General description of Dirac spin-rotation effect with relativistic factor

TL;DR

This paper analyzes the Dirac spin-rotation effect using the parallelism approach in general relativity, addressing high-speed rotation issues by proposing a position-dependent nonuniform rotation to maintain physical consistency.

Contribution

It introduces a novel method to handle relativistic rotation-spin coupling at high speeds by making the rotation nonuniform and position-dependent, avoiding singularities in the Lorentz factor.

Findings

The new rotation-spin coupling energy expression aligns with previous results at low speeds.

A position-dependent rotation model resolves the divergence of the relativistic factor at high speeds.

The approach provides a consistent framework for high-speed rotational effects in relativistic quantum mechanics.

Abstract

The Mashhoon rotation-spin coupling is studied by means of the parallelism description of general relativity. The relativistic rotational tetrad is exploited, which results in the Minkowski metric, and the torsion axial-vector and Dirac spin coupling will give the Mashhoon rotation-spin term. For the high speed rotating cases, the tangent velocity constructed by the angular velocity $\Ome$ multiplying the distance r may exceed over the speed of light c, i.e., $\Ome r \ge c$, which will make the relativistic factor $\gamma$ infinity or imaginary. In order to avoid this "meaningless" difficulty occurred in $\gamma$ factor, we choose to make the rotation nonuniform and position-dependent in a particular way, and then we find that the new rotation-spin coupling energy expression is consistent with the previous results in the low speed limit.