  Magnetic effects on free electron systems have been studied extensively in
the context of spin-to-orbital angular momentum conversion. Starting from the
Dirac equation, we derive a fully relativistic expression for the energy of
free electrons in the presence of a spatiotemporally constant, weak
electromagnetic field. The expectation value of the maximum energy shift, which
is completely independent of the electron spin-polarization coefficients, is
computed perturbatively to first order. This effect is orders of magnitude
larger than that predicted by the quantum mechanical Zeeman shift. We then
show, in the non-relativistic limit, how to discriminate between achiral and
completely polarized states and discuss possible mesoscopic and macroscopic
manifestations of electron spin states across many orders of magnitude in the
physical world.
