Obviously, the answer to this question can be "maybe, if you make the torsion tensor small enough", but my question is, given some "typical" size to the torsion tensor, do the spin-orbit couplings that cause non-geodesic motion become large enough that they contradict known solar system and high-precision tests of general relativity?

I don't remember seeing this type of thing investigated in the Clifford Will articles on the matter.

  • $\begingroup$ That the torsion tensor coupling has to be unmeasurably small at the scale of planetary spin-orbit coupling already follows from the agreement of Gravity Probe B with GR, does it not? Another, probably stronger limit should come from binary pulsar data. $\endgroup$
    – CuriousOne
    Jul 2, 2015 at 1:25
  • $\begingroup$ @CuriousOne: that's actually kind of my point. Measurements like gravity probe B and just ordinary solar system constraints should put constraints on the size of the torsion tensor, which explicitly causes non-geodesic motion for spinning particles. $\endgroup$ Jul 2, 2015 at 6:44
  • $\begingroup$ They do, but not enough to rule EC out, it seems, at least not with current limits. $\endgroup$
    – CuriousOne
    Jul 2, 2015 at 6:55
  • $\begingroup$ Einstein-Cartan theory reduces to general relativity without spinor fields in the matter fields. Since the coupling constant is usually assumed to be around the Planck length, you wouldn't find any effect without some pretty big fermion effects. Might be of note in neutron star dynamics, for instance. $\endgroup$
    – Slereah
    Jul 2, 2015 at 8:36
  • 1
    $\begingroup$ Related: physics.stackexchange.com/q/27746 $\endgroup$
    – Kyle Kanos
    Jul 20, 2015 at 14:09

1 Answer 1


To quote from Will's book (Theory and Experiment in Gravitational Physics, Rev. Ed., Cambridge, 1993), "[...] in almost all experiments discussed in this book, the observable effects of torsion are negligible".

Will then mentions a counterexample (Ni, Phys. Rev. D 19, 2260 (1979)), but that example is a specific theory in which torsion propagates and couples to the electromagnetic field.

In another reference cited by Will (Hehl et al., Rev. Mod. Phys. 48, 393 (1976)), which is a review of spin and torsion, the authors explain that torsion normally does not propagate, and that therefore "there can be no torsion of space-time outside the spinning matter distribution itself. Torsion is inextricably bound to matter and cannot propagate through the vacuum as a torsion wave or via any interaction of nonvanishing range" (emphasis is the authors').

In short, Will then concludes that although torsion is one of the subjects that "could generate a monograph of its own", its effects are indeed negligible, and other than providing the aforementioned references, he then ignores the topic in the rest of his book. In particular, torsion plays no role in the parameterized post-Newtonian (PPN) expansion employed in the monograph.

I ran into this "nondynamical" nature of torsion myself when I was exploring an idea related to Moffat's STVG (Scalar-Tensor-Vector Gravity) modified gravity theory.


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