Brownian Motion

Abstract

In 1827 the botanist Brown discovered under his microscope vigorous irregular motion of small particles originating from pollen floating on water [1.1]. He also observed that very fine particles of minerals undergo similar incessant motion as if they were living objects. This discovery must have been a great wonder at that time. The idea of combining such a motion — Brownian motion — with molecular motion became fairly widespread in the latter half of the nineteenth century when atomism had not yet been fully recognized as reality. It was, however, the celebrated work of Einstein, which appeared in 1905, that gave the first clear theoretical explanation of such a phenomenon which could be directly verified quantitatively by experiments and thus established the very basic foundation of the atomic theory of matter [1.2]. Einstein did not know that Brownian motion had actually been observed many years before when he first came upon this idea to verify the reality of the atomic concept At any rate, Einstein’s theory had a great impact at that time, finally convincing people of the theory of heat as molecular motion, and so paved the way to modern physics of the twentieth century. It also greatly influenced pure mathematics, that is, the theory of stochastic processes.