Gravitomagnetic Stern-Gerlach Force.

Bahram Mashhoon

doi:10.3390/e23040445

Abstract

A heuristic description of the spin-rotation-gravity coupling is presented and the implications of the corresponding gravitomagnetic Stern–Gerlach force are briefly mentioned. It is shown, within the framework of linearized general relativity, that the gravitomagnetic Stern–Gerlach force reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force.

Highlights

Consider a free test particle of mass m moving with velocity V in an inertial frame of reference in Minkowski spacetime
We expect that the intrinsic spins of the constituent particles all remain fixed with respect to the local inertial frame; the intrinsic spins all appear to precess with respect to the body-fixed frame
The Mathisson–Papapetrou equations for a spinning test particle together with the Frenkel–Pirani supplementary condition imply that the spin vector of a test pole-dipole particle is Fermi–Walker transported along its world line [57]

Summary

Introduction

Consider a free test particle of mass m moving with velocity V in an inertial frame of reference in Minkowski spacetime. Let us imagine that the static inertial observer at the origin of the spatial coordinates in Minkowski spacetime decides to refer the motion of the free particle to axes that rotate with angular velocity Ω(t) about the Z axis. This static observer becomes noninertial and its new reference frame has coordinates (ct, r), where r = ( x, y, z). Where J := L + S is the total angular momentum of the free particle This is a natural result, since J is the generator of rotations in the quantum theory. For further discussion and references, see [48,49]

Spin-Vorticity Coupling

Stern–Gerlach Force due to Spin-Vorticity Coupling

Spin-Gravity Coupling

Linear Gravitational Waves

Discussion