Nonlinear effects in Thomas precession due to the interplay of Lorentz contraction and Thomas--Wigner rotation

TL;DR

This paper reveals that the spin vector in an inertial frame experiences dilation rather than contraction due to Lorentz effects, and introduces a corrected vector with nonlinear rotational dynamics involving Thomas precession.

Contribution

It identifies a dilated spin vector and derives its nonlinear equation of motion, advancing understanding of relativistic spin dynamics and Thomas precession effects.

Findings

The spin vector dilates in the direction of velocity.

The correct spin vector differs from the commonly used one.

The equation of motion includes nonlinear rotational terms.

Abstract

It is demonstrated that the 3--vector $\bs{S}$ currently associated to the spin in an inertial frame does not contract, but rather dilates, in the direction of the velocity. The correct vector $\bs{T}$ is individuated. The equation of motion for the two vectors is shown to contain two terms, a common linear rotation, identified with Thomas precession, and also a nonlinear rotation depending on the direction of the spin itself.