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.
Would you recommend the book to a somewhat well-read layman?
Yes, especially one not afraid of a little mathematics. This is not another “Road to Reality”, which was more technical. There will be sections though where I think a layman will likely get lost (an example is the discussion of twistors), but only few of those.
” they hired Lubos Motl to write an evaluation of it…”
I know I shouldn’t be curious, but was the evaluation ever published?
The full story is that parts of Lubos’s review first appeared as a review on Amazon, see
and I wrote a little about this here
At the time I was perplexed by what version of the manuscript he was writing about. He later explained about the PUP story, see
The original link to his full review no longer works, but you can find this via the wayback machine, for instance at
Enough though about this history, further comments should be about Penrose’s book, a much more interesting topic than Lubos’s reaction to mine over ten years ago.
Penrose’s entire 10 video lecture series is available on YouTube. start with https://www.youtube.com/watch?v=5jXj1TwiFys and you can locate all the lectures from there.
@Richard that youtube link goes to his lecture at Penn State given many years after his Princeton lectures (even though it has the same title).
Anything about consciousness/QM? That was one of his pet topics.
I’m looking forward to this book. I met Penrose a few years ago; he was extremely pleasant, and of course, extremely insightful about physics.
As far as I can tell, there’s exactly one and only one sentence about consciousness/QM in the book, basically noting that he has written about this and giving a reference.
in the book,
if Penrose thinks that the extra dimensions can cause instability
does Penrose discuss the KKLT construction for stabilizing the extra dimensions? does it in fact work, in creating 3 large spatial dimensions and 6 curled up and stable?
does Penrose discuss the latest results from LHC on SUSY i.e no-show?
One reason I find the book refreshing is there’s not much about such tired topics. He’s got a couple pages on SUSY and the fact that it hasn’t appeared, as well as the danger that proponents will just argue that higher energies are needed. He discusses the moduli stabilization problem, but in the context of explaining that the problems he sees with extra dimensions are much wider than that, with the freedom to vary parameters characterizing Calabi-Yaus the least of the problems introduced by the huge number of new degrees of freedom coming with extra dimensions.
Anyone else try buying directly from Princeton University Press and run into problems with the shopping cart? I am using the most up to date version of Chrome. If it is not an intermittent thing then I will have to go to Amazon I suppose.
Peter, thank you for the wonderful review. Based upon it I’ve picked up the book and reading through Chapter 1 now. One minor nitpick is that Penrose takes issue not with the huge number of degrees of freedom involving the extra dimensions, but rather the *much* larger number of functional freedom that is involved. He emphasizes this in the last paragraph of Appendix 2:
“The phrase ‘degrees of freedom’ is frequently used in the context of physical situations and, indeed, I frequently make use of that terminology in this book. It should be emphasized, however, that this is not the same as ‘functional freedom.'”
… where he goes on to explain the difference in that “degrees of freedom” are associated with the components of the field in question whereas the “functional freedom” is far greater and completely swamps the “degrees of freedom” when extra dimensions are involved.
To my mind, the “number of degrees of freedom” here is infinite-dimensional, since the configuration spaces are function spaces, and I didn’t mean anything more precise than that by my usage. I didn’t want to get into explaining exactly how Penrose quantifies “functional freedom” since a short attempt at that would likely just be confusing.
For exactly what this means, if you have a copy of “The Road to Reality”, see section 16.7. The argument Penrose is making against extra dimensions is not a new one for him. He developed it in detail quite a while, see for instance his paper “On the instability of extra space dimensions” in the Hawking 60th birthday celebration volume, published in 2003.
I see, thanks. The degrees of freedom available to a theory with extra dimensions is “utterly unassailably” vastly larger because of the functional freedom as Penrose says. In his book, Penrose states that he does not think anyone has really responded in good faith and detail to his “functional freedom” objections to string theory and now I see this objection really has been out there for some time. While I’m reading the book it would be nice to see some counter-argument. Do you know of any attempt to rebut or explain away his objection in good faith and earnest?
I’m not aware of any, and I recently talked to Penrose about this, and he said he hadn’t gotten any counter-argument.
My guess is that string theorists approach this question like a lot of possible arguments against what they are doing, figure it is best to just push forward, assume that things decouple in some way to avoid the problem, and see what you can do. To my mind the deadly argument against string theory is not any argument like Penrose’s, but that, even if you optimistically ignore all such problems, you end up with an empty theory that can’t predict anything.
Put differently, if string theorists ignored Penrose’s problem, then went on to find a calculational framework that was vindicated by success in explaining the real world, that would be fine. His problem would be an interesting issue to think about in terms of better understanding string theory, but it would not be a compelling argument against string theory. On the other hand, if you have a good argument that something is not going to work, and it doesn’t, you should take that argument quite seriously, it might show you where you’re going wrong. Some string theorists I’ve talked to actually do say that they’re not interested in the higher dimensions, believe that string theory needs to find a proper 4d formulation.
I don’t understand this supposed argument against extra dimensions. If there was an argument that implies that the 3+1 d standard model cannot be an EFT for a higher dimensional theory, how does the same argument not rule out 2+1 Chern Simons theory as an EFT for 3+1 electrons in a quantum hall state? Or, how does it not imply that 2-d domain walls in 3d broken symmetry states must be unstable?
thanks for replying
i posted this question and a string theorist replied. In his view Penrose objections were satisfactory resolved in 2002 with the KKLT paper, and is no longer an issue for string theory. the string theorist then updated the string FAQ
Penrose explicitly explains in the book that the problem of fixing the finite-dimensional moduli that KKLT is supposed to solve is not the problem he is discussing.
Have you tried reading his argument? I don’t see how your objection has anything to do with it.
It’s a little unfortunate for the scientific discourse that the argument is hidden behind a paywall. Looking around, I find this old video recording of a talk by Roger Penrose, which from 3:55 on explains what “functional freedom” is meant to refer to. (Go to 6:56 to see the key slide.)
The presentation there is aimed at non-experts, but what it says in technical paraphrase is that if a physical field takes values in a manifold V, then a field configuration is a section of a V-bundle over spacetime, hence locally a function from spacetime to V. The point of the slide is to highlight that the space of functions to V (field configurations) is an infinite-dimensional manifold (and in fact that’s true only if the local domain is compact, otherwise things become more wild still). So if the pointwise degrees of freedom of a field are parameterized by a finite dimensional manifold V, then the actual spacetime-wide degrees of freedom are parameterized by an infinite-dimensional mapping space.
What I wonder is in which way this basic fact is meant to be something not appreciated in traditional literature. What is traditionally meant by moduli stabilization is precisely the argument that on-shell the dependency of those V-valued functions along the compact dimensions disappears due to them picking up a potential, in direct analogy to how the Higgs field has a constant (absolute) value throughout spacetime (at least locally) since it sits at the bottom of a potential well.
Possibly there is room to argue that the existing arguments for moduli stabilization in string theory (Acharya 02, KKLT 03, Buchbinder-Ovrut 03) are lacking in rigor, but I don’t see how one would argue that they are based on an elementary misunderstanding of what the problem is.
For the N’th time, Penrose is not talking about the moduli stabilization problem. Why do you insist he is? If you want to know what his argument is, find a copy of the book, or lookup up his article “On the instability of extra space dimensions” in the Hawking 60th birthday volume. If you can’t be bothered to read his argument, why post things on the internet saying it is wrong?
FYI, Penrose’s paper is (mostly) available via Google, a few pages missing. More than enough to see what he is talking about. Which is NOT moduli stabilization. Very interesting stuff, I have to go back now and read the original Cartan paper. Penrose also has interesting things to say about ADS/CFT.
In “On the instability of extra space dimensions” section 10.2 focuses on vacuum solutions of Einstein gravity:
This is the assumption that is shown to be false by the stabilization mechanisms from 2002/03 by Acharya, KKLT, and others cited above: they work with two extra ingredients present in string theory but not in KK-gravity: effective potentials introduced by the presence of higher form fields (fluxes) and non-perturbative effects.
I suppose it would be worthwhile for mathematical physicists to have a closer inspection of these string theoretic arguments, but what is discussed in “On the instability of extra space dimensions” is the problem without string theoretic effects.
Now, of course “On the instability of extra space dimensions” was written for a meeting in 2002, hence just a moment before string theorists presented their solution to the stabilization problem.
Yes, there’s nothing in there about KKLT, which is irrelevant to his argument. If you now have access to his paper, why don’t you read it and try and understand his argument, instead of insisting that it is something it isn’t, and which he explicitly says it is not (in the latest book)?
Peter, something OT. videos of talks at Cosmo-16 including on particle physics subjects
To be clear, Penrose also declares that the responses he’s seen to his talk on Hawking’s 60th birthday have been, “dismissed with what would appear to be a somewhat hand-waving quantum-mechanical argument of a general nature that I regard as basically fallacious.” He goes on to restate the argument, “in a more forceful form” in section 1.10 of his new book which I am just getting to read now.
The general tone I see is one of frustration that string theorists have not addressed the overall geometrical and physical considerations he sees as obvious. Coming from Penrose with his manifest expertise in geometry and general relativity I’m surprised that his concerns haven’t been taken more seriously. Here is some flavor:
“It is my impression that many of the most obvious geometrical and physical issues arising from the perspective of string theory are never really properly discussed at all!”
“I find this curious lack of a coherent geometrical picture of how string theory is to be viewed in ordinary physical terms to be very odd.”
“The acceptance, by a highly knowledgeable section of the physics community, of such a hybrid of great geometrical sophistication on the one hand and a seeming disregard for an overall geometrical coherence on the other is something that I find extremely puzzling!”
FWIW, in section 1.10 of his new book he brings up your objection regarding the quantum hall effect as a 2-space quantum phenomenon taking place within ordinary 3-space. Penrose says it is a “completely false analogy” because the quantum hall effect is an example where the lower-dimensional space is a “subspace” of the higher one rather than the “factor space” in String Theory’s 10 dimensional spacetime with the 6-space and regular 4-spacetime in an M x X factor space. He then goes on to say that the analogy is better suited to “very different brane-world picture” which he is going to discuss later. But please read the book as I am probably botching something.
more useful than quoting passages about Penrose’s puzzlement and reactions to reactions, would be to quote some actual mathematical or physical arguments (or, gasp, even a sketch proof), so everyone can see what all the fuss is about. I’m not about to pop out and buy a book (or rather wait for international delivery, or else find a bookstore to order it for me) to check what might be one page of proof in an area which is not my own, but I am interested to know what the various arguments are.
If we all had the relevant passage in front of us people wouldn’t be trying to second-guess what it might contain based over lectures over a decade old, and could make progress.
Thanks for pointing me to this section. I only skimmed the book and missed it.
I think the question is relevant. Penrose argues (in the same chapter) that the motion of the sun will excite extra-dimensiona modes. If this was true, I would expect that a two-dimensional current excites three-dimensional electronic states, which contradicts standard EFT arguments (and experiment).
I fail to understand Penrose’s claim that this is a false analogy, and the distinction he makes between subspaces and factor spaces.
If I thought I could do his argument justice in just a few well-placed quotes I might try, but I have no such belief. Penrose wrote a chapter of a book about it so I think you would be best advised to read it when you get the chance if you are interested rather than have a layman try and paraphrase his argument in a blog comment.
I will note that he also devotes a considerable bit to throwing shade on AdS/CFT as well using some of the same types of arguments. Seems he respects the mathematical tools, but finds the possible connection to our actual physical universe tenuous at the very best. Mostly, I think he is just frustrated that no one bothers to respond other than Lenny Suskind basically telling him that his reservations are well founded, but please hush up about it so as not to discourage the kids working on string theory.
It’s always refreshing to hear from Penrose. I don’t always agree with his criticisms or answers to questions — but he’s asking the right questions and raising important issues.
My main problem with Penrose’s arguments is his weird prejudice against inflation. Surely, he’s right that deeper questions need to be addressed about the connection between gravity and thermodynamics, or why the inflationary universe starts in the first place in a low- or zero-entropy state. I doubt if gravity or consciousness plays a fundamental role. Rather, I think gravity, quantum mechanics, and thermodynamics have a basic relationship that we don’t fully understand but that we can reasonably guess is important, on the basis of gravitational event horizons and singularities, for example.
Similarly, consciousness is a prime candidate for an essentially quantum phenomenon at the macroscopic scale. But it’s the quantum that’s fundamental, not consciousness. Free will is fine, too, if we’re careful to define it without recourse to dualism. Aristotle comes in handy here, as he answered a similar difficulty, in a different context, in his disagreements with Plato. In fact, modern physics, with quantum mechanics, thermodynamics, and gravitation, is in a position to sensibly ask ontological and teleological questions not legitimate in a scientific framework since the death of Aristotelianism three or four centuries ago. But we’re asking these questions in a completely different context, not within exploded philosophical and theological frameworks. Maybe that’s what Templeton is after, in a misguided way. Nice try.
It’s likely in the next decade that the evidence in favor of inflation will become decisive. So it’s important to keep up the effort to stop the false association in lay people’s minds (and even the minds of scientists) between inflation and the multiverse (in the string or “landscape” sense). The two are logically and historically unrelated. Technically, it’s difficult to get inflation to work in string-infused QFT models. If a future BICEP or Planck nails the case for inflation, it should be viewed as a highly prejudicial against string theory.
Then surely *someone* who has access to the book can supply the concrete mathematical/physical arguments in enough detail so that those familiar with the necessary technical bits and pieces can see what he’s getting at? If in these discussions so far experts are misunderstanding what the issues are that Penrose claims, then insufficient detail has been given.
Ok, with the risk that I am probably grossly simplyfing or misrepresenting his argument I’ll try.
Penrose’s biggest critique – but by no means sole critique – of String Theory’s cavalier attitude towards extra spacial dimensions is presented in chapter 1.10 of his book. The argument goes that the extra spacial dimensions will necessarily entail a (vast!) functional freedom above and beyond those of our familiar four dimensional space-time. He explains this in detail, but here I just take it as acknowledged. Penrose says that String Theorists usually dismiss this and say it will never come into play because of the huge energy required to excite these 6 small dimensions and activate their degrees of freedom.
To be clear, he is not talking about *zero-modes*, but rather excitations that *do* require energy. In the types of String Theory which purport to address quantum gravity in a serious way he says the energy necessary to excite these degrees of freedom would be on the order of the Planck energy.
Here, he says String Theorists usually argue that to excite them would need a process involving individual particles accelerated to this approximate Planck energy. Penrose finds this argument utterly unconvincing for many reasons, but the chief being that the space-time presented in this picture – at least in the ground state – is a *product space* M x X. In this space, M represents our familiar classical 4-space-time and X is represents the extra spatial dimensions. Were X to be excited, then the ‘excited mode’ as opposed to the ground state, would be given by M x X` and this is to be thought of as representing the space-time of the *entire universe.* In this context, the Planck energy is not large at all.
He goes on to explain the nonlinear instability involved when considering this 10-space as representing a space-time where some Einstein equations are presumably taken to be controlling the evolution of both sets of degrees of freedom in the 6-space of the small dimensions and the regular 4-space.
That’s the nut of the biggest critique I think, but he explains in far more detail than I can provide here. I really recommend if you are interested to go to amazon and get his book which is available on kindle right now.
Ok, arguments that assume a compactification is just a product always seemed slightly fishy to me. This is not fatal, though, if the argument is really local in nature, but the fibres should probably be some sort of interesting orbifolds, and the fibration may not be locally trivial etc etc.
I realise there is yet more detail, but it’s not going to be forthcoming here at the present rate. I’m not going to buy a Kindle book any time soon, so perhaps I’ll take a peek if and when my local shop gets it in, or some kind soul gives a thorough breakdown of the relevant material.
A buddy of mine with some friends at Princeton found the following links to these lectures. You can even download them.
They are just hard to find, I guess.