Single-Particle Electrodynamics - Assassination Science

This would seem to imply, by the use of the relativistic centre of energy
theorem, that, for a system of particles, one should have
P ≡ MΓ V , (4.47)
where P is the mechanical momentum of the system as a whole (the sum
of the mechanical momenta of its constituents), M is the mechanical restenergy
of the system, V the velocity of the centre of energy of the system,
and Γ is the gamma factor corresponding to V .
The problem is that this use of the centre of energy theorem relies on the
fact that the system is isolated. For an isolated system, (4.47) is indeed true.
But if the system is not isolated, it need not remain true. For an electric
charge, it is still true. For an electric dipole, it therefore also remains true.
For a magnetic-charge dipole, it still remains true. . . .
The author has stopped his list one short of the end. The problem with
the electric-current magnetic dipole is not that its constituents are electric
charges, but that these constituents are free to move around their constraining
“tube”: they retain one degree of freedom. When the electric-current
magnetic dipole is isolated, it of course still obeys the centre of energy theorem
result (4.47). But when it is in the electromagnetic field of other electric
sources in the Universe, the result (4.47) fails. This was first recognised
by Penfield and Haus [170, 171, 102]. The author shall now outline their
argument, using the formalism and notation of the previous section.
The essential agent of causation in the Penfield–Haus effect is the presence
of an external electric field E whose direction is in the plane of the current
loop (i.e., perpendicular to the magnetic moment µ), at the position of the
electric-current magnetic dipole. The spatial variation of E over the loop may
be neglected; the corresponding corrections vanish in the point limit. Since
our current loop formalism of the previous section is circularly symmetric in
the plane of the loop, we may choose an arbitrary direction, in the x–y plane,
for the direction of the external electric field E: let us choose the positive-y
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