Single-Particle Electrodynamics - Assassination Science

6.8.4 Duality symmetry considerations
By considering the duality of the fields generated by an electric and a magnetic
dipole moment, and the force expressions for these moments,—excepting
the extra Maxwell magnetic field contribution, and the contact force, for
a magnetic dipole,—it is clear that, apart from these exceptions, the selfinteractions
between d and µ will cancel. (This, of course, relies on the
assumption that the two moments are parallel, as is the case for spin-half
particles.)
The extra magnetic dipole moment contributions are considered in Sections
6.8.7 and 6.8.8.
6.8.5 Constituent spin derivative
Clearly, at t = 0, the time rate of change of the spin of the constituent r,
namely, ˙σ r (0), will be related to that of the body as a whole by means of the
chain rule:
d tr σ r | t=0
≡(d tr τ)(d τ σ r )| t=0
≡(d τr τ)(d τ σ)| t=0
≡d τr τ| t=0 ˙σ.
But d τr τ is just the reciprocal of the accelerative redshift factor λ(r) ≡ d τ τ r ;
thus,
˙σ r (0) = 1
λ(r)
˙σ. (6.120)
(This may also be obtained, as an expansion in t, from the expression (3.24);
but the result (6.120) is of course exact.)
In practical terms, the result (6.120) is implemented by simply replacing
the factor ˙σ that appears in each constituent force law of (6.116) by ˙σ of
the body as a whole; the factor of 1/λ(r) “cancels out” the factor of λ(r)
inserted to compute the correct power, force and torque on the body as a
whole.
(This latter phenomenon can be understood in simple terms, by recognising
that the factors of λ appearing in the power, force and torque expressions
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