One of those who missed a Nobel

In the early days of 20th-century physics, Dutch physicists played a leading role in deciphering the enigmas of quantum mechanics and relativity. Dutchmen such as Hendrik Antoon Lorentz, Pieter Zeeman and Kammerlingh Onnes all won Nobel prizes for their pioneering contributions - but another eminent colleague, Hendrik Anthony Kramers, did not. In this book, one of Kramers's former research students, Dirk ter Haar, attempts to make a case for Kramers, being counted amongst the great theoretical physicists of the first half of the century. Certainly, as ter Haar says, Kramers was one of the last physicists able to master essentially all of physics and to make significant contributions to many different fields. Physicists still speak of the Kramers opacity formula, the Kramers dispersion theory, the Kramers-Kronig relations, the Kramers degeneracy, the WKB approximation and even the Kramers problem. For most physicists this would be recognition enough, but ter Haar argues that Kramers deserves consideration on a par with Nobel prize winners such as Werner Heisenberg (who regretted that Kramers was not recognised by the Swedish Academy) and Paul Dirac - physicists credited, respectively, with laying the foundations of non-relativistic and relativistic quantum mechanics.

This book suggests that the relative obscurity of Kramers is due, at least in part, to Kramers's hesitancy to publish anything not of the highest standard. After a commentary and overview by ter Haar, 12 of Kramers's papers are reprinted in this volume. A major purpose of this book is to bring his scientific work to the attention of present-day physicists. However, to a large degree the motivation for it appears to be the publication of a recent biography of Kramers by Dresden: in the opinion of ter Haar, Dresden places too much emphasis on Kramers's "near misses".

Unfortunately, this book proves to be a frustrating read in that it makes no attempt to be self-contained. Not many present-day physicists study the historical rights and wrongs in the development of theoretical physics, and it is a pity to be presented with such an uncompromisingly academic book, its opening pages littered with footnotes.

Although the avowed intent of this work is an analysis of Kramers's scientific work, it is irritating not to be given anything more than an occasional glimpse of Kramers the man. Fellow Dutch physicist Abraham Pais, in his classic scientific biography of Einstein, blends analysis, biography and anecdote to create a much more absorbing read. Indeed, in his recent autobiography, Pais reveals far more about Kramers as a person than we find here - resigning from the Royal Dutch Academy of Sciences in protest against the exclusion of Jews; maintaining a dialogue with Pais during his time in hiding from the Nazis; writing to Heisenberg asking him to intercede when Pais was captured. Despite being an excellent mathematician, Kramers also warned Pais against an undue reverence for mathematics:

"Mathematics should forever be an unrequited love to the physicist, like a woman worshipped from afar." In ter Haar's book, almost the only personal note about Kramers is relegated to a footnote: "I am convinced that, if the actual numerical calculations had not been made by a young research student, whose first publication this paper was to be, Kramers would never have published this purely academic exercise." The grateful student was ter Haar.

Despite these shortcomings, there is much of interest in this account of Kramers's work. For example, ter Haar claims that Kramers not only independently noted the connection between Poisson brackets and quantum mechanics, usually credited to Dirac, but also independently invented the Dirac equation for a relativistic electron. Furthermore, Kramers was apparently dissuaded from publishing a paper, predicting what is now known as the Compton effect, by the great Danish physicist, Neils Bohr. Working as Bohr's right-hand man clearly helped Kramers enormously - but on this occasion Bohr's antipathy towards photons, coupled with his force of character, contributed to one of Kramers's "near misses".

There is one further aspect of Kramers's work that deserves comment. In attempting to explain why Kramers's textbook on quantum mechanics was not more widely used, ter Haar refers to his "uncompromising style" with "no spoon-feeding". But even a former research student of Kramers, van Kampen, refers to a typical Kramers paper as "containing many gems, but as a whole somewhat confusing". What finally convinced me that ter Haar and I do not share the same ideas about communication is his endorsement of "Herzberg's monumental textbook" on molecular spectra - a book I thought deeply obscure. Thus, although ter Haar's book undoubtedly represents a valuable and thoughtful assessment of Kramers's scientific work, I fear it will make little progress towards its stated goal of remedying the ignorance of most present-day physicists about Kramers.

Tony Hey is professor of computation, University of Southampton.