Roger Penrose’s Fashion, Faith and Fantasy in the New Physics of the Universe is finally being published this week. This is a bit of a landmark event, since the book has a long history, going back to a series of lectures that he delivered in 2003 at the university and IAS. At one point I remember watching videos of these lectures hosted by Princeton here, but these no longer seem to be available.
In giving these lectures, Penrose was walking into the lion’s den, bringing a forceful critique of string theory to the academic institution where it is most popular. Congratulations to Princeton University Press for publishing this despite it challenging the hegemonic viewpoint at Princeton (I had less luck with them: when my British publisher sent them my book for consideration way back when, they hired Lubos Motl to write an evaluation of it…).
Besides a mathematical appendix, the book is divided up into four parts:
- Fashion: This is the section that deals with string theory, and 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 one can take four space-time dimensions very large, and the rest very small, 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.
The problem is that one doesn’t actually have a non-perturbative string theory in which one could properly study this issue. There’s no consistent theory, so Penrose can’t rigorously prove there’s a problem of this kind. He faces the generic problem of arguing not with a well-defined theory, but with people’s speculative hopes of what kind of theory might exist. I agree with him though that the extra dimensions are a deadly problem for the theory. Even if you accept the most optimistic hopes that Penrose’s and other problems will go away, you are still going to be left with the landscape problem. Everything known about conjecturally stable states with 4 large dimensions indicates an infinite complexity of such conjectural things, capable of giving you any physics you want, leaving the theory able to predict nothing and empty of explanatory power.
- 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 I think he does an excellent job of explaining the usual story and why there’s a problem, but personally I’ve never been convinced that this problem requires new physical laws, non-linearities, or the introduction of gravitational effects. To me the “ontological shift” has always seemed due to the standard story being not a full theory of what happens in a real measurement process, but being 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” I think will become clearer, and 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.
I don’t think I can 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 seems to me that it should be required reading for anyone trying to make sense of 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 I 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 of theories with more spatial dimensions.
I’m less convinced by his speculation about quantum state reduction, and by what he refers to as his “Conformal Crazy Cosmology”, although the emphasis on conformal invariance may very well be a correct one.
In a final “Personal Coda” he explains that he sees himself not as a “maverick”, but as rather embodying an “inner conservatism”, somewhat allergic to the appeals of fashion. In particular:
So when I heard that string theory – to which I had been distinctly attracted, partly because of its early use of Riemann surfaces – had moved itself in the direction of requiring all those extra spatial dimensions, I was horrified, and far from being tempted by the romantic attractions of a higher-dimensional universe. I found it impossible to believe that nature would have rejected all those beautiful connections with Lorentzian 4-space – and I still do.
A wonderful aspect of the book are Penrose’s many and detailed graphical illustrations, which have been made available separately by Princeton here. At their website you can also read the Preface, and an interview. Unfortunately I’ll be in Germany next week, missing Penrose’s book tour events here in New York, at the American Museum of Natural History and MoMath.
The range of non-crackpot speculative ideas about fundamental physics that normally get much attention is unfortunately quite narrow. In this environment Penrose is a breath of fresh air, providing here a different point of view on several topics, backed by serious and detailed argument. In some ways this is a popular book, but in others it is something else, deserving the attention of experts in the subject. I can’t recommend it too highly to anyone with a serious interest in fundamental questions about physics.
Update: A somewhat different version of this review is up at MAA Reviews.