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.