Only a truly renaissance physicist, a scientific polymath, would be able to extract the maximum mileage from this very valuable compilation - out to celebrate the 250th anniversary of Princeton University - of leading research in various branches of physics. While most practising physicists would find typically only about a third of this book to be fully comprehensible, all of them would find it invaluable for understanding or evaluating research in fields other than their own.
However, this restriction to specialists has the advantage that each chapter presents an account of cutting-edge research, with no apologies made or needed for the lack of introduction. At its most extreme, this can lead to inaccessibility (because of insufficient definition, or over use of jargon) or a lack of general interest (where the progress of physics in certain disciplines appears to be related to the detailed evolution of acronyms per page); but at its best, one sees a coming together of fundamental physics ideas in related branches of a particular field, through the presentation of extremely contemporary work.
One of the most beautifully written chapters, involving humour and style, is the opening one by James Langer on nonequilibrium physics and complexity. His suspicions that "complex systems will not fall usefully into a small set of universality classes", that "this world is larger than we had expected", and that "we may be much closer to the beginning than to the end of this chapter in the history of science", though put with typically temperate moderation, have a ring of truth about them. These are all the more to be admired since in voicing them, Langer runs the gauntlet of modern theories of everything, whose remit is that the world is bound together by simple, almost simplistic, global maxims. A beautiful illustration of his contention that complexity cannot be oversimplified without becoming simplistic, is given via the comparison of dendritic growth and fracture dynamics. Langer's original intuition was that these phenomena were very similar, as both involved "nonequilibrium, finger-like structures that moved under the influence of external forces" leading to sidebranching, and that "the elastic stress concentration at a crack tip (occurred) for much the same reason that diffusion flux (was) concentrated near the tip of a dendrite".
However, by using simple arguments, Langer is able to demonstrate even within the confines of this chapter that such apparent similarities can be misleading - far from leading to grand unifying principles, it seems that nonequilibrium dynamical situations lead generically to highly specific effects, because of their sensitivity to initial conditions. "Whether we like it or not", says Langer, "that is where we must look to understand the real world I We shall have to resist drawing conclusions from superficial similarities." As Philip Anderson said in his memorable and almost prophetic essay, "More is Different": "The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe I at each level of complexity entire new properties appear, and the understanding of the new behaviours requires research which I think is as fundamental in its nature as any other."
John Hopfield's chapter on the physics of the nervous system is similarly inspiring; by drawing distinctions between physics (an "information-poor" science) and biology (an "information-rich" science), where attempts to compactify information into predictive theories are traditional in the former and rare in the latter, he nevertheless defines a basis for the applications of physical principles in biology. More fascinating, however, than his ideas on the physics of neural networks, are some of the general insights he presents us with. He contrasts the specificity of behaviour with the disparateness of cell structure in the organisms manifesting this, bringing in concepts of collective dynamics to explain the way in which ensembles of disparate objects can nevertheless produce similar behaviour. Even more fascinating is the section on object recognition via sight, smell and hearing, and its links to computational algorithms. Most remarkable, in my view, is Hopfield's illumination of a truly complex field (where details play a real part and disallow the passing off of truisms as respectable theories) within an almost conversational, jargon-free stylistic framework - a simple account of real complexity in biophysics.
Harry Swinney's chapter on pattern formation is yet another example of luminous pedagogy, involving limpid introductions to the phenomenology of nonequilibrium hydrodynamics via the Navier-Stokes equation, Taylor flows and Rayleigh-Benard convection. A good blend of experimental results and theoretical outlines make these complex issues very digestible, and in the process, via an example involving reaction-diffusion systems, Swinney is able to illustrate a remarkable (and all-too-rare) symbiosis between theory and experiment. The theory concerns a two-species model which initially was devised to match the results of a many-species reaction in its chemical patterns; later, and much more remarkably, it was able correctly to predict details of the experimentally observed patterns.
Another well-made point in this connection concerns the situations when a full mathematical solution is still not the answer, in the sense that simulations and experiments are more vital for exploring the true behaviour of, say, a chaotic system in the vicinity of a bifurcation than "pages of elliptic integrals". Swinney also gives interesting insights into far-from-equilibrium states via the illustration of order in turbulence; snapshots of a disordered liquid surface in a time-averaged sequence reveal, intriguingly, the signatures of the symmetry of the container. Finally the mention of very current work involving oscillons in granular flow, makes this a chapter combining contemporaneity with tradition, showing fully the extent of the hard work put into making this vast range of ideas flow seamlessly.
Ed Witten's account of developments in particle physics shows truly consummate skill in managing to compress into a few pages developments in particle physics over the last decades, in describing without recourse to jargon, concepts as abstruse as supersymmetry, string theory and the mystery of the cosmological constant. One of the outstanding parts of this immensely readable, coherent chapter is the one concerning the big questions, and some of Witten's speculations about the answers. The most intriguing one of these concerns a new non-commutativity in physics, involving "D-branes", which are extended objects of various dimensions, and their connection with the quantum states of a black hole. This beautifully concise account is manifestly the result of a true mastery of the field it describes.
Last, but not least, in this selection of the more outstanding chapters, is the one by Franz Wilczek involving a critique of the Standard Model, with an overview of its successes and failures. A proponent of supersymmetry and its role in grand unification, Wilczek gives a clear account of why he thinks it is likely to be (close to) the final answer. Something of his interesting ideas concern the links of particle physics to other fields, like cosmology and condensed matter physics: Wilczek's answer to why theoretical concepts developed for one length scale could be applicable to scales which are vastly different, is that in each domain, "the same principles of symmetry and duality are basic".
This sort of intriguing, if somewhat speculative, statement is typical of the many gems to be found in this treasure trove of a book. As with all treasure troves, it can be difficult to locate the buried treasure because of its sheer size and complexity. Some of the gems are bound to be less incandescent, less authentic, and ultimately less valuable than others. But this is a small criticism of what is an extremely worthwhile book, a valuable addition to the library of any physicist.
Anita Mehta is reader in physics, S N Bose National Centre for Basic Sciences, Calcutta, India. She is currently an EPSRC visiting fellow, Clarendon Laboratory, Oxford.
Critical Problems in Physics
Editor - Val L. Fitch, Daniel R. Marlow and Margit A. E. Dementi
ISBN - 0 691 05785 0 and 05784 2
Publisher - Princeton University Press
Price - £ 49.50 and £ 14.95
Pages - 308
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