Single-Particle Electrodynamics - Assassination Science

In upgrading to Einsteinian mechanics, one finds that the mechanical
energy is in fact given by the expression
W ≡ mγ. (2.3)
Expanding (2.3) as a power series in v, one finds
W = m + 1 2 mv2 + O(v 4 ). (2.4)
The first term in (2.4), m, is referred to as the mechanical rest-energy. The
second term shows that the Galilean result (2.2) is the first correction to the
mechanical energy, i.e., the lowest-order term that has a velocity dependence.
The full mechanical energy, minus the rest-contribution, is often referred to
as the kinetic energy,
W k ≡ m(γ − 1).
The mechanical energy and mechanical momentum in fact constitute a
four-vector in relativistic physics:
p ≡ mU = (mγ, mγv),
where we are applying the notation and conventions of Section A.8.
2.3.3 Forces
As described above, the fundamental concept in Newtonian mechanics is the
force. For a body of mass m, the force due to some outside agent is defined
to be the time rate of change of the mechanical momentum, when the force
in question is the only force applied to the body:
F ≡ d t p. (2.5)
To upgrade from Galilean to Einsteinian mechanics, the only changes
required in (2.5) are that the lab-time derivative is converted into the propertime
derivative, and the left-hand side needs to be given a distinguishing label
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