In 1905, theoretical physicist Albert Einstein (1879-1955) provided an elegant explanation of how tiny, randomly moving molecules could budge particles large enough to be observable under a microscope.
In his paper "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat," Einstein used statistical methods to show that a suspended particle would get shoved in different directions by the combined effect of the modest impacts of many molecules.
For particles smaller than about twenty micrometers in diameter, the impact would generally fail to average out equally on all sides, giving the suspended particle a net shove in some direction.
The erratic jiggling of a microscopic particle suspended in water stems from the uneven distribution of impacts by water molecules at any given moment.
Interestingly, Einstein had not been aware of the experimental work on Brownian motion. His paper came about because he had begun to consider what effects might follow from the existence of atoms and molecules moving at high speeds that depended on the temperature.
His main goal, Einstein later wrote, was "to find facts which would guarantee as much as possible the existence of atoms of definite size." But, he continued, "in the midst of this, I discovered that, according to atomistic theory, there have to be a movement of suspended microscopic properties open to observation, without knowing that observations concerning the Brownian motion were already long familiar."
A few years later, physicist and chemist Jean-Baptiste Perrin (1870-1942) confirmed experimentally some of Einstein's key predictions.
In particular, Perrin and his students were able to track the movements of nearly spherical Brownian particles, which they recorded every thirty seconds and plotted on sheets of paper. Armed with these data, the researchers then used a formula derived by Einstein to determine the number of molecules present in a given volume of fluid.
The experiments gave Perrin a sense of the complexity of the path of a Brownian particle. His plots showed a highly irregular track, yet they gave "only a meager idea of the extraordinary discontinuity of the actual trajectory," Perrin noted.
If the researchers could have increased the resolving power of their microscope to detect the effects of bombardment by progressively smaller clusters of molecules, they would have found that parts of a path that originally appeared straight would themselves have had a jagged and irregular structure.
As the number of steps in a computer simulation of Brownian motion increases from 1,000 (left) to 10,000 (middle) to 100,000 (right), the same overall pattern of erratic movements persists, though on increasingly larger scales. G.M. Viswanathan
In fact, Brownian motion isn't the only place where such self-similar patterns occur.
"Consider, for instance, one of the white flakes that are obtained by salting a solution of soap," Perrin wrote in 1906. "At a distance, its contour may appear sharply defined, but as we draw nearer, its sharpness disappears…. The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification, and we never succeed in getting a sharp, smooth impression, as given, for example, by a steel ball."
Nowadays such patterns, in which the magnified structure looks similar to and just as complicated as the overall structure, are known as fractals. And the paths of Brownian particles can be modeled mathematically as random walks.
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