Roger Penrose has had a long career as one of the most original thinkers in the field of mathematical physics. His early work included ground-breaking results on general relativity and singularity theorems for solutions of Einstein’s equations. He later went on to invent “twistor theory”, which is based on a radically different approach to the geometry of space-time, one that describes Minkowski space and spinor fields in terms of the classical geometry of the Grassmanian of complex two-planes in \(\mathbf C^4\). His 2005 *The Road to Reality* is a huge (over 1000 page), often technical, and masterful summary of the geometrical viewpoint on the fundamentals of physics, masquerading as a semi-popular book.

Penrose is sometimes described as a “maverick”, but his point of view on physics and mathematics is in many ways quite conservative. In his new book, *Fashion, Faith and Fantasy in the New Physics of the Universe*, he turns a skeptical eye on some popular speculative ideas about theoretical physics. This book has been a long time in gestation, starting out as a planned write-up of lectures given back in 2003 at Princeton University. In delivering those lectures, Penrose was walking into the lion’s den, bringing a forceful critique of string theory to the academic institution where it has been the hegemonic viewpoint.

Besides a mathematical appendix, the book is divided up into four parts:

**Fashion:** This is the section that deals with string theory as a conjectural unified theory of physics. Penrose’s central objection is to the use of extra spatial dimensions as a crucial part of the theory. When trying to use string theory as a unified theory, an assumption is made that strings propagate in ten dimensions. The ideas is that one can take four of these to be our very large space-time dimensions, and the rest very small, while successfully decoupling the large and small dimensions. Penrose argues that there is no reason to believe one can consistently do this, that there should be couplings between these degrees of freedom that cannot be ignored, leading to instability of the theory, rather than a stable ground state with large dimensions.
While this is a different critique of string theory than others, it is consistent with others in identifying the main problem of the theory its introduction of a huge new set of unobserved degrees of freedom via the use of extra spatial dimensions. Even if these do not, as Penrose suspects, destroy the consistency of the desired model, the evidence is that they allow just about any conceivable physics to be modeled, ruining any conventional sort of predictivity.

**Faith:** In this section Penrose addresses the measurement problem of quantum mechanics, pointing out correctly that our standard story about quantum mechanics introduces an “ontological shift,” indicating that something more is going on than a well-understood consistent framework. He favors the idea that perhaps the introduction of gravity into the usual framework could resolve this problem, backing this up with a dimensional analysis argument that a relevant effect could come from gravity, while being too small to be observable so far.
Here Penrose does an excellent job of explaining the usual story and why there’s a problem, but it is not clear that this problem requires new physical laws, non-linearities, or the introduction of gravitational effects. The “ontological shift” may be due to the standard story being not a full theory of what happens in a real measurement process, but instead a phenomenological approximation of what happens, with approximation needed to get a tractable description. As people build and study more complicated and larger fully quantum systems, the inadequacies of the standard story about “measurement” will likely become clearer. Quite possibly we’ll get a better understanding of how classical behavior emerges from quantum laws, with no need to change those laws.

**Fantasy:** Here Penrose describes in detail some basic problems in the theory of cosmology, and how they are supposedly resolved by the theory of inflation. He explains that characterizing this as “fantasy” is not meant to be purely critical, that “fantasizing” about the moment of the big bang is what theorists do in the absence of compelling evidence, and that he just has other fantasies he thinks worthwhile.
This reviewer can’t here do justice here to the depth and complexities of his arguments in this section. This is a topic involving subtle questions about the behavior of general relativity where Penrose is one of our deepest thinkers and greatest experts. While acknowledging some of the achievements of inflationary theory, part of his critique is related to that of Paul Steinhardt and others, showing that the theory doesn’t accomplish what it sets out to do, with the exponential expansion not providing a way to get observed homogeneity from arbitrary initial conditions. At the same time there is a lot more there, and this section should be required reading for anyone trying to make sense of our various fantasies of the description of the big bang itself.

**A new physics for the universe?:** In a final section, Penrose describes some of his more positive ideas addressing the problems pointed out in the earlier sections. This begins with a wonderful summary of the theory of twistors, and this reviewer strongly suspect that he’s right that this very different way of thinking about space-time geometry will ultimately be part of any successful integration of our understanding of quantization and geometry. That this geometry is very specific to four space-time dimensions provides yet another reason for skepticism about the fashion for theories with more spatial dimensions.
Less convincing is his speculation about quantum state reduction, and what he himself refers to as his “Conformal Crazy Cosmology”, although the emphasis on conformal invariance may very well be a correct one.

An unusual and wonderful aspect of the book are the many drawings from Penrose’s own hand, which illustrate a wide range of physical and mathematical ideas. Princeton University Press is making these drawings available for teaching purposes on their website.

The technical level of the book varies from section to section, in some places written in a way that a large audience can appreciate, in others requiring some significant background in mathematics and physics, with much of it deserving the attention of experts in the subject. I can’t recommend it too highly to any mathematician with a serious interest in fundamental questions about physics.

Peter Woit is Senior Lecturer in the mathematics department at Columbia University and since 2004 has been blogging on topics in physics and mathematics at http://www.math.columbia.edu/~woit/blog. He is author of the 2006 book *Not Even Wrong,* as well as a forthcoming textbook on quantum mechanics and representation theory, to be published next year by Springer.