the fact that it cannot fully describe the behavior of matter with spin. While there may not be any observable effects at the macroscopic level, the mathematical framework of general relativity breaks down when trying to describe the behavior of matter with spin. This is where Einstein-Cartan theory comes in - it provides a more complete and accurate description of the behavior of matter with spin.

The proof mentioned in #2 is a mathematical proof that shows that general relativity must be extended to Einstein-Cartan theory when dealing with matter with spin. This proof is based on the fact that general relativity cannot fully describe the behavior of spin, as mentioned before.

So, even though the experimental effects may be too small to be observed at the present time, there is still a theoretical basis for the need for Einstein-Cartan theory. And as technology advances and we are able to observe smaller and smaller effects, we may eventually be able to confirm the predictions of Einstein-Cartan theory.