By Frank Close, New York: Basic Books, 2011, 417 pp. & index, illustrated, $28.99By Frank Close, New York: Basic Books, 2011, 417 pp. & index, illustrated, $28.99

Reviewed by Michael Riordan

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, appealing physical theories have however been plagued by infinities that erupt as theorists try to prod their calculations into new domains. Ridding them of these infinities has likely occupied far more effort than was spent in their origination.

In quantum electrodynamics, or QED, the equations initially led to infinite results for the self-energy or mass of the electron. After nearly two trying decades, this problem was solved by a the "renormalization" procedure (See article by Silvan Schweber, Fall 2011 issue) and thereafter conveniently ignored. Richard Feynman referred to this sleight of hand as "brushing infinity under the rug."

In The Infinity Puzzle, Oxford University theorist and writer Frank Close tells the intriguing tale of the dogged efforts of physicists to apply quantum field theories to Nature, from QED to today's dominant Standard Model of particle physics. Much of his account concerns attempts to cure the infinities of these and similar field theories, hence the book's title. Close focuses on the minutiae of the calculations involved, to the nearly total exclusion of experimental and other contemporaneous theoretical work.

Because of seemingly unresolveable infinities, quantum field theory came to be perceived during the 1960s as a backwater of particle theory. But in 1970 Dutch theorists Gerhard t'Hooft and Martinus Veltman showed how to renormalize gauge field theories, throwing the door wide open to a magnificent revival—"the moment when field theory was reborn as the golden path for understanding" Nature.

Close was himself one of these true believers. 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 in fact exist. Then he came to the Stanford Linear Accelerator Center late in that decade, just as these fractionally charged fundaments started to turn up in electron-scattering experiments there.

The core strength of this book is its discussion of how the electromagnetic and weak forces were painstakingly unifed into the "electroweak" force, a drama that took nearly two decades to unfold and involved over a dozen principal actors. Five of them have already received Nobel Prizes, and more now wait in the wings, hoping for the discovery of the Higgs boson at the LHC. In fact, as Close explains in detail, there are six theorists who made worthy contributions to the electroweak theory's mass-generating mechanism, widely associated with theorist Peter Higgs.

Close has done his homework researching this and other breakthroughs. He unrelentingly called and emailed the physicists involved in a given advance (myself included) until their accounts began to gel into a coherent picture. And where they sometimes do not, he duly acknowledges the difficulties in his copious footnotes—a treasure trove of additional insight for historians of physics.

Unfortunately, however, Close's intense focus on theoretical minutiae means that the experimental side of the story gets short shrift. One egregious example is his discussion of quantum chromodynamics—the theory of the interquark force. Its source is a radically different property of matter called "color" that emerged from theoretical and experimental work of the 1970s. But color pops onto the page in a few paragraphs two thirds of the way through the book, with almost no explanation of how it arose. By contrast, Close's discussion of asymptotic freedom, whereby this force weakens as two quarks approach, gets 15 pages plus extensive footnotes.

Card-carrying historians might scoff at this account as "Whig history"—one told by the winners. Indeed, the great majority of particle theory going on from the mid-1950s to 1970 gets only passing mention. But such a Whiggish, "internalist" account serves a valuable purpose: to record in superb detail the inner workings of what was a small but successful theoretical subculture that few particle physicists paid much heed until 1970. And for physicists interested in following such details, The Infinity Puzzle makes for a gripping read.

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