Review of Treiman's 'The Odd Quantum' 
  published in Contemporary Physics

A Tradition of Excellence

The tradition of 'popular science' writing extends over more than 200 years. The definitive second edition of Thomas Young's Royal Institution Lectures on Natural Philosophy and the Mechanical Arts was published in 1807, edited by the mathematician, P. Kelland.  In his preface Kelland compared Young favourably with "other popular science writers", implying that popular science writing was already an established field.   Thirty-five years later Sir David Brewster aimed his biographies of The Martyrs of Science at a lay public in an age

when Science constitutes the power and wealth of nations, and encircles the domestic hearth with its most substantial comforts.

In 1892 Hermann von Helmholtz's first series of popular Lectures on Scientific subjects was published, and was reprinted twice in the next five years - clear evidence of public demand for such works.

The next 40 years, leading to the second world war, saw the emergence of a new type of popular science book, written to introduce a general (and in particular non-mathematical) readership to specific topics in science or technology.   In this category Sir James Jeans's Science and Music (1923) became a classic.   Sir Arthur Eddington's Space, Time and Gravitation (1923) and The Nature of the Physical World (1928), were also very successful.   The first aimed to introduce to the public some of the implications of general relativity, and the second to spread the author's revolutionary ideas on the possibility of arriving at the basic laws of physics by pure thought unaided by experiment.   Other popular science books of this period - also by outstanding scientists - were Sir W H Bragg's The World of Sound (1929) and his son Sir Laurence Bragg's The Universe of Light (1933).   Then in 1935 Max Born described current ideas about quantum and atomic physics in The Restless Universe.   This brilliantly designed book was enriched with marginal 'moving pictures' illustrating dynamic processes.

The later 1930s saw the publication of two extraordinary books - Mathematics for the Million (1936) and Science for the Citizen (1938).   These were described by the author, Lancelot Hogben, as "primers for the age of plenty", and they told the story of the development of mathematics and science respectively, and their social relevance, through the ages.   At the time, Mathematics for the Million was hailed by H.G.Wells as "a great book, a book of first-class importance" and by another reviewer as "one of the, if not the, most important works published in this century".   This was the book which sold in large numbers to the fishermen who escaped from occupied Norway and went to south-west Scotland to join the Norwegian armed forces, which were being reformed there.   The delighted local bookseller opined that they were buying Hogben's book "to improve their English".   Yes, and other things too, perhaps.

The period following the second world war saw a demand for explanations of the new technologies which had evolved during those tense years, e.g. atomic energy and radar.   Among the first of the atomic energy books were two of quite different natures - Report on the Atom (1954) by Gordon Dean, who was Chairman of the U.S. Atomic Energy Commission from 1950 to 1953, and Brighter than a Thousand Suns (1958) by Robert Jungk.   The first was subtitled "What you should know about atomic energy", and the second "The moral and political history of the atomic scientists".   The subtitles identify two very different attitudes to the atomic age – the need to learn, and the need to question.

The radar literature did not involve such morally fraught issues, although the tactics of RAF Bomber Command were still troubling Freeman Dyson when he wrote in his autobiographical Disturbing the Universe (1979) about his wartime experiences with the RAF.   Other titles reporting scientific or technological advances during those years included R.V.Jones's Most Secret War (1978), Ultra goes to War (1978) by Robert Lewin, and Radar Days (1987) by E.G. Bowen.

The post-war thirst for illumination on these scientific topics, and in particular on atomic energy, was also served by the response of the scientific community to requests from local community-based groups - Rotary Clubs, W.R.I. branches, church groups, and so on - for lectures on the subject.   The late Sir Rudolph Peierls, who in 1940 had co-authored a seminal report showing the possibility of establishing an explosive chain reaction in enriched Uranium, frequently lectured to such gatherings.   He was interested to find that the post-lecture questions always included some about fundamental physics - the uncertainty principle, why do the protons in the nucleus stick together instead of repelling one another, and so on.   Mulling over the frequency of such questions, he decided to try to write a book setting out "the principles of modern physics in simple language and without assuming any previous knowledge".   That book, The Laws of Nature (1955) was a success, and has been followed by a growing stream of similarly motivated books by, among many others, Steven Weinberg, Richard Feynman, Euan Squires, and Sam Treiman.

One of the problems confronting authors in this field - and probably more generally - is that the subject keeps growing but the starting-point hardly moves.   For non-scientific readers the development has to start from Newtonian physics, the physics of the familiar macroscopic world.   This is where Peierls's 1955 book began, and where Treiman's The Odd Quantum begins. But the endpoint for Peierls's  The Laws of Nature was in 1954 or 1955, whereas Treiman's coverage extends over a further, enormously productive, 44 years.  Of course, Treiman is aiming at a better-prepared readership than many of his predecessors did.   To quote from his preface:

It is aimed at a wide audience of the curious - scientists in non-quantum mechanical disciplines, as well as non-scientists - at any rate those in either class who are not put off by equations and technical particulars.

Others may find it interesting, even rewarding, to dip into the book; and indeed, at an earlier point the author wrote: "I will be pleased if the book is received as a series of related, short essays", implying that the 9 chapters may be read independently.   But the word "related" conveys a warning that readers who adopt this more casual approach may from time to time have to refer to earlier chapters for clarifications, depending on their own backgrounds.

The text has been skilfully planned and is well written.   The first chapter starts with a brief history of 19th century physics, and proceeds immediately to indicate the various respects in which the developments of quantum physics overturned the certainties of that previous age.   The chapter ends with a bare outline of the events associated with the names of Planck, Einstein, Bohr, Rutherford, Heisenberg, Schrödinger, Born, Jordan, Dirac and Pauli.   Dramatic stuff - and new problems appearing all the time!

In the next chapter - classical background - the foundations of a more formal approach are laid down.   Simple equations appear.   The essentials of classical mechanics, electromagnetism, and special relativity are introduced.   Whether special relativity really belongs in the 'classical physics' chapter may be questioned, but the author justifies it on the grounds that special relativity is non-quantum-mechanical; others might prefer to fall back on an older perception that special relativity is the 'completion of classical physics'.   In any case, I would have preferred to see this classical chapter enlarged by the transfer to it of that section of chapter 3 which describes the experiments by Rutherford and his colleagues Geiger and Marsden, experiments which demonstrated the remarkable compactness of the nucleus of the atom.   The arguments used by Rutherford et al to interpret their results were purely classical; thereafter their conclusions provided the starting point for Bohr's model of the atom, with its massive positively charged core and circulating planetary electrons.   However, it is undoubtedly for the author to make the decisions on such matters of order and presentation, and as he does so he may challenge the reader to pause, reflect and deepen his (or, of course, her) insight.

The next (third) chapter, titled The 'Old' Quantum Mechanics, discusses blackbody radiation, the Bohr atom (with a glance at Sommerfeld's elliptic orbits) and de Broglie waves.   The treatment of the blackbody problem is particularly good, and the importance of different types of spectroscopic information in that case and in the working out of the details of the Bohr atom is made clear.

The fourth chapter, Foundations, is the one where the reader's willingness to tolerate some mathematical symbolism will be most severely tested, though some of the later chapters require a willingness to follow a mathematical type of thinking and reasoning; as the author explained in the preface, this is so characteristic of the field that it can't be avoided completely.  In this chapter the reader encounters mathematical operators, second order differential equations (the Schrödinger equation), and probability distributions.   The preliminary qualitative discussion of the 'two slit' experiment is marred by the drawing of an analogy between an electron-optical experiment with an unspecified source and a light-optical experiment in which the source is specified simply as "a light bulb".   Such a light-optical experiment might well not produce detectable interference fringes!   Ignoring this minor blemish, and passing over whatever important mathematical technicalities are detailed in the pages devoted to the Schrödinger equation, we arrive at the interpretation of the quantum mechanical state function in terms of a probability distribution.   The consequences of this are clearly discussed, and lead to an account of the Uncertainty Principle.   The chapter ends with an account of the phenomenon of Tunnelling.

That rather demanding chapter is followed by two very welcome descriptive chapters, 5 and 6.   Chapter 5 gives pleasantly readable accounts of topics which are, in the author's phrase, Some Quantum Classics.   These are solvable problems which appear in full mathematical detail in practically every Honours level course on quantum physics.  Here, though, only simple algebra is required of the readers.   Topics in this chapter include the free particle, the particle trapped in a box, the harmonic oscillator, the hydrogen atom, and radioactive decay; with the author's guidance quite detailed features of these topics can be grasped.   This is both challenging and illuminating.

The next (sixth) chapter seems to me the best in the book.   It deals with the topic of Identical Particles, and illustrates the enormous range of phenomena that follow from the notion that identical particles are indistinguishable; this itself follows from the need - explained in chapter 4 - to describe quantum systems in probabilistic terms.   Atomic structure, the laws of chemical combination, the characters of stars, and the formation of black holes, are all shown to follow from quantum theory's probabilistic description of identical particles.

After this, chapter 7, enticingly titled What's going on?, is perhaps the most difficult.   It deals with what is called 'the quantum theory of measurement'.   As Treiman writes: "Quantum mechanics deals with probabilities. Observers deal with facts . . . how do probabilities get converted into facts?"   This is a valid question, but many serious users of quantum mechanics manage to get by without ever asking it.   Yet there are real experiments which do raise this and related questions.   One such was proposed and analysed by Einstein, Podolski and Rosen in 1935 in an attempt to expose what they saw at that time as inadequacies in quantum theory.   The subsequent controversy is discussed at some length; the conclusion is that the EPR argument fails because it is based on presuppositions which are themselves insecure.

The essential issue underlying the EPR discussion was whether there are undetected or 'hidden' variables at present inaccessible, a knowledge of which would enable a completely deterministic and nonprobabilistic theory of physics to be constructed.  John Bell reopened the discussion in the 1960s; he derived a theorem - 'Bell's theorem' - which in effect shows that what are called 'local hidden variable theories' are incompatible with quantum mechanics.   Critical experimental tests have since been carried out which appear to confirm the validity of quantum theory in situations which can discriminate between quantum theory and the hidden variable theories.   Of these recondite matters Treiman remarks that "Everyone has weighed in: philosophers, physical scientists, science journalists, talk show hosts, theologians . . . At the end of the day quantum mechanics remains both intact and puzzling."

Next, Chapter 8 - Building Blocks - introduces new particles - neutrinos, mesons, and others.   Some of these (nowadays over three hundred have been identified) decay into other particles, or interact with one another to produce still others.   Particle physics is now, it seems, in an age of "rampant discovery".  As more particles have been discovered, measured, identified, it has been found possible to sort them into groups, and to point to the possible existence of so far undiscovered particles whose identification would complete the symmetry of this or that group.   Even the quarks, which have yet to be seen by experimenters, are firmly believed to be fundamental constituents of the proton and the neutron on the basis of such symmetry arguments.

The final chapter is about quantum field theory.   In 1928 Dirac developed a relativistic wave equation which predicted - although this was not realised immediately - a new particle, the positron.   More recently it has been shown that particles may be regarded as the quanta of fields; 'photons', for instance, are the quanta of the electromagnetic field.  The appropriate quantization procedure is outlined briefly, and the inclusion of interaction terms, by the insertion of a 'coupling constant' into the equation for the energy eigenvalues, is shown to lead to the prediction of inter-particle reactions.   The rest of the chapter is devoted to a breath-taking discussion of the possible interactions and their classification.

This is a spectacular finale to a remarkable book.   As has been indicated previously, the standard of difficulty varies from chapter to chapter, or even within some of the chapters.  Some potential readers will find it a good idea to follow the author's suggestion to treat the book as a set of related essays; having sampled some of it they may well be stimulated to try the rest.   Others, better prepared, will simply plunge in at the start, and will emerge later, challenged and excited.

This, of course, is not the end of the story.  Some day, someone will be writing about the fusion of quantum mechanics and general relativity into a true 'theory of everything'.   But that is for another generation!

Richard M Sillitto, 30 March, 2000

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