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Tackling Infinity

THE INFINITY PUZZLE: Quantum Field Theory and the Hunt for an Orderly Universe. Frank Close. xii + 435 pp. Basic Books, 2011. $28.99.

In the early 1980s, Nobel laureate Paul Dirac told Princeton University theorist Ed Witten that the most important challenge in physics was “to get rid of infinity.” Some of the most beautiful and thus appealing physical theories, including quantum electrodynamics and quantum gravity, have been dogged for decades by infinities that erupt when theorists try to prod their calculations into new domains. Getting rid of these nagging infinities has probably occupied far more effort than was spent in originating the theories.

In quantum electrodynamics, which applies quantum mechanics to the electromagnetic field and its interactions with matter, the equations led to infinite results for the self-energy or mass of the electron. After nearly two decades of effort, this problem was solved after World War II by a procedure called renormalization, in which the infinities are rolled up into the electron’s observed mass and charge, and are thereafter conveniently ignored. Richard Feynman, who shared the 1965 Nobel Prize with Julian Schwinger and Sin-Itiro Tomonaga for this breakthrough, referred to this sleight of hand as “brushing infinity under the rug.”

In The Infinity Puzzle, University of Oxford theoretical physicist and writer Frank Close tells the intriguing tale of the dogged efforts of physicists to apply quantum field theories to nature, starting with quantum electrodynamics and ending with today’s dominant Standard Model—the current paradigm of particle physics. Much of his account concerns attempts to overcome the infinities that have cropped up in these and other field theories—hence the book’s title. Close’s narrative focuses on the minutiae of the calculations involved, and the interactions of the theorists doing them, to the almost total exclusion of the experimental and other theoretical work that was being done simultaneously. Because of its seemingly unresolvable infinities, quantum field theory came to be perceived during the 1960s as a backwater of particle theory, not very conducive to career advancement. But in 1971 Dutch theorists Gerard ’t Hooft and Martinus Veltman showed how to renormalize certain field theories, throwing the door wide open to a magnificent revival that continues to this day. Their revelation was “the moment when field theory was reborn as the golden path for understanding the fundamental forces” of nature.

Close at the time was himself one of these true believers in quantum field theory. He did his graduate work in the mid-1960s at Oxford under Richard Dalitz, one of the few theorists at the time who thought quarks might actually exist. Then he came to the Stanford Linear Accelerator Center (SLAC) late in that decade, just as these curious, fractionally charged fundamental particles began turning up in surprising electron-scattering experiments there. He ably portrayed the new subatomic landscape in an earlier book, The Cosmic Onion: Quarks and the Nature of the Universe (Heinemann, 1983). Since then, he has published another half-dozen general books on particle physics.

The core strength of The Infinity Puzzle is its discussion of how the electromagnetic and weak forces were painstakingly combined into the “electroweak” force, a drama that took nearly two decades to unfold and involved more than a dozen major actors. Five of them—’t Hooft, Veltman, Sheldon Glashow, Abdus Salam and Steven Weinberg—have already received Nobel Prizes for their contributions. And more are waiting in the wings, hoping for the discovery of the elusive Higgs boson at the Large Hadron Collider. In fact, as Close explains in extensive detail, six theorists made worthy contributions to the crucial mass-generating mechanism, widely associated by the media with Edinburgh University theorist Peter Higgs, that lies at the heart of electroweak theory. In 2010 this “gang of six” shared the American Physical Society’s J. J. Sakurai Prize, its most prestigious award for achievements in theoretical particle physics. But the vaunted Nobel Prize can go to a maximum of only three individuals.

Close has done his homework in researching this and other breakthroughs (as I personally experienced when he contacted me about the origins of Feynman’s parton model of electron scattering). He unrelentingly called and e-mailed the physicists involved in a given advance until their accounts began to add up to a coherent picture of what actually transpired. And where they sometimes do not, Close duly acknowledges the difficulty in his copious footnotes. For avid historians of physics like myself, these notes are a treasure trove of additional insights. Serious readers are encouraged to consult them to obtain a fuller picture of the Standard Model’s theoretical underpinnings.

Unfortunately, however, Close’s intense focus on theoretical minutiae means that the experimental side of the story gets short shrift. An egregious example of this bias occurs in his discussion of quantum chromodynamics—the theory of the force between quarks that imprisons them within protons, neutrons and other strongly interacting particles. The source of this force is a radically new property of matter dubbed color that emerged from both theoretical and experimental work of the 1970s. But color pops magically onto the page in a few paragraphs two thirds of the way through the book, with almost no explanation of how it came into being. By contrast, Close’s discussion of asymptotic freedom, a curious attribute of this force whereby it weakens as two quarks approach, gets 15 pages plus extensive footnotes.

Card-carrying historians might scoff at this account as “Whig history”—as told by the winners, ignoring everything else that was occurring simultaneously in the discipline. Indeed, the great majority of theoretical work going on in particle physics from the mid-1950s to 1970 gets only passing mention here. But had Close tried to include it, his book would have exceeded a thousand pages and his narrative focus would have been ponderously diluted. A Whiggish, “internalist” account such as The Infinity Puzzle serves a valuable purpose: to record in superb detail the inner workings of what was a small (but very successful) theoretical subculture to which few particle physicists paid much heed until 1971.

But the book is not for the fainthearted. I cannot imagine readers without a graduate-level knowledge of physics really understanding the discussions and arguments in any detail. Although he is a good science writer, Close is unfortunately too close to this subject matter professionally; what may be obvious to him will not be so clear to general readers. More effort to explain arcana would have been helpful.

To end on a personal note, I was pleased to see many paragraphs and even pages devoted to the contributions of SLAC theorist James “BJ” Bjorken—a mild-mannered, unsung hero of particle physics who did much of the theoretical research underlying the quark-parton model that emerged in the late 1960s and became a crucial element of the Standard Model. Close believes BJ’s work to be of Nobel caliber, and many of us in the field agree. Perhaps The Infinity Puzzle will finally cinch the case for him.

Michael Riordan has taught the history of physics at Stanford University and the University of California, Santa Cruz. He is author of The Hunting of the Quark: A True Story of Modern Physics (Simon and Schuster, 1987) and is coauthor, with Lillian Hoddeson, of Crystal Fire: The Birth of the Information Age (W. W. Norton, 1997).

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