Single-Particle Electrodynamics - Assassination Science

3.2 Notions of rigidity
In this section, we briefly review the philosophical assumptions underlying
Galilean (Section 3.2.1) and Einsteinian (Section 3.2.2) notions of rigidity.
3.2.1 Galilean rigidity
The Galilean concept of rigidity—namely, that the three-positions of the
constituents of the rigid body maintain a fixed three-geometrical relationship
with respect to one another, up to three-rotations—clearly is nonsensical in
a Lorentz world: it is not formulated in Lorentz-covariant terms.
There are two ways in which one can view the problem. The first is
to invoke the FitzGerald–Lorentz contraction [87]: as the body’s velocity
increases, the body should effectively “contract” in length along the direction
of its motion. The Galilean model would require extra, contrived forces to
bring about such a contraction.
The second way to view the problem—which the author overwhelmingly
prefers—is to start with a stationary body. According to Galilean mechanics,
a boost by a velocity v of this system does not affect the three-geometrical
relationships between the constituents: they all move coherently, with the
same velocity, and the same separation vectors between them, as when the
body is static. But according to relativistic mechanics, we find that a boost
by velocity v should actually take us into a new Lorentz frame, which mixes
the temporal and spatial components of the original frame. Thus, if the
three-geometry is fixed in one Lorentz frame, then it will not, in general, be
so in another.
The reason that the second way of looking at the problem is preferred by
the author is that the former, “contraction” argument clings somewhat to
the pre-relativistic concept of Newton’s “universal time”: it “measures” the
lengths of objects over a constant-time hypersurface of the measurer, rather
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