Mathisson's helical motions demystified

TL;DR

This paper clarifies the nature of helical motions in spinning particles in general relativity, showing they are physically meaningful and related to fundamental quantum phenomena like zitterbewegung.

Contribution

It demonstrates that helical motions under the Mathisson-Pirani condition are physically valid, explaining them via hidden momentum and linking their frequency to electron zitterbewegung.

Findings

Helical motions are physically meaningful, not unphysical.

The frequency of these motions matches the electron's zitterbewegung frequency.

Hidden momentum provides a dynamical explanation for the helical motions.

Abstract

The motion of spinning test particles in general relativity is described by Mathisson-Papapetrou-Dixon equations, which are undetermined up to a spin supplementary condition, the latter being today still an open question. The Mathisson-Pirani (MP) condition is known to lead to rather mysterious helical motions which have been deemed unphysical, and for this reason discarded. We show that these assessments are unfounded and originate from a subtle (but crucial) misconception. We discuss the kinematical explanation of the helical motions, and dynamically interpret them through the concept of hidden momentum, which has an electromagnetic analogue. We also show that, contrary to previous claims, the frequency of the helical motions coincides exactly with the zitterbewegung frequency of the Dirac equation for the electron.