The physics begins around page 400 and includes uncompromising discussions of space-time and Minkowskian geometry, general relativity theory of course, Lagrangian and Hamiltonian approaches to dynamics, quantum particles and entanglement including the standard illustrations (the two-slit experiment, Schrodinger's cat, and Einstein-Podolosky-Rosen non-locality), the measurement problem, Hermitian operators, black holes, the Big Bang, time travel, quantum field theory, the anthropic principle, Calabi-Yau spaces, as well as many other topics of current research.
As in his previous works the author is not afraid to strike an iconoclastic pose. He sides with Einstein and against most modern physicists, for example, in thinking that the EPR experiment demonstrates that quantum theory is incomplete.
The experiment, described very simplistically since this column has fewer words than Penrose's book has pages, involves identical particles moving rapidly apart. A physicist measures the spin of one of the particles realizing that quantum theory stipulates that the particle doesn't have a definite spin -- it could go either way -- until it is measured and its wave function collapses. Astonishingly, the other particle, which by the time of the measurement may be in a different galaxy, has a wave collapse at the same moment that always results in its having an opposite spin. How does the second particle instantaneously "know" the first particle's spin? Eerie entanglement, an incomplete theory, something else?
Penrose's skepticism extends to more modern developments as well.
He is unenthused about inflation theory and particularly so about string theory. (Inflation, very roughly, refers to the lightning fast expansion of a part of the very early universe, and string theory, even more roughly, refers to the notion that fundamental particles are composed of minuscule strings, vibrating and multi-dimensional.) Inflation theory has considerable evidence backing it, but Penrose seems correct to emphasize that string theory and its offspring M-theory are largely speculative. Why their appeal? He offers an interesting discussion of the role of fads and fashion even in theoretical physics.
The end of the book is devoted to a sketch of M-theory's main competitor, twistor theory and loop quantum gravity, which he invented decades ago and has been developing with colleagues ever since. He also seems less than impressed with Brian Green's "The Elegant Universe," a book that is far more accessible.
Coming every few pages, Penrose's well-done drawings and illustrations may ease the book's near vertical learning curve. Like some New Yorker subscribers, many readers of this book will, I suspect, confine themselves largely to the pictures and the pages that are more broad-gauged and less technical.
There is something to be said for inducing even this level of involvement in mathematics and physics, and if "The Road to Reality" succeeds in doing this, it may become a (sturdy) coffee table book and popular success. My hunch, however, is that this truly magisterial book will be appreciated primarily by those who have already spent considerable time in school learning a substantial portion of what's in it.
-- Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books, including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.