THE NEW KINEMATICS 145which is an immediate consequence of Eq. 7.9: let y, = c/n, v 2 = v and
expand to the first order in vlv 2 /c^2. I find the absence of this derivation in the
June paper more remarkable than the absence of any mention of Michelson
and Morley. The labor involved is not excessive, the Fizeau experiment had
been very important for Einstein's thinking, and a successful aether-free der-
ivation might have pleased even a man like Einstein, who was not given to
counting feathers in his cap. The honor of the first derivation (in 1907) goes
to Max von Laue, who pointed out that 'according to the relativity principle,
light is completely dragged along by the body [i.e., the streaming fluid], but
just because of that its velocity relative to an observer who does not participate
in the motion of the body does not equal the vector sum of its velocity relative
to the body and [the velocity] of the body relative to the observer' [LI]. As was
noted in Chapter 6, for small v/c it is possible to derive Eq. 7.13 by means of
a dynamic calculation that does not explicitly involve relativity [P5]. The
kinematic derivation just given does not mean that such a calculation is incor-
rect, but rather that it is not necessary. Lorentz invariance suffices to obtain
the desired result.
g) Einstein rather casually mentioned that if two synchronous clocks G, and C 2
are at the same initial position and if C 2 leaves A and moves along a closed
orbit, then upon return to A, C 2 will run slow relative to C,, as often observed
since in the laboratory. He called this result a theorem and cannot be held
responsible for the misnomer clock paradox, which is of later vintage. Indeed,
as Einstein himself noted later [E6], "no contradiction in the foundations of
the theory can be constructed from this result" since C 2 but not C, has expe-
rienced acceleration.
h) Covariance of the electrodynamic equations. Using a horrible but not uncom-
mon notation in which each component of the electric and magnetic field has
its own name,* Einstein proved the Lorentz covariance of the Maxwell-
Lorentz equations, first for the source-free case, then for the case with sources.
He also discussed the equations of motion of an electrically charged particle
with charge e and mass m in an external electromagnetic field. In a frame
(x,t) in which the particle is instantaneously at rest, these equations are
Applying the transformations (Eq. 7.8), he found that in a frame with velocity
v in the x direction:- Hertz, Planck, and Poincare did likewise. Lorentz used three-vector language.