einstein

though it did not help him get an academic job, it did make it possible for him to become known, finally, as Dr. Einstein.
Brownian Motion, May 1905
Eleven days after finishing his dissertation, Einstein produced another paper exploring evidence of things unseen. As he had been doing since
1901, he relied on statistical analysis of the random actions of invisible particles to show how they were reflected in the visible world.
In doing so, Einstein explained a phenomenon, known as Brownian motion, that had been puzzling scientists for almost eighty years: why small
particles suspended in a liquid such as water are observed to jiggle around. And as a byproduct, he pretty much settled once and for all that atoms
and molecules actually existed as physical objects.
Brownian motion was named after the Scottish botanist Robert Brown, who in 1828 had published detailed observations about how minuscule
pollen particles suspended in water can be seen to wiggle and wander when examined under a strong microscope. The study was replicated with
other particles, including filings from the Sphinx, and a variety of explanations was offered. Perhaps it had something to do with tiny water currents
or the effect of light. But none of these theories proved plausible.
With the rise in the 1870s of the kinetic theory, which used the random motions of molecules to explain things like the behavior of gases, some
tried to use it to explain Brownian motion. But because the suspended particles were 10,000 times larger than a water molecule, it seemed that a
molecule would not have the power to budge the particle any more than a baseball could budge an object that was a half-mile in diameter. 32
Einstein showed that even though one collision could not budge a particle, the effect of millions of random collisions per second could explain the
jig observed by Brown. “In this paper,” he announced in his first sentence, “it will be shown that, according to the molecular-kinetic theory of heat,
bodies of a microscopically visible size suspended in liquids must, as a result of thermal molecular motions, perform motions of such magnitudes
that they can be easily observed with a microscope.” 33
He went on to say something that seems, on the surface, somewhat puzzling: his paper was not an attempt to explain the observations of
Brownian motion. Indeed, he acted as if he wasn’t even sure that the motions he deduced from his theory were the same as those observed by
Brown: “It is possible that the motions to be discussed here are identical with so-called Brownian molecular motion; however, the data available to
me on the latter are so imprecise that I could not form a judgment on the question.” Later, he distanced his work even further from intending to be an
explanation of Brownian motion: “I discovered that, according to atomistic theory, there would have to be a movement of suspended microscopic
particles open to observations, without knowing that observations concerning the Brownian motion were already long familiar.” 34
At first glance his demurral that he was dealing with Brownian motion seems odd, even disingenuous. After all, he had written Conrad Habicht a
few months earlier, “Such movement of suspended bodies has actually been observed by physiologists who call it Brownian molecular motion.” Yet
Einstein’s point was both true and significant: his paper did not start with the observed facts of Brownian motion and build toward an explanation of
it. Rather, it was a continuation of his earlier statistical analysis of how the actions of molecules could be manifest in the visible world.
In other words, Einstein wanted to assert that he had produced a theory that was deduced from grand principles and postulates, not a theory that
was constructed by examining physical data (just as he had made plain that his light quanta paper had not started with the photo-electric effect data
gathered by Philipp Lenard). It was a distinction he would also make, as we shall soon see, when insisting that his theory of relativity did not derive
merely from trying to explain experimental results about the speed of light and the ether.
Einstein realized that a bump from a single water molecule would not cause a suspended pollen particle to move enough to be visible. However,
at any given moment, the particle was being hit from all sides by thousands of molecules. There would be some moments when a lot more bumps
happened to hit one particular side of the particle. Then, in another moment, a different side might get the heaviest barrage.
The result would be random little lurches that would result in what is known as a random walk. The best way for us to envision this is to imagine a
drunk who starts at a lamppost and lurches one step in a random direction every second. After two such lurches he may have gone back and forth
to return to the lamp. Or he may be two steps away in the same direction. Or he may be one step west and one step northeast. A little mathematical
plotting and charting reveals an interesting thing about such a random walk: statistically, the drunk’s distance from the lamp will be proportional to
the square root of the number of seconds that have elapsed. 35
Einstein realized that it was neither possible nor necessary to measure each zig and zag of Brownian motion, nor to measure the particle’s
velocity at any moment. But it was rather easy to measure the total distances of randomly lurching particles as these distances grew over time.
Einstein wanted concrete predictions that could be tested, so he used both his theoretical knowledge and experimental data about viscosity and
diffusion rates to come up with precise predictions showing the distance a particle should move depending on its size and the temperature of the
liquid. For example, he predicted, in the case of a particle with a diameter of one thousandth of a millimeter in water at 17 degrees centigrade, “the
mean displacement in one minute would be about 6 microns.”
Here was something that could actually be tested, and with great consequence. “If the motion discussed here can be observed,” he wrote, “then
classical thermodynamics can no longer be viewed as strictly valid.” Better at theorizing than at conducting experiments, Einstein ended his paper
with a charming exhortation: “Let us hope that a researcher will soon succeed in solving the problem presented here, which is so important for the
theory of heat.”
Within months, a German experimenter named Henry Seidentopf, using a powerful microscope, confirmed Einstein’s predictions. For all
practical purposes, the physical reality of atoms and molecules was now conclusively proven. “At the time atoms and molecules were still far from
being regarded as real,” the theoretical physicist Max Born later recalled. “I think that these investigations of Einstein have done more than any
other work to convince physicists of the reality of atoms and molecules.” 36
As lagniappe, Einstein’s paper also provided yet another way to determine Avogadro’s number. “It bristles with new ideas,” Abraham Pais said
of the paper. “The final conclusion, that Avogadro’s number can essentially be determined from observations with an ordinary microscope, never
fails to cause a moment of astonishment even if one has read the paper before and therefore knows the punch line.”
A strength of Einstein’s mind was that it could juggle a variety of ideas simultaneously. Even as he was pondering dancing particles in a liquid, he
had been wrestling with a different theory that involved moving bodies and the speed of light. A day or so after sending in his Brownian motion
paper, he was talking to his friend Michele Besso when a new brainstorm struck. It would produce, as he wrote Habicht in his famous letter of that
month, “a modification of the theory of space and time.”