  In a recent article, Kholmetskii, Missevitch and Yarmin ["On the classical
analysis of spin-orbit coupling in hydrogenlike atoms," Am. J. Phys. 78(4),
April 2010 (428-432)] examine in detail the spin-orbit coupling in the
semiclassical hydrogenic atom, and identify a need to account for non-Coulomb
forces not included in the standard analysis. Kholmetskii, et al., showed that
the experimentally-measured coupling continues to be obtained when the new
forces are incorporated in the analysis. This requires that the change in
orbital radius due to non-Coulomb forces is also properly accounted for. In
response to a comment, Kholmetskii, et al., showed that the
experimentally-measured coupling continues to be obtained when so-called
"hidden momentum" forces are also included. However it has been postulated that
when hidden momentum is nonvanishing, a corresponding hidden energy must also
be present, that was not included in the total energy by Kholmetskii, et al.
Hidden energy is postulated necessary to obtaining a relativistically covariant
description. Inclusion of hidden energy leads to disagreement with the
experimentally-determined spin-orbit coupling magnitude if the Bohr postulate,
that orbital angular momentum is quantized in whole multiples of the reduced
Planck constant, is assumed to apply to kinetic momentum alone. The empirical
result may be recovered in the semiclassical picture and using the general
approach developed by Kholmetskii, et al., if the Bohr postulate is
reinterpreted to apply to orbital angular momentum that consists of hidden as
well as kinetic momentum.
