IX
The background has now been presented for Ein-
stein's accomplishments of 1905, which we shall con-
sider in conjunction with the accomplishments of
Poincaré. Along with the later fame of Einstein there
grew a popular mythology correctly attributing the
theory of relativity to him, but seriously slighting the
work of Poincaré. A considerable controversy was
created when Whittaker claimed that the 1905 theory
of relativity was due to Poincaré and Lorentz, with
Einstein playing a negligible role. Whittaker was justi-
fied in seeking to bring the situation into better per-
spective, but in his zeal he went too far, forsaking his
usually impeccable scholarship. This led to a counter-
reaction that has also sometimes gone too far. And
meanwhile the work of Larmor has received less rec-
ognition than it merits.
Maxwell led Larmor, Lorentz, and Poincaré to
mathematical equations identical with equations be-
longing to the theory of relativity. Poincaré had so
many of the crucial ideas that, in retrospect, it seems
amazing that he did not put them together to create
the theory of relativity. He raised aesthetic objection
to the piecemeal, ad hoc patching up of theory to meet
emergencies—Fresnel's entrapped aether to account
for the null results of first order experiments, and the
contraction to account for the second order experiment
of Michelson and Morley—and as early as 1895
Poincaré adumbrated a principle of relativity that
denied the possibility of detecting uniform motion
through the aether. His were the aesthetic strictures
that led Lorentz to seek a transformation to a moving
frame that would leave Maxwell's equations invariant
in form. Since, for example, the Lorentz contraction
factor √1 - v2/c2 reduces lengths to zero when
v = c, Lorentz had limited the application of his 1904
theory to systems moving through the aether with
speeds less than c; it was Poincaré who suggested in
1904 the need for a new dynamics in which speeds
exceeding c would be impossible. And in 1905 he wrote
a major article, sent in almost simultaneously with that
of Einstein, in which extraordinary amounts of the
mathematics of relativity are explicitly developed.
Einstein, in his epoch-making paper of 1905 “On
the Electrodynamics of Moving Bodies,” introduced a
new viewpoint. He began by discussing an aesthetic
blemish in electromagnetic theory as then conceived.
When a magnet and a wire loop are in relative motion,
there is an induced electric current in the wire. But
the explanation differed according as the magnet or
the wire was at rest. A moving magnet was accompa-
nied by an electric field that was not present when
the magnet was at rest and the wire moving. Thus what
was essentially one phenomenon had physically differ-
ent explanations within the same theory.
Because the phenomenon depended on the relative
motion of magnet and wire and not on any absolute
motion through the aether, and because experiments
to detect motion through the aether had given null
results, Einstein postulated as a basic principle that
there is no way of determining absolute rest or uniform
motion—he worded it more technically—and he called
it the principle of relativity, as Poincaré had done.
The phrase was not wholly new with Poincaré. In
1877 Maxwell, in his little book Matter and Motion,
had spoken of “the doctrine of relativity of all physical
phenomena,” which he proceeded to explain in these
eloquent words (emphasis added): “There are no land-
marks in space; one portion of space is exactly like
every other portion, so that we cannot tell where we
are. We are, as it were, on an unruffled sea, without
stars, compass, soundings, wind or tide, and we cannot
tell in what direction we are going. We have no log
which we can cast out to take a dead reckoning by;
we may compute our rate of motion with respect to
the neighboring bodies but we do not know how these
bodies may be moving in space.”
It is surprising that these words should have come
from Maxwell. Not only did he build his electromag-
netic field theory on the concept of an aether but, in
later propounding the idea that led to the Michelson-
Morley experiment, he was envisaging the light waves
that ruffle the ethereal sea as a means for determining
our motion through the aether. It is not clear precisely
what Maxwell had in mind when speaking of the rela-
tivity of all physical phenomena. There is in the phrase
an echo of the views of Berkeley, of which more later.
Perhaps Maxwell was not here regarding the aether
as kinematically synonymous with absolute space. But
later in the book, citing Newton's bucket experiment
and the Foucault pendulum, he specifically contradicts
the “all” by affirming the absoluteness of rotation.
Poincaré's concept of the principle of relativity, like
Einstein's, went beyond what, for convenience, we
have been referring to as the Newtonian principle of
relativity. That principle referred to the impossibility
of detecting one's absolute uniform motion by dynam-
ical means. The new principle, while retaining the
restriction to uniform motion, extended the impossi-
bility to include the use of all physical means, particu-
larly the optical. Yet it is fair to say that in Newton's
time, in the absence of a generally accepted wave
theory of light, the Newtonian principle of relativity
could have been thought of as implying the impotence
of all physical phenomena to detect one's absolute
uniform motion. If so, the Newtonian principle, after
a period of grave doubt as to its validity, was now
being reaffirmed. But, as will appear, its reaffirmation
in the Maxwellian context played havoc with funda-
mental tenets of Newtonian mechanics.
In speaking of the principle of relativity, Poincaré
had an aether in mind. But Einstein declared that in
his theory the introduction of an aether would be
“superfluous” since he would not need an “absolute
stationary space.” Moreover, unlike Poincaré, Einstein
audaciously treated the principle of relativity as a
fundamental axiom suggested by the experimental hints
already available but not in itself subject to question.
Einstein next introduced a second postulate: that the
speed of light in vacuo is constant and independent
of the motion of its source—again he expressed it more
technically. In terms of an aether, this postulate seems
almost a truism. For a wave, once generated, is on its
own. It has severed its connection with the sources that
gave it birth and moves according to the dictates of
the medium through which it travels.
On these two principles Einstein built his theory.
Each by itself seemed reasonable and innocent. But,
as Einstein well realized, they formed an explosive
compound. This is easy to see, especially if, for con-
venience, we begin by talking in terms of an aether.
Imagine two unaccelerated spaceships, S and S′, far
from earth and in uniform relative motion (Figure 3).
In S and S′ are lamps L, L′ and experimenters E, E′
as indicated. Assume that S happens to be at rest in
the aether. E measures the speed with which the light
waves from L pass him and obtains the value c. In
S′ a similar measurement is performed by E′ using light
waves from L′. What value does E′ find? Since the
speed of the light waves is independent of the motion
of their sources, the waves from L and L′ keep pace
with one another. And since S′ is moving towards the
waves with speed v we expect him to find that they
pass him with speed c + v. But the principle of rela-
tivity forbids this. For if E′ found the value c + v, he
could place another lamp at the opposite end of S′
and measure the speed of the light waves in the oppo-
site direction, obtaining the value c - v. By taking half
the difference of these values he could find his speed
through the aether, in violation of the principle of
relativity. Therefore he must obtain not c + v, nor
c - v, but simply c, no matter how great his speed
v relative to S, or indeed relative to any source of light
towards which, or away from which, he is moving.
Viewing this without reference to the aether, we see
from Einstein's two postulates that no matter how fast
we travel towards or away from a source of light, the
light waves will pass us with the same speed c. Clearly
this is impossible within the context of Newtonian
physics. Either we must give up the first postulate or
else give up the second. But Einstein retained both,
and found a way to keep them in harmony by giving
up instead one of our most cherished beliefs about the
nature of time.
