Vorticity, Gyroscopic precession, and Spin-Curvature Force

TL;DR

This paper explores the relationship between vorticity and gyroscopic precession across various spacetime metrics, revealing how torsion influences spin-curvature interactions and mimics quantum spin behavior in classical contexts.

Contribution

It demonstrates the calculation of vorticity vectors in different metrics and shows how torsion affects vorticity and spin-curvature force, linking classical and quantum spin phenomena.

Findings

Vorticity vector equals gyroscopic precession angular velocity.

Torsion reverses the sign of vorticity and spin-curvature force.

Classical torsion effects resemble quantum spin properties.

Abstract

In investigating the relation between vorticity and gyroscopic precession, we calculate the vorticity vector in Godel, Kerr, Lewis, Schwarzschild, Minkowski metric and find out the vorticity vector of the specific observers is the angular velocity of gyroscopic precession. Furthermore, considering space-time torsion will flip the vorticity and spin-curvature force to opposite sign. This result is very similar to the behavior of positive and negative helicity of quantum spin in Stern-Gerlach force. It implies that the inclusion of torsion will lead to analogous property of quantum spin even in classical treatment.