Roger Penrose’s new book The Road to Reality is being released in the U.S. in a week or so. I’d been intending to write something about the book ever since I got a copy of the British edition a couple months ago, but this is quite a daunting task. The book is nearly 1100 pages long and actually comes close to living up to its subtitle: “A Complete Guide to the Laws of the Universe”. It certainly is the most wide-ranging book on theoretical physics that I can think of, offering not just a summary of a lot of material, but an in-depth treatment of many of the more sophisticated ideas of the subject.
Penrose’s point of view is that of a relativist, so his treatment of geometry, general relativity and classical field equations is the deepest and most detailed part of the book. But he also discusses quantum theory extensively as well as the various attempts to quantize gravity. Compared to the general relativity parts, his treatment of particle physics and quantum field theory is rather sketchy, but quite original.
One of the unique aspects of the book is its extensive use of drawings to illustrate mathematical, geometrical and physical concepts. In this respect it is unparalleled by any other mathematically sophisticated text I’ve ever seen. One of Penrose’s main fascinations is the crucial role that complex numbers play, both in quantization and in the geometry of spinors. He has always been motivated by the idea that complex structures provide an important link between these two subjects, one that is still poorly understood. I very much agree with him about this. Related to this issue, some of the topics covered in the book that aren’t in any non-technical reference that I know of are his discussions of hyperfunctions and the Fourier transform, the geometry of spinors and twistors, and the use of complex structures in quantization and quantum field theory.
Penrose also carefully lays out areas in which his point of view differs from the general consensus of most theoretical physicists. An example is his emphasis on the importance for cosmology of understanding why the universe had such low entropy at the Big Bang. For more about this, see a posting by Sean Carroll.
A second area where Penrose is less than orthodox is his belief that quantum gravity somehow modifies quantum theory and resolves its measurement paradoxes. He explains an experimental set-up that could in principle test whether gravity plays a role in quantum state reduction, but he doesn’t have a concrete proposal for how standard quantum mechanics is to be modified.
Finally, there’s a remarkable chapter on supersymmetry, extra dimensions, and string theory. Penrose is very skeptical of the whole idea of introducing more that 4 space-time dimensions. One reason is that the beautiful spinor and twistor geometry that fascinates him is special to 4 dimensions. Another reason he gives is the classical instability of higher-dimensional space-times. Under a small perturbation, such space-times should collapse and form singularities. The difficulties in stabilizing extra dimensions are at the heart of the problems of string theory, with the only known way of doing it leading to the “Landscape” picture and ruining any ability to get predictions out of the theory.
Penrose is critical of the supposed calculation of black hole entropy from string theory, noting: ” As appears to be usual with such string-theoretic proclamations, this conclusion is very considerably overblown.” He has quite a few other very critical comments about string theory and the way in which research in the field has been pursued. As you might guess, I’m very much in agreement with his point of view and glad to see it in print. I’d be very curious to know whether recent ideas about strings in twistor space and Yang-Mills theory have changed his views much on the whole topic of string theory.
Update: A commenter pointed out that Science magazine has a review of Penrose’s book by Frank Wilczek (subscription required). Wilczek is right that there isn’t very much about particle physics in the book and Penrose gets something wrong about neutral K-meson mixing. Wilczek also says Penrose makes incorrect statements about electroweak symmetry breaking, but in a quick look at the book I couldn’t find what he was objecting to. He seems to object strongly to the speculative later parts of the book, but I don’t quite understand why. Penrose is up-front about what is speculation (e.g. relations between twistor theory and QM) and what is solid science, and Wilczek’s comment that “at present twistor ideas appear more as the desire for a physical theory than the embodiment of one”, could equally be applied to string theory, leaving one wondering why he doesn’t write strongly critical reviews of books on that subject.
If you want to read Lubos Motl’s comments on a book he hasn’t read, they’re here.