Fundamental Forces of Nature: The Story of Gauge Fields ,

World Scientific
Hackensack, NJ
, 2007. $54.00, $30.00 paper (270 pp.). ISBN 978-981-270-644-7, ISBN 978-981-270-645-4 paper

Sometimes physicists, in the twilight of their careers, undertake a coherent account of what they have learned about nature at its most fundamental level. The occasional one will even publish the result of the exercise. An example of such a summation is the late Sam Treiman’s The Odd Quantum (Princeton University Press, 1999); Kerson Huang’s Fundamental Forces of Nature: The Story of Gauge Fields is another. Treiman found his most profound insight in the concept of quantum field theory; Huang zeroes in more narrowly on gauge fields. Both books should be read in the way one listens to the reminiscences of one’s grandparents: patiently, indulgently, and respectfully. The value of Treiman’s and Huang’s books lies not in their details but in their perspective and wisdom.

Huang is a professor emeritus of physics at MIT and has taught theoretical physics there for half a century. His contributions have been chiefly in the areas of many-body theory and high-energy physics. He has written several graduate-level textbooks, and I have personally enjoyed teaching from his classic Statistical Mechanics (Wiley, 1965). Fundamental Forces of Nature is his first venture into what he calls “semi-popular exposition.” But more about that later.

In the preface, Huang describes his aim: “The story of gauge fields is the story of our quest for the fundamental law of the physical world.” His work is not a textbook, a history book, or a technical monograph; it is a narrative, with lots of equations and figures, about the evolution of a central component of modern physics. Huang’s use of the word “law” in the singular suggests that he hopes to understand the world once and for all, to find a world-formula, as it were. A couple of paragraphs later, also in the preface, he writes, “Theoretical physics has given us a true understanding of the physical world” (his italics). In support of this bold assertion he cites the one-part-in-a-trillion accuracy of quantum electrodynamics. I hear an echo of Albert Michelson’s premature claim in 1894 that the most important fundamental principles of physics have all been discovered.

Huang’s story starts with F = ma and ends with the standard model of particle physics. The major intermediate steps are sketched in lapidary style—with the exception of general relativity, which motivated the original, unsuccessful gauge theory of Hermann Weyl. Maxwell’s, Schrödinger’s, and Dirac’s equations; Pauli matrices; commutation relations; electromagnetic field tensors; SU (3) generators; and Feynman’s path integral are displayed in full splendor. But to try to get at the real meaning of gauge theory, Huang reaches for a visual analogy. In the past, others have invoked, with varying levels of success, imaginary stopwatches, rolling ping-pong balls, and color exchanges among quarks to explain the concept. Huang, inspired by the name of the mathematical theory of fiber bundles, pictures gauge fields as beads sliding along fibers anchored at spacetime points. Eventually each fiber picks up a ring around its foot, and finally a miniature gyroscope. The resulting picture is clumsy, but better analogies are very hard to come by.

The difficult story is further fleshed out by anecdotes and lots of images, including thumbnail photographs of most of the physicists mentioned. The pictures, together with Huang’s relaxed style, lend a very appealing texture to the book, a little like a family album or a personal diary. God, Napoleon Bonaparte, and the ancient Chinese poet Qu Yuan make discreet cameo appearances. There is also a physics poem, The Waste Lecture , attributed to T. S. Eliot and first published in John Lowell’s “Mr. Eliot’s Guide to Quantum Theory,” on page 46 of the April 1989 issue of Physics Today. The unsuspecting reader might be misled into believing in its authenticity by Huang’s failure to flag it for what it is: an April Fools’ joke.

Who should read Huang’s book? Huang contends that mathematics cannot be avoided in any discussion of physics, but that this does not mean one “has to understand the equations. One could get the flavor of what is being discussed without the equations, just as one could enjoy a foreign movie without the subtitles.” I disagree. A reader with no knowledge of physics would no more understand this book than I would enjoy a movie in Chinese. However, people with some physics background, including readers of Physics Today, understand what the equations are supposed to achieve, even if their explicit terms become increasingly arcane as the story unfolds. To such an audience, the book delivers what it implicitly promises: an instructive and thoughtful tour of 20th-century physics, with special emphasis on the theory of the fundamental constituents of matter and the forces among them, led by a friendly guide who knows the territory and its inhabitants from personal experience.

Unfortunately, the book has many typos and other slips, such as a statement of the right-hand rule that has no mention of the thumb and has a botched drawing of the magnetic field around a current-carrying coil. Perhaps the silliest mistake is the graph of Murray Gell-Mann’s famous decuplet (incorrectly called “decaplet”) featuring five charge states instead of four for the delta resonance (page 159). Both Huang and his readers deserve more careful editing.