Single-Particle Electrodynamics - Assassination Science

this can, by writing the computer algebra programs of Appendix G to complete
the radiation reaction computations for him before the termination of
his Ph.D. scholarship (indeed, looking now at the expressions in Appendix G,
before the end of the millenium). He has, however, discovered that this lid
is in fact the base of an even larger can of worms, arising from the final
equations of motion (6.128), (6.129) and (6.130) above. He is informed by
those of wiser years that this is actually a general phenomenon of Nature: as
far as anyone can tell, it’s all worms from here on up.
It would therefore probably be either overly ambitious, or else foolish
(or quite possibly both), for the author to attempt a comprehensive discussion
of all of the issues that arise from a consideration of equations (6.128),
(6.129) and (6.130). Instead, we shall only give here a brief indication of the
successes of these equations, their failures, their questionable aspects, their
complications, and their intriguing properties. We shall also, in the following
section, analyse a simple yet instructive application using just a small subset
of these equations, which will bring their successes and limitations into
starkest relief.
Let us begin with the unquestionable successes of the equations (6.128),
(6.129) and (6.130) (which we shall, for sanity, refer to as simply the “final
equations” for the remainder of this section). Firstly, it will be noted that,
as promised, the electric charge mass term
− 1 2 q2 η 1 ˙v
has the correct coëfficient: in Section 5.5.8 of Chapter 5, we found that
− 1 2 q2 η 1 ≡ m q e.m..
This is in contrast to the incorrect factor of 4/3 in Lorentz’s [137] result,
equation (6.1). Now, it is instructive to note just which aspect of the theoretical
framework used in this thesis repaired Lorentz’s erroneous result.
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