Single-Particle Electrodynamics - Assassination Science

time τ. Finally, in Section 3.3.6, we define the spins of the constituents of
the body in terms of the spin of the body as a whole.
3.3.1 What is a “constituent”?
If we consider a body which has some finite three-geometry in its rest frame,
we need to have a way of describing the parts of the body making up the
whole. We shall call these the constituents of the body.
If a body is constructed from discrete constituents, then we can name
them individually, and thereafter refer to them by name; but if the body is
(as it will be for the considerations of this thesis) formed from a continuum of
constituents, then we need some other way of identifying them individually.
Consider the body in its instantaneous rest frame. Let us place the mechanical
centre of energy of the body at the origin of coördinates. We can
then identify any constituent by its relative three-position, r, in this rest
frame.
It may seem that we should really be talking about not a single point
at the position r as a “constituent”, but rather a small elementary volume
surrounding the position r, since, rigorously speaking, a mere point in a uniformly
distributed region does not actually contain anything. But we do not
particularly care that the “point” contains “nothing”, since we know that we
shall, ultimately, be integrating over an infinite number of “points”,—which
does yield “something”; these are simple concepts of elementary calculus.
Thus, we shall continue to refer to the point r as “a constituent”; the reader
may, if they like, place a solid stone at this point if they feel the conceptual
need to do so.
We shall also consider the three-vector r to serve as a suitable name for
the constituent at the point r. For example, we shall refer to “the constituent
r”, as if “r” were a name like Tom or Dick. This will avoid an unnecessary
amount of circumlocution in the remainder of this thesis. Mathematical
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