View article

If you sprinkle powdered charcoal on the surface of alcohol and look at it under a microscope, you will see the charcoal particles undergoing a random walk. This motion is due to the alcohol molecules colliding with the larger charcoal grains. This experiment was first reported by the Dutch physician Jan Ingenhausz in 1785, who is best known as the discoverer of photosynthesis. The observed random walk is known as Brownian motion, after its extensive investigation by Robert Brown published in 1828. Brown also is known for making the first observation of a plant cell nucleus. Brownian motion was mysterious in those early days before the existence of atoms was demonstrated, and it was not clear why the Brownian particles should jump seemingly on their own. The eventual explanation came from Albert Einstein in 1905, 1 but he did not refer to it as Brownian motion, because he had not yet seen Brown’s papers. Einstein was able to determine the mean square displacement of a Brownian particle in terms of Avogadro’s number. Jean Perrin won the 1926 Nobel Prize in physics for determining Avogadro’s number in this manner. 2

Since 1905, Brownian motion has became the canonical example of a random process. 3 Actually, Louis Batchelier in his 1900 Ph. D. thesis on stock market fluctuations independently derived several mathematical properties of Brownian motion, including the equation for the probability P (x, t) for the position x of a Brownian random walker at time t, when the walker starts at the origin at time t 0. The equation for P (x, t) in one dimension is given by