Drunkard's Walk - Leonard Mlodinow [86]
The groundwork for the understanding of Brownian motion was laid in the decades that followed Brown’s work, by Boltzmann, Maxwell, and others. Inspired by Quételet, they created the new field of statistical physics, employing the mathematical edifice of probability and statistics to explain how the properties of fluids arise from the movement of the (then hypothetical) atoms that make them up. Their ideas did not catch on for several more decades, however. Some scientists had mathematical issues with the theory. Others objected because at the time no one had ever seen an atom and no one believed anyone ever would. But most physicists are practical, and so the most important roadblock to acceptance was that although the theory reproduced some laws that were known, it made few new predictions. And so matters stood until 1905, when long after Maxwell was dead and shortly before a despondent Boltzmann would commit suicide, Einstein employed the nascent theory to explain in great numerical detail the precise mechanism of Brownian motion.34 The necessity of a statistical approach to physics would never again be in doubt, and the idea that matter is made of atoms and molecules would prove to be the basis of most modern technology and one of the most important ideas in the history of physics.
The random motion of molecules in a fluid can be viewed, as we’ll note in chapter 10, as a metaphor for our own paths through life, and so it is worthwhile to take a little time to give Einstein’s work a closer look. According to the atomic picture, the fundamental motion of water molecules is chaotic. The molecules fly first this way, then that, moving in a straight line only until deflected by an encounter with one of their sisters. As mentioned in the Prologue, this type of path—in which at various points the direction changes randomly—is often called a drunkard’s walk, for reasons obvious to anyone who has ever enjoyed a few too many martinis (more sober mathematicians and scientists sometimes call it a random walk). If particles that float in a liquid are, as atomic theory predicts, constantly and randomly bombarded by the molecules of the liquid, one might expect them to jiggle this way and that owing to the collisions. But there are two problems with that picture of Brownian motion: first, the molecules are far too light to budge the visible floating particles; second, molecular collisions occur far more frequently than the observed jiggles. Part of Einstein’s genius was to realize that those two problems cancel each other out: though the collisions occur very frequently, because the molecules are so light, those frequent isolated collisions have no visible effect. It is only when pure luck occasionally leads to a lopsided preponderance of hits from some particular direction—the molecular analogue of Roger Maris’s record year in baseball—that a noticeable jiggle occurs. When Einstein did the math, he found that despite the chaos on the microscopic level, there was a predictable relationship between factors such as the size, number, and speed of the molecules and the observable frequency and magnitude of the jiggling. Einstein had, for the first time, connected new and measurable consequences to statistical physics. That might sound like a largely technical achievement, but on the contrary, it represented the triumph of a great principle: that much of the order we perceive in nature belies an invisible underlying disorder and hence can be understood only through the rules of randomness. As Einstein wrote, “It is a magnificent feeling to recognize the unity of a complex of phenomena which appear to be things quite