On the free rotation of a polarized spinning-top as a test of the correct radiation reaction torque

TL;DR

This paper compares two formulas for radiation reaction torque on a polarized spinning-top, showing that the commonly used Larmor-like formula leads to unphysical results, highlighting the importance of the Schott term in accurate modeling.

Contribution

The paper derives and compares two equations of motion for a polarized spinning-top using different radiation reaction formulas, revealing the physical plausibility of each.

Findings

Larmor-like formula yields unphysical solutions for the spinning-top.

Including the Schott term results in physically plausible behavior.

The Schott term may influence the dynamics of micro- and nanoparticles in nature.

Abstract

The formula for dipole radiation reaction torque acting on a system of charges, and the Larmor-like formula for the angular momentum loss by this system, differ in the time derivative term which is the analogue of the Schott term in the energy loss problem. In the well-known textbooks this discrepancy is commonly avoided via neglect of the Schott term, and the Larmor-like formula is preferred. In the present paper both formulae are used to derive two different equations of motion of a polarized spinning-top. Both equations are integrable for the symmetric top and lead to quite different solutions. That one following from the Larmor-like formula is physically unplausible, in contrast to another one. This result is accorded with the reinterpretation of Larmor's formula discussed recently in the pedagogical literature. It is appeared, besides, that the Schott term is of not only academic significance, but it may determine the behavior of polarized micro- and nanoparticles in nature or future experiments.