BOLTZMANN’S ATOM: The Great Debate That Launched a Revolution in Physics.

By David Lindley. Free Press. 272 pp. $24

Though they may grasp little of its meaning, most reasonably educated people who encounter the equation E = mc2 immediately think of Albert Einstein. But only true physics aficionados know that the equally illustrious expression S = k log W is inscribed on the grave of Ludwig Boltzmann (1844–1906).

The Viennese theorist’s work marked the transition between two great ages of scientific thought: the classical and the quantum. His formula describes entropy, a measure of disorder. Implicit in the arrangement of the symbols is an explanation of why, as the Second Law of Thermodynamics holds, entropy tends to increase in the universe. Lindley, the author of The End of Physics (1993), provides a lucid account of Boltzmann’s discovery and its implications. By the time readers reach the end, they will have a good idea of what his epitaph means.

In the late 19th century, when Boltzmann was making his mark, physicists knew how to describe a gas using such measures as temperature and pressure. Inject a gas into a container, heat it with a flame or squeeze it with a plunger, and the outcome could be foretold by a collection of seemingly ironclad laws. For many physicists, that was enough. Temperature and pressure were treated as irreducible components of the physical world.

Boltzmann was among those determined to look deeper, to show that temperature, pressure, viscosity, heat conduction, and other qualities were epiphenomena arising from the jostling of invisible specks of matter: molecules and atoms. The motion of each of these tiny objects could, like that of marbles or billiard balls, be described by simple laws of mechanics. But because there were far too many individual trajectories to track, their mass behavior had to be treated statistically using the mathematics of probability. First, though, one had to believe in atoms—and the only evidence for them seemed to be that positing their existence made the theories work. Skeptics, led by the physicist/philosopher Ernst Mach, denounced the "atomists" and the statistical magicians for straying into metaphysics.

Boltzmann ultimately prevailed by showing that his approach could explain the Second Law. Given a collection of atoms or molecules, there are vastly more disorderly arrangements than orderly ones. So it was most likely that, without outside intervention, order would give way to entropy. Before long, almost everyone believed in atoms, and statistical methods became an important tool in the development of quantum mechanics. More significantly, Lindley shows, the constricting Machian philosophy—rejecting any phenomenon that could not be directly perceived by human senses—gave way to the rigorous creativity of modern physics.

Boltzmann wasn’t content with his accomplishment. Plagued by depression and still surrounded by doubters, he hanged himself at age 62. Though his fate may sound romantically tragic, his dyspeptic, neurotic manner keeps him from being a very sympathetic character. But the unfolding of his ideas, rendered so well by Lindley, makes for a very absorbing story.

—George Johnson