Is there a dynamical cause of the spin-statistics connection?

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Extant proofs of the spin-statistics connection (SSC) are kinematical. C S Unnikrishnan has suggested that a dynamical interaction leading to the SSC would involve spin and perforce gravity, the only known universal force. For the scattering of two identical particles, he considers [arXiv: gr-qc/0406043] the interaction of their spins with the gravito-magnetic field generated by their scattering motion through cosmic matter-energy. There the direct and particles-exchanged scattering amplitudes accumulate different quantum phases which provide the relevant bosonic/fermionic sign between them without applying the ad hoc SSC rule. Here it is shown that the scattering probabilities given by the standard implementation of SSC in quantum mechanics are actually not obtained from the above interaction for most initial spin states of the scattering particles. Instead, an unrealized peculiar dynamical interaction is required. Further, a spin-gravito-magnetic interaction as above (with caveats) would result in a large unmeasured spin-orbit coupling type effect on atomic energy levels. A comparison with a typical rotation based proof is also provided.