Einstein on Brownian Motion, by David Cassidy

Adapted from David Cassidy's book, Einstein and Our World.

The Challenge of Heat

At the turn of the century Einstein, by holding to the nineteenth-century ideal of unifying physics on the foundation of mechanics, was in a dwindling minority. Most other theoretical physicists sought unity in one of two nonmechanical alternatives: the so-called energetic and electromagnetic points of view. These alternatives arose from nineteenth-century challenges to the mechanical program in studies of heat and electromagnetism. It was in an effort to reform mechanics and electrodynamics in the wake of these developments that Einstein produced his 1905 works.

The study of the dynamics of heat flow, or thermodynamics, had culminated in two fundamental laws regarding heat. The first law related heat, energy, and useful work to each other in thermal processes. This law could be understood in terms of the motions and collisions of Newtonian atoms. The second law could not. According to the second law, the flowing of heat in natural processes, such as the melting of an ice cube, is always irreversible; that is, heat will not naturally flow of its own accord in the opposite direction—the melted cube at room temperature will not refreeze by itself. How to account for this in mechanical terms?

If, as Newton and others had suggested, all matter consists of atoms (or molecules), then heat is nothing but the energy of motion, or kinetic energy, of the atoms. But, like so many bouncing marbles or billiard balls, all atoms in their microscopic interactions must obey Newtonian mechanics. Those interactions are reversible: a motion picture of a collision between simple atoms will look perfectly normal if it is run backwards in time. So how does the irreversibility of macroscopic events, such as melting ice cubes, arise?

This and other paradoxes encouraged those who, like Ernst Mach, chose to deny the very existence of material atoms. One group, led by physical chemist Wilhelm Ostwald, seeing their chance in paradox, rejected the entire mechanical program, holding the laws of thermodynamics, not mechanics, as fundamental."1 Mechanics required hypotheses about matter and invisible atoms in motion, but thermodynamics referred only to energy and its observed transformations in the everyday world. Because thermodynamic laws were closer to laboratory observations, universal, freed of paradox, and independent of matter, Ostwald and his followers proclaimed the predominance of a new "energetic" worldview: energy and the laws of thermodynamics are the bases for understanding all processes within physical science, and even beyond. Upholders of this view, known as "energeticists," though unable to make much of their position, maintained it even into the depths of World War 1, which they condemned as an enormous waste of energy (to say little of human lives).

Others, of course, held tightly to material atoms. They found support in the work of Maxwell, Rudolf Clausius, and Ludwig Boltzmann, who managed to resolve the reversibility paradox in favor of atoms. The second law of thermodynamics says that most natural processes are irreversible, in contradiction to the Newtonian mechanics of atoms. Boltzmann in particular resolved this contradiction by interpreting the second law as a new type of law: a statistical, not an absolute, law. Since there are so many atoms or molecules, even in a tiny ice cube, it is extremely unlikely—but not impossible—for the myriads of molecules in a melted cube to return in a finite time from the disorder of a liquid to their original orderly, crystalline arrangement. The macroscopic properties of heat and material objects, such as irreversibility, arise from the statistical behavior of numerous mechanical atoms, a behavior to be described by a new "statistical mechanics."

Boltzmann and the American physicist J. Willard Gibbs provided the first accounts of how exactly the second law of thermodynamics arises from the statistical behavior of myriads of randomly moving atoms, Unaware of these writings, Einstein devoted three brilliant early papers during the years 1902 to 1904 to an independent derivation of the second law in the course of developing his own "statistical mechanics," based on atoms and mechanics. Continuing in this work, Einstein used mechanics, atoms, and statistical arguments to achieve what he called a "general molecular theory of heat," confirming that both laws of thermodynamics are, indeed, fully explicable on mechanical grounds.2

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In his doctoral dissertation, submitted to the University of Zurich in 1905, Einstein developed a statistical molecular theory of liquids. Then, in a separate paper, he applied the molecular theory of heat to liquids in obtaining an explanation of what had been, unknown to Einstein, a decades-old puzzle. Observing microscopic bits of plant pollen suspended in still water, English botanist Robert Brown had noticed in 1828 that even tinier particles mixed in with the pollen exhibited an incessant, irregular "swarming" motion — since called "Brownian motion." Although atoms and molecules were still open to objection in 1905, Einstein predicted that the random motions of molecules in a liquid impacting on larger suspended particles would result in irregular, random motions of the particles, which could be directly observed under a microscope. The predicted motion corresponded precisely with the puzzling Brownian motion! From this motion Einstein accurately determined the dimensions of the hypothetical molecules.3

By 1908 the molecules could no longer be considered hypothetical. The evidence gleaned from Brownian motion on the basis of Einstein's work was so compelling that Mach, Ostwald, and their followers were thrown into retreat, and material atoms soon became a permanent fixture of our knowledge of the physical world. Today, with the advent of scanning tunneling microscopes, scientists are nearly able to see and even to manipulate actual, individual atoms for the first time—a circumstance that would satisfy even the most entrenched Machian skeptic.

In the course of his fundamental work on applications of statistical methods to the random motions of Newtonian atoms, Einstein discovered a connection between his statistical theory of heat and the behavior of electromagnetic radiation—the first step toward his hoped-for unification of these two fields. Einstein obtained a mathematical expression for the fluctuations, or oscillations, in the average energy of any system, using his statistical theory of heat. He applied this expression to the average energy of thermal radiation—the electromagnetic waves given off by glowing bodies—in a perfectly reflecting box (often called "blackbody radiation"). He obtained results in close agreement with experimental observations. This connection, he declared in obvious understatement, "ought not to be ascribed to chance."4 For a physicist like Einstein interested in uniting perspectives, the connection provided an extraordinary opportunity. Einstein's fundamental papers on relativity and quantum theory, also submitted in 1905, may be seen as far-reaching explorations of the connection.


1. John T. Merz, A History of European Thought in the Nineteenth Century, 4 vols. (1904-1912), vol. 3, 391; Christa Jungnickel and Russell McCormmach, The Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, 2 vols. (1986), vol. 2, 217-20. BACK

2. Albert Einstein, The Collected Papers of Albert Einstein, ed. John Stachel et al. (1987-), vol. 2, 41-55; Martin J. Klein, "Fluctuations and Statistical Physics in Einstein's Early Work," in Gerald Holton and Yehudi Elkana, eds., Albert Einstein: Historical and Cultural Perspectives (1982); Thomas S. Kuhn, Black-Body Theory and the Quantum Discontinuity, 1984-1912 (1978). .BACK

3.Albert Einstein, Investigations on the Theory of Brownian Movement, ed. R. Fürth, translated by A.D. Cowper (1926, reprinted 1956); Einstein, Collected Papers, vol. 2, 170-82, 206-22. BACK

4. Einstein, Collected Papers, vol. 2, 107. BACK

This text is adapted from David Cassidy, Einstein and Our World (Humanities Press, 1995, reissued Amherst, NY: Humanity Books, 1998). Copyright 1995, 2004 by David Cassidy.

David Cassidy is Professor of Natural Sciences at Hofstra University. He has served as an editor of the Einstein Papers and is author of a number of works in history of physics, including Uncertainty: The Life and Science of Werner Heisenberg (1991) and a related Web exhibit, Heisenberg/Uncertainty.

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