“Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics.” These are the opening sentences of an excellent textbook, States of Matter (1975), by David L. Goodstein. Somehow the suicide of Boltzmann seems too alluring (lurid) an episode to be left out of either popular or pedagogical accounts of the science of which he was a chief architect. So it is with the book under review here, a lucid and engaging one addressed to the general readership. I am delighted to recommend the slim volume both to the general reader and to teachers and scholars of the physical sciences.
The warp and woof of Eric Johnson's exposition are the extraordinary life of Boltzmann and his monumental scientific achievement. When I first read the title of the book and its opening sentences (“It was an inelegant death. Hanging there. He was a fat man.”), my expectations of the book were not high. Should some readers have a similar reaction, I would urge them to get past that hurdle, because Johnson explains the science commendably, and weaves in Boltzmann's biography with sensitivity and wit. Read on.
It is easy to get the impression from hearing about Boltzmann's suicide that his life was one of unrelieved misery. On the contrary, Johnson's book, and his main source of biographical material, David Lindley's Boltzmann's Atom, make it abundantly clear that Boltzmann was a complex and interesting man. Consider the dinner party hosted in 1905 by Mrs. Phoebe Hearst with Boltzmann as the guest of honor. Says Boltzmann, “At table I sat on Mrs. Hearst's right, as I was the only European present. The first course was blackberries. I declined them. There followed a melon which my hostess had most appetizingly salted for me with her own hands. I declined again. Then came oatmeal, an indescribable paste on which people might fatten geese in Vienna—then again perhaps not, since I doubt whether Viennese geese would be willing to eat it…” and on he goes. Ungracious maybe, but quite funny, as he often was. With a taste for melodrama in art and life, blunt, at times exuberant and vivacious, Boltzmann was also eccentric and caused unintended mirth by his behavior. As a doting father, concerned that his young daughters were not getting good milk, he bought a cow in Graz and marched it through the streets to his house. Able theorist that he was, he knew that milk comes from cows. But he was in the dark as to the experimental procedure by which the substance could be usefully extracted from the animal. So rather than contact the dairyman from whom he bought the cow, he turns to a professor of zoology! Johnson's biographical account, where he goes beyond his sources, is a running meditation on Boltzmann's mental condition. While I enjoyed reading his droll, funny, and kind-hearted speculations, I did not always find his psychoanalytic forays compelling.
It is in his explanation of the microscopic basis of the second law of thermodynamics as Boltzmann's greatest contribution to science that Johnson's work shines. He introduces a simple situation of an auditorium whose left and right halves are the “states.” First there are two people (particles) and hence four microstates of the system, then four particles, and before long many. The reader is led to the results of a large number of particles and a mindboggling number of microstates. Throughout this expository journey, I found the sequencing of ideas were tuned perfectly. Readers of this book are likely to be enlightened as well as entertained. The greatest difficulty in communicating Boltzmann's prime ideas to the general public is explaining how a “mere” statistical law could seem so inviolable. Many great minds in Boltzmann's time, rightly impressed by the majesty and sweep of the newly discovered laws of thermodynamics, could not brook demoting the second law to one of just high probability. Johnson explains and resolves this central conundrum beautifully. Boltzmann's own contribution initially seemed to derive irreversible behavior from reversible microphysics. It was hard to locate exactly where an assumption regarding irreversibility lurked in Boltzmann's original paper, and he did not fully clear up the puzzle in his lifetime. His student, Paul Ehrenfest and Paul's brilliant wife Tatiana, the Russian/Dutch mathematician and physicist, would complete that task a few years after Boltzmann's death. But what Boltzmann clearly understood, and stated forcefully, was how ridiculously low the probability of a violation of the second law would be for a macroscopic system. To any rational mind, a probability such as , say, should obliterate the complacent and formal distinction between what is absolutely forbidden and what is so very improbable. That it did not in the minds of some of his influential contemporaries was a big part of Boltzmann's tragedy. That the lesson is made available to the general reader most effectively is Johnson's triumph.
[Disclosure: While the book was in production, the editor of the press asked me to provide a blurb which I did. I had some email correspondence with the editor, Jermey Matthews. I have not met him, nor am I acquainted with Eric Johnson or corresponded with him. Beyond receiving a free copy of the book for supplying the blurb, and my words and name appearing on the back cover, I have not sought or been offered any compensation or benefit for the task.]
Kannan Jagannathan is a professor of physics at Amherst College. He was trained as a theorist in high energy physics.
