Brownian Motion and the Reality of Atoms

The Puzzle

In 1827 the botanist Robert Brown watched tiny particles from pollen grains suspended in water and saw them jitter ceaselessly, with no apparent cause. In 1905 it was still possible for serious scientists to doubt that atoms were real. They were a useful bookkeeping device for chemists, but nobody had seen one.

Einstein's Idea

Einstein's paper, received on 11 May 1905, argued that if liquids are made of molecules in constant thermal motion, then a particle large enough to see in a microscope must be knocked about by unequal bombardment from all sides. He worked out exactly how far it should wander.

The answer is statistical. A particle does not travel steadily; its average squared displacement grows in proportion to time, at a rate set by the diffusion coefficient $D$. Einstein then tied $D$ to quantities that can be measured in a laboratory:

Here $T$ is the temperature, $\eta$ the viscosity of the liquid, $r$ the radius of the particle, and $N_A$ is Avogadro's number, the count of molecules in a mole. Watch a particle, time its wandering, and you can count molecules.

The Doctoral Thesis

Less than two weeks earlier, Einstein had finished his dissertation, "A New Determination of Molecular Dimensions." It estimated the size of sugar molecules and Avogadro's number from how dissolved sugar thickens water. It is far less famous than his other 1905 work and far more practical: the result is still used in chemistry and engineering to describe suspensions.

How It Was Confirmed

The French physicist Jean Perrin carried out the experiments around 1908 and 1909, tracking particles under a microscope. The motion matched the theory, and the values of Avogadro's number from several independent methods agreed. That agreement ended the argument about atoms. Perrin received the 1926 Nobel Prize for the work.

What People Get Wrong

• Brown did not see whole pollen grains dancing. He saw far smaller particles released from them.
• Einstein did not prove atoms exist on his own. He supplied a prediction precise enough to test; Perrin's measurements did the convincing.
• He was not the only one on the trail. Marian Smoluchowski reached similar results independently at almost the same time.

Where It Stands

The mathematics of random walks that Einstein used now describes diffusion in cells, noise in electronics, and the movement of prices in financial models. On that last point he was not first: Louis Bachelier had applied the same mathematics to the Paris stock market in 1900.