Professor Newton’s Principles
Chris Quigg

Thinking About Physics. By Roger G. Newton. Princeton: Princeton University Press, 2000. 208 pp. $24.95, 15.95. ISBN 0-691-00920-1.

An ant making its daily rounds was nearly run over by a centipede that streaked across its path. Awestruck by the larger arthropod’s effortless grace and speedy motion on so many legs, the ant inquired, “Please tell me how you know when to move leg number 57 and when to move leg number 62.” The centipede’s face contorted in thought. Its mouth opened to speak, but no sound issued forth. Then its hundred legs began to convulse in chaotic motion; they became hopelessly entangled, and it fell in a confusion of twitching legs, never to walk again. Perhaps it is fear of the centipede’s fate that discourages physicists from thinking too much about what they do.

Indiana University’s eminent mathematical physicist Roger Newton harbors no such fears. On the contrary, he argues that time spent understanding “what lies behind the solutions to large problems tackled in the past” makes physicists better scientists—and better problem solvers. In Thinking About Physics, a fast-paced and challenging collection of essays, Newton appears as an opinionated yet approachable discussion leader. He exhorts the reader to “use my arguments as starting points for your own thinking.” From the meaning of a theory to the nature of quantum-mechanical reality, Newton cuts a wide swath and sprinkles his analysis with provocations that make it hard to be a passive reader. Throughout the book, I found myself wanting to engage him in conversation—to ask, “Just what do you mean by that?” or to protest, “I don’t see it quite that way.”

Though he is an ardent believer in the power of mathematics as an instrument of thought, Newton takes issue with Galileo’s contention that mathematics is the language of nature. “Nature,” he writes, “just is; it speaks no language and follows no plan; language and plans are human additions.” Mathematics is, however, “the only language capable of describing nature unambiguously.” Newton opens a compact treatment of symmetries in physics with a clear statement of the modern view that symmetries “express themselves not in the world as we directly experience it, but in the underlying laws and theories.” We seek, in other words, symmetries in the laws of nature and the equations that express them, not necessarily in the solutions.

Thoughtful discussions of the arrows of time and of the meaning of causality and probability in physical theory illuminate Newton’s insightful assessment of the conflicts between quantum theory and everyday experience. “Many of the quantum paradoxes,” he writes, “ … have a linguistic nature, stemming from the use of the concepts of particles and waves, to which our everyday intuition and language seem to drive us, but the connotations of which, originating from the macroworld, are simply inappropriate to the microworld.” He also provides a clear-headed analysis of recent experiments that rule in favor of the probabilistic predictions of quantum mechanics.

Newton argues forcefully that “at the most basic level, nature is best described in terms of the quantum field.” He disagrees with those who think in terms of particles and Feynman diagrams, in part because the cartoon picture of particles interacting through the exchange of a few quanta may in some situations be uneconomical, incomplete, or even misleading. I am not sure that I recognize the battle lines here. Many of us slide effortlessly between particles and fields, according to the situation, without claiming that the dialect we choose more often is necessarily the more fundamental. A question of greater interest to me is where the essential information lies. I was disappointed that Newton chose not to explain the special nature of gauge invariance and the crucial role of the nonintegrable phase—not the potentials or the field strengths—in the gauge theories that govern the fundamental interactions.

The range of topics and allusions make Thinking About Physics a difficult book for an advanced undergraduate to read without encouragement and supervision. Teachers of undergraduates, aided by the useful index, will find many small nuggets of insight with which to enrich their problem-solving lectures. It would be very interesting to organize a graduate seminar around the book for students completing their course work. Practicing physicists will find the book a perceptive colleague’s scan on the foundations of the way we work. They may also catch themselves talking back to Professor Newton—which just might be his aim.

Published in Science 288, 447 (2000).