Spin-induced non-geodesic motion, gyroscopic precession, Wigner rotation and EPR correlations of massive spin 1/2 particles in a gravitational field

TL;DR

This paper studies how spin affects the motion and quantum correlations of massive particles in a gravitational field, revealing non-geodesic behavior and spin precession effects using covariant methods and WKB approximation.

Contribution

It introduces a covariant framework for analyzing spin-induced non-geodesic motion and Wigner rotation corrections for particles in curved spacetime, with specific applications to Schwarzschild geometry.

Findings

Wigner rotation correction is zero on geodesics but non-zero for non-geodesic trajectories.

Conditions are developed for observers to measure null Wigner rotation.

Entanglement of EPR pairs is affected by particle motion in gravitational fields.

Abstract

We investigate in a covariant manner the spin-induced non-geodesic motion of massive spin 1/2 particles in an arbitrary gravitational field for trajectories that are initially geodesic when spin is ignored. Using the WKB approximation for the wave function in curved spacetime, we compute the O(hbar) correction to the Wigner rotation of the spin 1/2 particle, whose O(1) contribution is zero on timelike geodesics. We develop conditions for the motion of observers in which the Wigner rotation is null. For the spherically symmetric Schwarzschild metric, we consider specific examples of particle motion in the equatorial plane for (i) circular orbits and (ii) radially infalling trajectories. For the former case we consider the entanglement for a perfectly anti-correlated EPR entangled pair of spins as the separate qubits traverse the circular orbit in same direction.