2
$\begingroup$

Spin is always explained as a sort of "intrinsic" angular momentum, and orbital angular momentum very clearly affects gravity via gravitomagnetic effects (frame dragging)

If the analogy between spin and OAM holds, why is there no incorporation of spin into the EFE? I know about Einstein-Cartan theory, but how would you test the differences?

I'm also assuming if spin is involved the universality of free fall is broken by a sufficiently spinning mass: is this the only way to find if spin actually influences gravity?

$\endgroup$
3
  • 1
    $\begingroup$ I actually do mean spin as in en.wikipedia.org/wiki/Spin_(physics) ; orbital angular momentum is already in the E-M tensor, but en.wikipedia.org/wiki/Spin_tensor is not (usually). What I'd like to know is if I had huge spin density (lots of non-zero spin particles smashed together), why wouldn't it couple to the EFE? If it did influence spacetime, would it be observable like frame dragging? $\endgroup$
    – nimish
    Commented Mar 23, 2021 at 14:05
  • 2
    $\begingroup$ @ChiralAnomaly Spin does not affect the electromagnetic energy-momentum tensor. For a free wave the EM tensor is the same for linear and circular polarisation. For a scalar massless field, only existing in thought experiments, of the same frequency of momentum the EM tensor is the same as for an electromagnetic wave of arbitrary polarisation. If your statement is that spin should be accompanied by energy, that makes sense, however I don't have a model to translate that into a rotational contribution to the EM tensor. $\endgroup$
    – my2cts
    Commented Mar 23, 2021 at 16:05
  • 2
    $\begingroup$ @ChiralAnomaly Ctd. Spin may cause frame dragging through the spin angular meomentum distribution, a third rank tensor. $\endgroup$
    – my2cts
    Commented Mar 23, 2021 at 16:07

1 Answer 1

3
$\begingroup$

The possibility most often discussed is that intrinsic spin couples to torsion. This is what happens in the Einstin-Cartan theory, and is what is being searched for in experiments such as the ones done by the Eot-Wash group at UW using a spin-polarized torsion pendulum. A positive result from such an experiment would prove that gravity does couple to spin in this sense. There is no way to prove that it doesn't couple, since a null result can only put an upper limit on the phenomenon.

The "why" could just be that God gets to pick the laws of physics. Or you could say that you find the equivalence principle to be very aesthetically attractive, in which case torsion is ruled out.

I'm also assuming if spin is involved the universality of free fall is broken by a sufficiently spinning mass: is this the only way to find if spin actually influences gravity?

This is not a violation of the e.p., nor is it a demonstration that gravity couples to spin in the sense that people normally mean. According to GR, this effect goes to zero in the limit of small test particles, provided that we assume an appropriate energy condition: Ehlers and Geroch, http://arxiv.org/abs/gr-qc/0309074v1 That limiting behavior is considered to be enough to satisfy the e.p.

$\endgroup$
1
  • $\begingroup$ Great -- the "why" was more in the sense of: what is stopping SAM from behaving like OAM and doing something to spacetime? And it seems like "we haven't observed any deviation that would need it" -- more or less? $\endgroup$
    – nimish
    Commented Mar 23, 2021 at 17:25

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.