Einstein's random walk

By Aussiegirl

A long but very interesting article on Brownian motion -- that's what the illustration is of-- and its importance in the history of physics. Once again we meet Ludwig Boltzmann, whom I've devoted several posts to recently -- and learn how Brownian motion helped prove that atoms are real.
The title is actually a play on words, since according to the relevant Wikipedia article , [i]n mathematics and physics, a random walk, sometimes called a "drunkard's walk," is a formalisation of the intuitive idea of taking successive steps, each in a random direction. Further, [t]he simplest random walk is a path constructed according to the following rules: There is a starting point. The distance from one point in the path to the next is a constant. The direction from one point in the path to the next is chosen at random, and no direction is more probable than another.

Einstein's random walk (January 2005) - Physics World - PhysicsWeb

Einstein's random walk
Author, Mark Haw

The story of Brownian motion began with experimental confusion and philosophical debate, before Einstein, in one of his least well-known contributions to physics, laid the theoretical groundwork for precision measurements to reveal the reality of atoms

Most of us probably remember hearing about Brownian motion in high school, when we are taught that pollen grains jiggle around randomly in water due the impacts of millions of invisible molecules. But how many people know about Einstein's work on Brownian motion, which allowed Jean Perrin and others to prove the physical reality of molecules and atoms?

Einstein's analysis was presented in a series of publications, including his doctoral thesis, that started in 1905 with a paper in the journal Annalen der Physik. Einstein's theory demonstrated how Brownian motion offered experimentalists the possibility to prove that molecules existed, despite the fact that molecules themselves were too small to be seen directly.

Brownian motion is one of three fundamental advances that Einstein made in 1905, the others being special relativity and the idea of light quanta. Of these three great works, Einstein's analysis of Brownian motion remains the least well known. But this part of Einstein's scientific legacy was the key to a revolution that is at least as important as relativity or quantum physics. One century later, Brownian motion continues to be of immeasurable importance in modern science, from physics through biology to the latest wonders of nanotechnology. Indeed, this is reflected in citation statistics, which show that Einstein's papers on Brownian motion have been cited many more times than his publications on special relativity or the photoelectric effect. [....]

Brown is, of course, better known among physicists for the phenomenon of Brownian motion. In the summer of 1827 he began to make microscopic observations of suspensions of grains released from pollen sacks taken from a type of evening primrose called Clarkia pulchella. What Brown saw surprised him: the tiny grains, which were suspended in water, appeared to be in constant motion, carrying out a tireless and chaotic dance. This motion never appeared to slow or stop. Moreover, as Brown verified, it was not caused by external influences such as light or temperature. He also quickly ruled out his first idea - that the grains were somehow alive - by examining grains from inorganic minerals. So, Brown had shown that whatever it was, this incessant dance was not biology after all: it was physics.

For decades the significance of Brown's observations went almost entirely unappreciated. A few scientists returned now and then to the phenomenon, but it was seen as little more than a curiosity. In hindsight this is rather unfortunate, since Brownian motion provided a way to reconcile the paradox between two of the greatest contributions to physics at that time: thermodynamics and the kinetic theory of gases. [....]

It was not until near the end of the 19th century that scientists such as Louis Georges Gouy suggested that Brownian motion might offer a "natural laboratory" in which to directly examine how kinetic theory and thermodynamics could be reconciled. In other words they decided to turn the problem around and use Brownian motion to throw light on the great paradox of the second law. [....]

Today we take atoms for granted, but even as recently as the turn of the 20th century not everyone accepted this "discontinuous" description of matter. Even Boltzmann and Maxwell tended to sit on the fence. Boltzmann described kinetic theory as a mechanical analogy, and Maxwell never expected that his illustrative mechanisms - the pictures that helped him build mathematical theories - would be taken literally. [....]

But Einstein took a different view. He was one of a new generation of physicists who had grown up on a diet of Maxwell and kinetic theory, and therefore saw little reason to doubt the physical reality of atoms. Indeed, by analysing Brownian motion, Einstein set out to obtain a quantitative measure of the size of the atom so that even the most cautious sceptics would be convinced of its existence. [....]

Perrin's group went on to measure the diffusion of the particles, confirming the square root of time law and validating Einstein's kinetic-theory approach. In further experiments over the following five years, Perrin produced a wealth of measurements that could not be contested. Soon enough even Ostwald - the arch sceptic - conceded that Einstein's theory, combined with Perrin's experiments, proved the case. It was official: atoms were real. [....]

From our more distant perspective, it is clear that the Brownian-motion papers of 1905 had just as much influence on science as did relativity or light quanta. Brownian motion was just a slower, subtler revolution: not a headlong charge, but more of a random walk into a vast and unsuspected future.