Single-Particle Electrodynamics - Assassination Science

) dependence to extract the three-gradient at t = 0. That this would begin
to blow out the length of the algebraic expressions involved is recognised simply
by considering the combinatorics of the available three-vector quantities.
Nevertheless, the calculations in progress (to one lower of ε than ultimately
required) were completed, for the kinematical expressions listed explicitly in
Chapter 6. From there, the retarded fields of the electric charge only were
expanded to this extra order in ε. This allowed a computation of all of the
radiation reaction effects due to the electric charge fields, since there was
now sufficient orders of ε to compute the gradient dipole forces.
When this was done, the “spin renormalisation” effect, described in Chapter
6, was one consequence. At first, this was perplexing. However, once the
origin in terms of the static fields was clearly understood—and, moreover,
agreement was found between the expression derived from the radiation reaction
calculations and that from first principles—the feeling that the computations
being undertaken were indeed physically correct was cemented.
The results, to this point, had all been extensively cross-checked. All
calculations were carried out twice, at separated intervals. The crucial threevector
Taylor series expressions have a nice consistency check: the quantity
γ(τ) may be computed two ways: from v(τ), or by taking the derivative
d τ t(τ); these results agree. Quantities such as n, n ′ and n ′′ were dotproducted
together, and the results compared with that expected (for example,
n 2 = 1). The high degree of cancellation of a number of the terms
in the integrated results also indicated that the calculations were most likely
sound.
The task of extending these calculations to another order in ε were then
begun. They were carried out—and double-checked—up to the calculation of
n. However, at this point, the combinatorical explosion began to wear down
the author. Simply writing out expressions with more than seventy terms,
with half a dozen or more factors in each, was excessively time-consuming.
Moreover, little insight is required from that point, to the end of the com-
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