31 March, 2015Issue 27.6MathematicsScience

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Scientia Gratia Scientiae

Robert Thomas

A.R.P. Rau
The Beauty of Physics
Oxford University Press, 2014
£25 (hardback)
240 pages
ISBN: 9780198709916

“It is,” wrote G. H. Hardy in beginning A Mathematician’s Apology, “a melancholy experience for a professional mathematician to find himself writing about mathematics.” Hardy maintained that it was the essential business of the mathematician, as for the physicist, to do and to create, and he preferred to leave criticism and appreciation to “second-rate minds”. In his pamphlet, however, he nonetheless presents a robust defence of the study of pure mathematics on its aesthetic merits, far beyond—indeed, in defiance of—any perceived utility. Melancholy he may have found it, but Hardy’s little tract established him as something of a lodestar for the school of scientia gratia scientiae, and his unwavering dedication to his subject and resolve to deploy his abilities to their fullest extent have proven a rich source of inspiration to many of those who have followed after him.

A.R.P. Rau’s The Beauty of Physics is not cast from quite the same mould as Hardy’s Apology; the practical purposes of physics, as Hardy himself pointed out, are rather more tangibly apparent than those of pure mathematics, and Rau can thus afford to be more champion and evangelist than apologist. Nevertheless, that physics is in need of a champion can hardly be in doubt. Where once it might have occupied the same place in the collective consciousness as pure mathematics, the triumphs of physics in the twentieth century—from the dawn of the nuclear age to the exploration of space—have brought with them controversies, and tragedies, which have left a stain on the subject in the public imagination.

In reminding the reader that “the beauty of physics lies in its coherence in terms of a few fundamental concepts and principles”, and allowing himself “to marvel at the overarching reach” of those principles, Rau offers a persuasive vindication to those he seeks to convince, and a fresh vantage point for those already converted. At some level, then, the comparison between his and Hardy’s projects is borne out: both are subjective reflections from esteemed contributors to their respective fields, both seek to stress the aesthetic qualities of their subjects over their mere utility, and both attempt to provide meaningful yet accessible perspectives for the non-specialist reader.

This last aim is an ambitious one, for writers of popular science must perform a difficult balancing act. Too much “science” risks making for a daunting and off-putting read, whilst too “popular” a tone renders the exercise self-defeating, sometimes more akin to romantic fiction than scholarly exposition. Refreshingly, Rau errs firmly on the side of “science”, and does not shy away from some of the more salient technical details of the topics at issue. Indeed, he is to be commended for the inclusion, in outline at least, of elucidations of the key mathematical concepts and formalisms which compose the physicist’s standard repertoire. As Richard Feynman well knew, “it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature” without some exposure to mathematics; Rau’s engaging explanations lift the veil on this too much shrouded beauty.

The Beauty of Physics, then, requires rather more than a casual glance from the interested layman if its high purpose is to be fully realised. Maxwell’s equations, Green’s theorems, and the tenets of the special theory of relativity all appear in the first chapter and, whilst these are all familiar to working physicists, they may present something of a challenge to those from different backgrounds. Certainly, a comprehensive appreciation of Rau’s argument requires some facility, if by no means fluency, with linear algebra and elementary calculus—not, it is fair to say, typical prerequisites for works of broad appeal. Its principal beneficiaries are therefore likely to be physicists—as Rau himself admits—but the book will have particular resonance for undergraduates and advanced school pupils keen to engage with the latest and most exotic ideas and problems to which their present endeavours might be leading.

Despite these necessary challenges, Rau’s explicit claim to address not only physicists, but also “the intellectually curious reader in other sciences and even outside the sciences and mathematics” is justified. The more advanced mathematical material is highlighted and separated in shaded boxes which the reader can omit if so inclined, and Rau’s style is, while not entirely pedagogical, clear and explanatory throughout. Indeed, it is testament to his rich command of his subjects that he can engage and include the non-specialist without provoking the pedantry of his more knowledgeable readers.

One of the chief strengths of The Beauty of Physics is that, despite its formal division into sections and subsections, it is not a textbook. Indeed, there is a great deal to be gained in reading it from start to finish, in order, following on the journey where Rau leads. Each new topic is introduced by means of widely familiar but pertinent examples, and proceeds via a deft use of metaphor and analogy to deliver the reader smoothly to the heart of some of the most pressing questions and concerns in that area. His discussion of symmetry, a subject of which a great many would claim some knowledge, but whose subtleties often prove a stumbling block for students in their early encounters, is particularly skilful. Rau employs examples as disparate as the structure of viruses and snowflakes, and the musical palindrome of Bach’s Musikalisches Opfer, to illustrate his initial discussions, equipping his reader for a rather compelling if rapid excursion through the rudiments of the mathematical machinery required for the systematic study of symmetry. The reader’s perseverance with these technicalities is rewarded with an overview of some of the most topical and widely-reported problems facing physics this century, from the acquisition of a theoretical understanding of the “fine-structure constant” to the broader implications of “spontaneous symmetry breaking” for general relativity and quantum mechanics.

Rau’s technique lends itself no less adeptly to conveying the notion of physics as Nature’s means of “expressing its underlying reality” and beauty. His section on “States and Transformations”, for example, succinctly summarises some of the quantum-theoretical language of operators and wave functions, whilst at the same time reflecting more broadly on the implications of the dual “wave-particle” picture of Nature, and extolling “the virtue of seeing the world from different points of view.” In so doing, Rau frames the study of physics as a captivating adventure, whose fields—as with the broader thrust of intellectual inquiry—seek to “capture some essence, together getting closer to a full comprehension.” He presents a subject as dependent upon new thinking as it is upon accumulated wisdom, as one in which “revolutionary upheavals” co-exist with a “persistence of the old”, painting an accurately—and attractively—dynamic picture of science.

That the “essence” which physics captures is undeniably beautiful is asserted with a vigour which nonetheless never strays into dogma. Many will remember school-room physics as a bewildering collection of laws and equations, but in “Complexity and Emergence”, Rau ably demonstrates the essential correspondence and coherence between the more familiar classical descriptions of reality and the famously counter-intuitive pictures of quantum mechanics. His argument is not merely couched as a facile appeal to parsimony, or even to the apparent harmony of the established laws, and in his description of the challenges and questions which are still to be faced and answered, Rau shows that the chief beauty of physics arises from its perpetual engagement with mystery and wonderment, from its revels in the unknown and not-yet-understood.

It is to the esoteric glory and grandeur of quantum theory which the majority of Rau’s discussions turn in finale. This corresponds, of course, to the central position which that theory occupies in the whole of science, but also highlights that Rau’s discussions are deeply personal reflections, born of his background as an atomic physicist and quantum-information scientist. The willingness to include such subjective perspectives and analyses is to Rau’s credit. His genuine fondness and enthusiasm for his subject will prove arresting for aspirant scientists and others alike, and his balance of technical detail and broad, affectionate overview provide a heartening demonstration of the principle that romance need not be lost at the expense of nuanced and considered argument.

These personal perspectives, coupled with Rau’s impressive poise in style and tone, ensure that The Beauty of Physics is not only accessible, but of rewarding interest and relevance to the broad audience which he seeks to address. It has often been remarked that there exists something of a gulf between those with a knowledge of the sciences and those without: this book represents a valiant attempt at bridging that divide. For the physicist, Rau provides a lucid and at times reverberant reminder of the essential elegance of his subject, while the interested non-specialist might consider approaching this work as a metaphor for endeavour in physics itself. It may seem to present an uncompromising challenge, but if one is prepared to read with an engaged and open mind (and a pencil and paper at the ready), the rewards are there for the taking, and in abundance.

Robert Thomas is reading for a PhD in quantum theory at Trinity College, Cambridge.