Single-Particle Electrodynamics - Assassination Science

Lorentz force equation of motion for charged particles works well in a wide
variety of applications; no one would deny its applicability to the real world.
Further than this, one must tread carefully.
In the early days of quantum mechanics, it was commonly stated that the
newly-invented spin degrees of freedom had no classical limit whatsoever.
But accelerator physicists know this to be an exaggeration: the Thomas–
Bargmann–Michel–Telegdi equation of motion [214, 25]—which is a completely
classical equation—describes the precession of spins to a high degree
of accuracy. (Indeed, in the interpretation of the extremely precise measurements
of the magnetic moments of fundamental particles, the Thomas–Bargmann–Michel–Telegdi
equation is generally used as an analytical tool [19].)
Of course, a classical object may indeed possess “spin” angular momentum:
it is simply the angular momentum of the object in its rest frame,
about its centre of energy; it therefore comes as no surprise that a classical
limit should exist. What is surprising, to some, is that this limit exists,
and is entirely valid, even for spin-half particles—the lowest non-zero quantum
of spin possible; in other words, it is not necessary to invoke the “large
quantum number” arguments of the Old Quantum Theory to make contact
with the classical formalism. In fact, one finds that, for a single particle, the
classical spin precession equation describes accurately the evolution of the
three-vector characterising the expectation value of the spin: its “latitude”
describes the ratio of the amplitudes in the “up” and “down” states; and its
“longitude” describes the relative phase between these two amplitudes. The
overall phase of the wavefunction is—as with any reduction to the classical
limit—lost. (See, e.g., [155, App. 1.3] for a thorough and rigorous derivation
of this correspondence.)
But the successes of the Lorentz force law, and the Thomas–Bargmann–
Michel–Telegdi spin precession equation, do not mean that classical equations
of motion may be used carte blanche. One must always recall that there will
be situations in which the wave-packets assumptions fail.
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