Should there be a spin-rotation coupling for a Dirac particle?

TL;DR

This paper investigates the existence of spin-rotation coupling for Dirac particles, analyzing how the Hamiltonian depends on tetrad choices and showing that the effect is frame-dependent and not universal.

Contribution

It demonstrates that the spin-rotation coupling term depends on tetrad selection and is not an inherent feature of Dirac particles in rotating frames.

Findings

Mashhoon's term appears only when the tetrad rotates with the frame

The Dirac Hamiltonian differs between frames mainly by angular momentum terms

The spin-rotation coupling is not universal but depends on tetrad choice

Abstract

It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We compute the energy operator in the inertial and the rotating frame, using three tetrad fields: one for each of two frameworks proposed to select the tetrad field so as to solve this non-uniqueness problem, and one proposed by Ryder. We find that Mashhoon's term is there if the tetrad rotates as does the reference frame --- but then it is also there in the energy operator for the inertial frame. In fact, the Dirac Hamiltonian operators in two reference frames in relative rotation, but corresponding to the same tetrad field, differ only by the angular momentum term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field must be selected in a specific way for each reference frame.