MARGINALIA
Lost in Einstein's Shadow
Einstein gets the glory, but others were paving the way
Tony Rothman
Now that the worldwide celebrations marking Einstein's miraculous
achievements of 1905 are over, let's take a moment to light a candle
to the runners-up, those poor fellows who were hot on Einstein's
heels, who almost got it right and perhaps would have, but who've
been lost in the shadow of his great triumphs. It is true; Einstein
was not the only person at the turn of the last century thinking
about molecules and relativity. What's more, he was up on much of
their work and, like any scientist, stood on the shoulders of his predecessors.
Tell Me It Ain't So
The central fixture of Einstein lore is that the lowly patent clerk
conjured from pure thought not only his theories but also the
questions they answered. Not quite: Einstein himself helped foster
this myth (more through carelessness than design, one suspects) by
being less than fastidious about providing references in his papers,
and since then credulous scientists have equated absence of evidence
with evidence of absence. Physicists are notorious for taking
history on faith, but none is required to prove this point—the
evidence is in plain sight if one cares to look. The papers of
Einstein and his contemporaries, as well as Einstein's letters, are
published. Anyone who reads them quickly realizes that Einstein had
a very good sense of the currents of science swirling about him and
once or twice relied on the insights of colleagues.
Take the Australian William Sutherland, for example. One of
Einstein's great 1905 papers explained "Brownian motion,"
the random jiggling of microscopic pollen grains suspended in water.
Einstein proposed that the movements were due to collisions between
the pollen and invisible water molecules and inferred from this the
size of the molecules themselves. In doing so, he provided one of
the final "proofs" of the existence of molecules, which in
1905 was still debated.
Sutherland was also interested in the motion of small particles
suspended in liquids. In 1904, he proposed to the Australian
Association for the Advancement of Science a method to calculate
their mass. In March 1905—at exactly the time Einstein was
working on his own paper—Sutherland submitted an improved
version of his idea to the Philosophical Magazine, the
leading English-language scientific journal of the day. It was
published in June. In this paper, Sutherland derives the
"diffusion coefficient," a number giving the rate at which
particles move through a liquid. Moreover, he does so by exactly the
same argument Einstein gives and arrives at exactly the same answer.
Einstein goes on to use this number to derive the well known
"diffusion equation." It tells him how far the particles
will move in a given time, depending on the size of the surrounding
molecules. A stopwatch and a microscope then allow him to measure
molecular dimensions.
So, yes, Einstein went further than Sutherland, but Sutherland got
one of the two crucial steps first. From letters to Einstein from
his best friend, engineer Michele Besso, we know that the two men
showed keen interest in Sutherland's work through 1903. After that,
the discoveries were certainly independent.
In any case, a Frenchman, Louis Bachelier, scooped both Sutherland
and Einstein. Bachelier was not actually interested in the twitching
of suspended pollen grains. He was interested in the motion of
prices on French stock market. But prices on the Bourse bounce
around like pollen in water and their "random walk" can be
treated mathematically like the diffusion of pollen in a liquid,
which is exactly what Bachelier did in his remarkable 1900 doctoral
thesis, "The Theory of Speculation." His paper is full of
the jargon of economists, but Bachelier's equation giving the drift
of prices with time is identical to Einstein's for pollen. Bachelier
anticipated the Black-Scholes approach to options trading (which
garnered its authors the 1997 Nobel Prize in Economics) and has been
crowned by modern economists the "father of mathematical
finance." Back then, though, academia ignored him, and it would
be surprising if Sutherland or Einstein had heard of him.
Of course, 1905 is remembered above all for relativity. As a result
of a famously vague statement in Einstein's own paper about
"unsuccessful attempts to detect the motion of the Earth
relative to the 'light medium'," pundits have long held that he
was only dimly aware of the celebrated experiments that failed to
reveal the mysterious medium—the ether—whose existence
was synonymous with the "absolute space" implicit in
classical physics. That is, sound waves travel in air, water waves
travel in water; physicists naturally assumed that light required a
medium in which to travel—the ether. The trouble was, a whole
series of experiments designed to detect it turned up empty handed.
It was these negative results that eventually led to relativity.
Did Einstein know about the vigorous search for the ether? Well, in
an 1899 letter to his fiancée, Mileva Maric, Einstein
mentions that he's written to renowned physicist Wilhelm Wein about
Wein's review of the ether experiments, and that he's anxiously
awaiting a reply. Einstein also read an 1895 paper in which Hendrik
Lorentz (independently of two others) postulated his famous
"Lorentz contraction"—that objects moving at high
speeds actually shrink. That paper was all about the ether
experiments, and Lorentz introduced the contraction precisely to
explain their failure.
Lorentz was no amateur. The Dutchman was considered the leading
physicist of his generation, and soon he and his colleagues were
waging a well-published attack on the hypothetical ether and all its
difficulties. In 1904 Lorentz tried to fix everything with his
celebrated "transformations" that mixed up space and time
in a way that—if true—would leave Maxwellian
electromagnetic theory intact but shake the foundations of Newtonian physics.
Lorentz didn't know why his transformations should be correct. With
relativity Einstein provided the explanation, but shortly before his
death, he claimed to have known only about Lorentz's 1895 paper, not
the later one containing the transformations. Memory is often too
good to be true. In Einstein's very paper of 1905 he says, "we
have thus shown that ... the electrodynamic foundation of Lorentz's
theory ... agrees with the principle of relativity." This
appears to be a direct reference to Lorentz's 1904 work.
Principle of Relativity
Einstein didn't call his creation "the theory of
relativity," but it was indeed based on two postulates, the
first being the "principle of relativity," the supposition
that any experiment done on a train moving with constant velocity
should give the same result as an identical experiment done on the ground.
It wasn't Einstein's idea. The great French mathematician Henri
Poincaré enunciated the principle of relativity at least as
early as 1902 in his popular book Science and Hypothesis.
We know from Einstein's friend Maurice Solovine that the two pounced
on Poincaré's book, indeed that it kept them "breathless
for weeks on end." It should have. In Science and
Hypothesis, Poincaré declares: "1) There is no
absolute space, and we can only conceive of relative motion; 2)
There is no absolute time. When we say that two periods are equal,
the statement has no meaning; 3) Not only have we no direct
intuition of the equality of two periods, but we have not even
direct intuition of the simultaneity of two events occurring in two
different places."
These ideas lie at the heart of relativity, and it is hard to
imagine that they did not have a profound effect on Einstein's
thinking. But Poincaré not only speculated—he
calculated, and in the same weeks that Einstein was writing his
paper on relativity, Poincaré completed a pair of his own.
The major one is quite remarkable. Mathematically, he has more than
Einstein does. Among other things, he notes that time can be viewed
as a fourth dimension (something Einstein doesn't do, by the way),
he predicts the existence of gravitational waves 10 years before
Einstein does and, perhaps most remarkable of all, he writes down an
expression exactly equivalent to E = mc
2 several months before his rival. But he fails to
interpret it.
Poincaré's paper, alas, is that of a mathematician. Right at
the start he sets the speed of light equal to a constant, "for
convenience." The second, and revolutionary, postulate at the
basis of Einstein's relativity is in fact that the speed of light is
always observed to be the same constant, regardless of the speed of
the observer. Perhaps if Poincaré had been less a brilliant
mathematician and more a dumb physicist he would have seen that the
whole edifice stands or falls on this
"convenience." He didn't.
Not long ago I had the opportunity to give a colloquium on these and
related matters at a major university. Among the 50 or so physicists
in the audience, not one had read Einstein's original papers, yet
alone Poincaré's. As I said, physicists are notorious for
taking history on faith. Such insouciance, though, has not stopped
physicists from repeating for several generations the usual
platitudes about the history of their field. One might make a case
that science is inherently anhistorical—certainly recent
editions of undergraduate physics texts are entirely bereft of
meaningful history. But if the history of science has any relevance
to the doing of it, surely it is to remind us that science is a
collective enterprise and to engender in us a humble awareness that
the landscape of science would appear very different had the vast
unrecognized majority never existed.