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Experimental tests of General relativity vs Cartan extension

  1. Feb 25, 2010 #1
    First, if there are tests that have ruled one way or the other, that pretty much ends this discussion. I couldn't find any, but if they exist please point them out here.

    That leaves the discussion of:
    1) How could these been distinguished experimentally, and
    2) How precise do tests have to be.

    For those that don't know, the Cartan extension to Einstein's GR is in some sense trivial. So much so, that when people are working to combine GR with QM, they actually mean GR with Cartan's extension but don't bother saying it. That is because:
    - for GR to handle matter with spin angular momentum, this leads to Cartan's extension
    - Cartan's extension (as far as I understand) still uses the same action: the Einstein-Hilbert action, but it considers additional things as physical degrees of freedom to "vary" in the action

    Einstein-Cartan theory is still a classical theory, so it should be possible in principle to distinguish from GR with classical experiments. (Although 'falling' neutron interferometer experiments may work well here if the neutrons could be spin polarized or something. Not sure how to calculate magnitudes of effects.)

    To start off discussion, I'll point out some things that came up recently that gave me hope such effects could be measured:
    1) In natural units, the spin of elementary particles is much larger than their mass. (That is why if any elementary particle was classically considered to be a point particle it would still not be a blackhole, they would be super-extremal. Well, except for the Higgs I guess if that is found.)
    2) Spin allignment in ferromagnets can involve so much angular momentum, that it can be seen in classical mechanics experiments (The famous original g = 2 experiments ... Einstein somehow was involved?)

    So, any ideas people?
    Are there already some experiments in the works?
  2. jcsd
  3. Feb 25, 2010 #2
    I'm not going to be able to help much, as I don't understand Cartan's extension, but if the wikipedia article is correct that GR cannot predict spin-orbital coupling, then Cartan theory is already the victor as spin-orbit coupling has been seen in precision measurements of two pulsars orbiting each other:


    In this case though the spin is not intrinsic spin. So maybe GR doesn't forbid the coupling? As I said, I do not know Cartan theory. So someone more knowledgeable will have to answer here.
  4. Feb 25, 2010 #3
    Great! Now the thread is simplified to:

    Does GR actualy forbid spin-orbit coupling?
    Does it matter whether "spin" is the angular momentum of a planet, vs intrinsic angular momentum of matter?
    And can someone give an intuitive picture of WHY? I'm having trouble visualizing this.
  5. Feb 25, 2010 #4
    @CuriousKid: I'm unfamiliar with the details of the extension, would you be kind enough to link to a good paper or article? This is genuine curiosity for the record, not a backdoor attempt to get you to cite.
  6. Feb 25, 2010 #5
    I do not have a detailed level of knowledge of the subject. So I won't be able to provide much assistance, but this is sometimes also referred to as the "torsion" extension. As GR has a (pseudo)Riemannian geometry, it doesn't have torsion. So searching for GR + torsion, may help.

    Along those lines, this may be a good intro, but I couldn't access it from this computer to check:

    A little searching found this free article, which gives some introductory material

    The famous Ashtekar variables reformulation of GR is actually a reformulation of GR+Cartan's extension, so searching for that, or anything that talks about the starting point for LQG may have some good intro material.

    Hopefully some of that helps.
  7. Feb 25, 2010 #6
    It does! Thank you very much CK, I appreciate you taking the time.
  8. Feb 26, 2010 #7


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    GR certainly does include spin-orbit coupling. Objects experience spin-dependent forces in GR just as charge distributions experience dipole forces in electromagnetism (angular momentum is essentially the dipole moment of a stress-energy tensor). That alone makes the Wiki article extremely suspicious.

    I have only a superficial knowledge of Einstein-Cartan theory, but my understanding is that it mostly leaves GR the same except for the addition of a torsion tensor that couples to an "intrinsic spin density" of the matter.

    You can model similar things in ordinary GR. The stress-energy tensor of the fluid is found to involve the divergence of the spin density. This is analogous to the equations of "macroscopic electrostatics" involving the divergence of a polarization density. I don't know how similar the predictions of EC and GR when they are both applied to this type of material.
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