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

TL;DR

This paper critically examines a proposed dynamical explanation for the spin-statistics connection involving gravity and finds it inconsistent with standard quantum mechanics, also predicting unobserved effects on atomic energy levels.

Contribution

It demonstrates that the proposed spin-gravito-magnetic interaction cannot produce the expected quantum phases for most initial spin states, challenging the dynamical approach to SSC.

Findings

Standard quantum mechanics does not support the proposed interaction as the cause of SSC.

The interaction would cause large, unmeasured spin-orbit effects in atoms.

A typical rotation-based proof of SSC remains more consistent with observations.

Abstract

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.