Regarding Llewellyn Thomas's paper of 1927 and the "hidden momentum" of a magnetic dipole in an electric field

TL;DR

This paper revisits Thomas's 1927 explanation of spin-orbit coupling, emphasizing the importance of including hidden momentum in the electron’s equation of motion, which affects conservation laws and the classical description of atomic phenomena.

Contribution

It demonstrates that neglecting hidden momentum in classical models leads to violations of momentum conservation and challenges the classical explanation of spin-orbit coupling.

Findings

Including hidden momentum restores linear momentum conservation.

Total angular momentum precesses in the presence of Thomas precession.

Classical electrodynamics cannot fully account for spin-orbit coupling without modifications.

Abstract

L. H. Thomas, in his 1927 paper, "The Kinematics of an Electron with an Axis", explained the then-anomalous factor of one-half in atomic spin-orbit coupling as due to a relativistic precession of the electron spin axis. Thomas's explanation required also that the total of the orbit-averaged, or "secular", orbital and spin angular momenta of the electron be a conserved quantity, as he found to be the case for either of two possible equations of translational motion of the magnetic electron. Thomas's finding is seen in the present work to require the "hidden momentum" of the electron intrinsic magnetic moment in the Coulomb field of the proton be omitted from its equation of translational motion. Omission of the hidden momentum is contrary to the position of standard modern electrodynamics texts, and leads to violation of Newton's law of action and reaction, negating Thomas's result. Including the hidden momentum results in linear momentum conservation, but in the presence of Thomas precession, the total angular momentum is not generally conserved. The total angular momentum precesses for non-aligned spin and orbit, even in the absence of externally-applied magnetic field. As Thomas observes that secular angular momentum conservation is a necessary condition for a consistent simultaneous description of spin-orbit coupling and the anomalous Zeeman effect, such is not possible within classical electrodynamics in its absence.