Single-Particle Electrodynamics - Assassination Science

the Lorentz force law, in the equation of motion for the particle, in the way
shown in the previous section.
Unfortunately, the incorrect “field mechanical momentum” explanation of
Shockley and James of the Penfield–Haus effect seems to have been accepted
carte blanche, in more recent years, by some authors: by Aharonov and
Casher in their paper on the effect that bears their name [7]; and, even more
recently, in a paper by Aharonov, Pearle and Vaidman [8] that attempts to
make the argument more rigorous. The latter is most unfortunate, because
the main message of the Aharonov–Pearle–Vaidman paper is most definitely
correct (the establishment of the correct law of motion for the current loop;
the fact that this leads to no force in the Aharonov–Casher effect); but their
use of the field mechanical momentum is badly described, and physically
incorrect. They also state that either the Shockley and James argument or
the Penfield and Haus argument may be alternatively chosen to explain the
Penfield–Haus effect: this is not so, of course, since the two arguments deal
with different physical aspects of the system, and so if they were both to be
correct, it would imply an effect twice as large!
Finally, if one wishes to examine a masterpiece of detective work, one
must look at the 1968 paper by Coleman and Van Vleck [55] on the Shockley
and James paradox. This paper establishes, in a most careful and rigorous
way, that there is indeed some amount of mechanical momentum that is
missing. They then employ the Darwin Lagrangian to show explicitly how
the interactions between the charges in the current loop and the external
charge arise. They establish the back-reaction force. They then quote the
Penfield and Haus analysis for the mechanical momentum excess possessed
by the circulating charges. But, most importantly, they do not invoke the
incorrect argument of Shockley and James involving the mechanical field
momentum. Although there are a few comments in the Coleman and Van
Vleck paper, about canonical and mechanical momentum, that the author
does not quite agree with, the bulk of the argumentation deals with the two
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