  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.
