Ludwig Boltzmann: The Man Who Trusted Atoms

Abstract

Boltzmann is one of the most interesting of the late nineteenth century physicists and is without doubt one of the most important. His work in kinetic theory and statistical thermodynamics laid the foundations for many of the major developments of twentieth century physics and it is a great pity that there are few English language biographies. Carlo Cercignani is Professor of Theoretical Mechanics at the Politecnico di Milano and is well equipped to describe and comment upon Boltzmann's theories - his own research includes applications of the Boltzmann equation. This book is published by OUP and reminds me of Abraham Pais's excellent scientific biographies of Bohr and Einstein (also OUP). In fact I suspect the intention was to conform to the style and standards set by those books. To this end Boltzmann's physics is the centrepiece of the story and subtle technical details are discussed in the main body of the text (albeit with a minimum of mathematics). However, there are substantial appendices in which some of the main results (e.g. the H-theorem) are derived. I am not convinced that this division has been entirely successful since the author seems so eager to get to grips with fine detail that the broad sweep of Boltzmann's ideas is not always clearly explained, and a reader lacking a foundation in statistical thermodynamics will struggle to follow the points being made. However, there is a great deal of interest here and the book is one I am sure I shall return to many times in the future. In fact it is probably more suited for reference than for reading - the author's English style is often rather awkward and some passages are a struggle, but the content and organization are good and there is plenty of exciting physics. The main part of the book begins with a short biography, but the next eight chapters deal with different aspects of his physics. The final chapters discuss his philosophy, his contemporaries and the influence of his ideas on twentieth century developments. There is an amusing postscript which is a translation of Boltzmann's own account of a trip to California: 'A German Professor's Journey into Eldorado'. I couldn't help feeling that the light-hearted self-aware character who wrote this funny little travel story seemed totally different from the character I had been reading about in the rest of the book. But then Boltzmann's suicide in Duino in 1906 also jars and it is obvious that we are dealing with a complex and multi-faceted man, a genius with just a touch of paranoia who was prone to bouts of deep depression. For the reader who has studied statistical mechanics the arguments about irreversibilty and the status of the H-theorem and the second law are fascinating. The comparison of Boltzmann and Gibbs (who gave a more generalized version of some of Boltzmann's results and whose work seems to have been accepted much more rapidly than Boltzmann's) is also interesting. The arguments with Mach and the energeticists are well known but worth reviewing - it is hard to believe that scientists and philosophers can fight so passionately over the status of their ideas; it perhaps helps to explain why so many Austrian intellectuals of that era took their own lives. In fact it has been suggested that the conflict about atoms (whether they are real, as Boltzmann seems to have believed, or merely abstract mathematical models, as claimed by Oswald and Mach) was one of the pressures that drove Boltzmann over the edge in 1906. However, what I found most interesting was reading about the way Boltzmann dealt with continuous energy distributions by introducing a mathematical process of quantization in order to derive his main results. This technique was adopted and adapted by Planck in order to derive the famous formula for the spectrum of black-body radiation, and by Einstein for the photon theory of light. In fact the development of quantum theory seems to have relied on methods first used by Boltzmann some 20 years earlier. This link is explained very clearly. I was also surprised to learn that Boltmann's philosophy of science pre-empted the ideas of Thomas Kuhn, and the author quotes a number of passages that make some of Kuhn's work sound like plagiarism! It is ironic that, as Boltzmann lost hope and hanged himself, Einstein had already published a paper on Brownian motion that established the reality of atoms - the energeticists were about to concede defeat. Boltzmann's discoveries and speculations are startlingly modern and he is without doubt one of the pioneers of the twentieth century revolution in physics. As we approach the twenty-first century this book will go some way toward cementing that reputation.

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