Single-Particle Electrodynamics - Assassination Science

5.5.14 Particle with all three moments
As noted in Secion 5.5.7, the nonlinearity of the mechanical field density expressions
(5.94), (5.95) and (5.96) means that we have to consider separately
the cases of all possible combinations of the three electromagnetic moments of
interest to us (charge, electric dipole moment, and magnetic dipole moment).
In Sections 5.5.8, 5.5.9 and 5.5.10, we considered the ( 3 1) = 3 combinations
of moments taken singly (q, d and µ); and then, in Sections 5.5.11, 5.5.12
and 5.5.13, the further ( 3 2) = 3 combinations of moments taken doubly (dµ,
qµ and qd). It therefore only remains for us to consider the ( 3 3) = 1 way of
taking all three moments triply (i.e., qdµ).
This remaining task is, however, rendered trivial by virtue of the fact
that the mechanical field density expressions (5.94), (5.95) and (5.96) are
all quadratic in the fields of the particle: if we insert into them the sums of
the fields from the three types of moment, the terms that will result from
an expansion via the distributive law will contain the fields of the moments
either taken pair by pair, or else quadratically in the field of a single moment;
and hence the results for the triply-momented particle are, in fact, the
superpositions of corresponding results found in Sections 5.5.8, 5.5.9, 5.5.10,
5.5.11, 5.5.12 and 5.5.13.
We shall, for conciseness, refer to this general propery of quadratic expressions
by the term pairwise superposition; the mechanical field self-densities
are thus pairwise superposable.
5.5.15 The relativistic worldline fields
Finally, we consider the problem of obtaining the correct contribution to the
retarded field expressions on the worldline of the generating point particle.
From the analyses of the previous sections, we know that, even for a static
particle, the dipole moments have a somewhat subtle behaviour at the position
of the particle. The question then arises: how are these results modified
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