Warped Passages

A couple days ago I got ahold of a copy of Lisa Randall’s new book Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions, and finished reading it last night. It’s a book intended for a popular audience, containing an overview of modern physics, but concentrating on the idea of extra dimensions beyond the standard four we know about. The last part of the book attempts to explain at a non-technical level work by Randall and others that generically goes under the name of “braneworld scenarios”, and involves various versions of the idea that our four dimensional space-time is embedded in some higher dimensional space. The specific ideas she describes in some detail are:

1. Work with Raman Sundrum (hep-th/9810155) on solving the flavor-changing problems that occur in supersymmetric models by “sequestering” the supersymmetry breaking sector on another brane, separated from ours.

2. The Arkani-Hamed, Dimopoulos and Dvali idea (hep-ph/9803315) of large extra dimensions, which explains the weakness of gravity as due to the large size of some of the extra dimensions, with gravity propagating in them, but not the other forces.

3. The Randall-Sundrum warped geometry with two branes (hep-ph/9905221).

4. The Randall-Sundrum warped geometry with an infinite extra dimension, using AdS geometry (hep-th/9906064).

5. Work with Karsch on “localized gravity” (hep-th/0011156).

I afraid I’ve never found these brane-world scenarios to be at all compelling. They don’t really seem to me either aesthetically appealing or able to explain in a convincing way any of the things we don’t understand about the standard model. They’re not derived from any fundamental theory, so the rules of what branes you’re allowed to postulate and what properties you can assign to them seem very loose, allowing all sorts of things. At one point Randall writes:

Other branes might be parallel to ours and might house parallel worlds. But many other types of braneworld might exist too. Branes could intersect and particles could be trapped at the intersections. Branes could have different dimensionality. They could curve. They could move. They could wrap around unseen invisible dimensions. Let your imagination run wild and draw any picture you like. It is not impossible that such a geometry exists in the cosmos.

which I guess is meant to be inspiring, but makes me worry there’s not enough structure to this game to make it useful. One virtue of some of these models is that they lead to new phenomena at potentially accessible energy scales. If the LHC sees the kinds of effects predicted by these models, there will be some well-deserved Nobel prizes for the people involved in this story, but this seems to me highly unlikely. Randall says in her book that she really does believe in these sorts of extra dimensions, but most particle theorists I know of (string theorist and non-string theorist) tend more to the opinion that while these are models worth investigating (since you may learn something, and it gives experimentalists something more specific to look for), there’s only the most outside chance that they correspond to what the LHC will see.

The one problem of the standard model that braneworlds do provide an interesting answer for is the hierarchy problem, that of why the weak and Planck scales are so disparate. In these scenarios, the fundamental gravitational scale is not the Planck scale, but something closer to the weak scale, so (unlike in the standard picture) gravity is not weak because the Planck scale is so large, but because braneworlds provide various mechanisms for making the gravitational force much weaker than the others. The idea that the gravitational scale may be closer to and maybe even directly related to the weak scale, and that this is somehow related to the electroweak symmetry breaking mechanism that we still don’t understand, is an appealing one, but the ways braneworlds accomplish this removes much of the appeal (at least for me). The choices just seem too arbitrary, and while there is some geometry involved, it is geometry of a crude sort. The standard model involves fascinating and beautiful spinor geometry and the geometry of Yang-Mills fields, which is pretty much ignored in these scenarios, which try and get everything out of simple Riemannian geometry and general relativity sorts of considerations.

There’s a lot about string theory in the book, with Randall clearly skeptical about many of the claims made for the theory. I remember a few years ago at a debate over string theory held at the Museum of Natural History here in New York, she scornfully responded to the argument that “string theory predicts gravity” with “sure it does, gravity in ten dimensions.” Here she says I’m an agnostic on this subject – I don’t know what string theory will ultimately be or whether it will solve the questions of quantum mechanics and gravity it sets out to address. She’s similarly agnostic about GUTs: Although unified theories have some appealing features, I’m not really sure whether studying them will lead to correct insights into nature. The gap in energy between what we know and what we extrapolate to is huge..

Randall describes being a student in 1984 at Harvard, seeing the field split into two camps that were at odds with each other: Gross/Witten doing string theory at Princeton, Georgi/Glashow doing model building at Harvard. About Princeton she says :

Physicists there were so certain that string theory was the road to the future that the department no longer contained any particle theorists who didn’t work on string theory – a mistake that Princeton has yet to correct.

She tells the story of the relation between model builders and string theorists over the last twenty years as follows;

Early on, the battles between the merits of the two opposing viewpoints – string theory and model building – were fierce, with each side claiming better footing on the road to truth. Model builders thought that string theorists were in mathematical dreamland, whereas string theorists thought that model builders were wasting their time and ignoring the truth.

Fortunately, things have now changed. ….many of us now think about string theory and experimentally oriented physics simultaneously. I have continued to follow the model building approach in my research, but I also incorporate ideas from string theory…. The communities are no longer so rigidly defined, and there is more common ground. Both scientifically and socially, there are now strong overlaps between model builders and string theorists.

The fact that branes are an important part of modern string theory meant that string theorists took an interest in this kind of model-building, with Randall noting that:

In fact, because our research didn’t directly challenge string theory models, the string theory community actually accepted and recognized the significance of our work sooner than the model-building community.

In particular, the fact that the Randall-Sundrum model uses the same AdS geometry and has interesting relations to AdS/CFT has drawn a lot of interest from string theorists. Whatever you think of all this as physics, as academic politics it was an absolute stroke of genius, defusing a bitter conflict. I confess to finding this unholy alliance between the model-builders and string theorists rather problematic. I’d much prefer to see the model-builders holding string theorists accountable for the theory’s inability to actually predict anything or even lead in any well-defined way to a specific class of models that could be tested. By reaching an accomodation with string theorists and agreeing on a central role for string theory in particle theory research, the model-builders have made the string theory juggernaut pretty much impregnable, leaving anyone interested in alternatives to string theory very much marginalized within the particle theory community.

In the acknowledgements, she prominently thanks one of her Harvard colleagues:

Lubos Motl, a brilliant physicist and dedicated science communicator (whose specious ideas about women in science we’ll ignore), read everything, even before it was readable, and gave extraordinarily useful suggestions and encouragement at every stage.

Update: Lubos has a new posting about Randall’s book. He ends by referring to some forthcoming book containing “dumb insults against the physicists”. I guess the rumors that he’s written something for publication must be true then.

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25 Responses to Warped Passages

  1. Chris Oakley says:

    In the absence of any evidence for hidden dimensions, especially those in need of unraveling, the title, “Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions” is somewhat misleading.

    I would prefer, “Exploring the possibility that extra dimensions might solve some problems in physics”.

    But, hey, when did honesty sell books?

  2. Very says:

    >The choices just seem too arbitrary, and while there is some >geometry involved, it is geometry of a crude sort. The standard model >involves fascinating and beautiful spinor geometry and the geometry >of Yang-Mills fields, which is pretty much ignored in these scenarios, >which try and get everything out of simple Riemannian geometry and >general relativity sorts of considerations.

    Crude??? The “beautiful” spinors you write about are one of the renormalizable local representations of the Poincare group, which is why they appear, not because of their underlying “beauty”. Similarly, gauge theories arise because when you try to describe massless spin-1 bosons using a vector field, we come up with unphysical gauge degrees of freedom. The only consistent way to make those massless spin-1 bosons self-interacting is if they happen to arrange themselves into a Lie algebra. There’s no underlying mathematical beauty here either.

  3. Chris Oakley says:


    Beauty is very much in the eye of the beholder, but I agree to the extent that the beauty of Yang-Mills evaporates as soon as one tries to quantize. If gauge fixing, ghosts or renormalization is beautiful then the Incredible Hulk ought to win Miss America.

  4. woit says:


    Some of us happen to think that the fact that gauge fields are connections and connections are the fundamental objects in modern geometry means that they’re mathematically beautiful. You’re welcome to the philosophy that this is just a coincidence, that what’s important is what gives consistent quantization of a massless spin-1 field, but my philosophy is different. We can’t really have a rational discussion about what is mathematically beautiful and what isn’t, but I’ll point out that I just spent a year teaching our graduate course in geometry in the math department here, so I have some idea what mathematicians consider the deepest and most beautiful constructions in the subject.

    Similar remarks apply to spinors. As to “crude”, Riemannian geometry is 19th century mathematics, spinor geometry and the geometry of general connections is 20th century mathematics.

  5. woit says:


    I agree with you that the way gauge invariance is handled in quantum Yang-Mills theory is not a pretty sight. It gets the Feynman rules right, but opens all sorts of other questions. I suspect there are better, more beautiful ways of doing it, and these are very much worth working on.

  6. Shantanu says:

    Peter, does this book discuss Loop quantum gravity , dynamical
    triangulations or anything else besides string theory?

  7. woit says:


    Nothing about loop quantum gravity, dynamical triangulations, etc., and very little about quantum gravity. Randall makes it clear she’s fundamentally a particle theory model builder, interested in making models of particle physics that have some hope of being tested at future accelerators or other particle physics experiments.

    I undoubtedly overemphasized how much there is about string theory in the book, since I was interested in her relation to string theory, and she does write extensively about this. But most of the book is basically a particle physics book, aimed at getting to and explaining her work on braneworld scenarios in particle physics.

  8. Who says:

    Shantanu that is a great question
    does [the Randall] book discuss Loop quantum gravity , dynamical
    triangulations …?

    I’m inclined to think that at this point any book that pretends to be about contemporary views of spacetime and does not give an adequate description of the loop and triangulation pictures is appealing to self-indulgent fantasists rather than to interested lay readers.

    So I am curious too. Maybe Peter will tell us. (Must say I dread the answer.)

  9. woit says:


    Already answered that question above. This is not in any way, shape or form a book about quantum gravity, and actually I think that’s fine. The problem of quantum gravity is not the only important one out there!

    Although after writing this comment I thought better of it. The assumption that the gravity scale is much lower than the Planck scale does mean one is saying something about quantum gravity in these braneworld scenarios. But Randall isn’t much interested in any of the standard conceptual problems about quantizing gravity, or in the question of what happens at very high energies, whether the theory is finite, whether there’s a background independent theory, etc. She’s taking a very pragmatic approach, not asking fundamental questions about space and time of the sort that normally are part of the subject of quantum gravity.

  10. dan says:

    “Lubos Motl, a brilliant physicist and dedicated science communicator (whose specious ideas about women in science we’ll ignore)”

    i’m kinda curious as to what lubos’ ideas about women in science, as we all clearly know his views on LQG.

  11. woit says:

    He seems to have gotten himself into trouble with his colleagues over this. Basically he was strongly supporting Summers in the recent controversy at Harvard over women in science. Like Summers, he seems to believe that the reason there are a lot fewer women than men in science is that, on the whole, they’re dumber.

    Oh, and please don’t start up a discussion of this whole controversy here, it’s been done to death already many places on the internet. So unless someone has a really informative and original comment on this (or Lubos wants to defend himself against mischaracterization of his views), I’ll probably delete more comments about this as off-topic.

  12. Gordon says:

    You should realize, that none of theories you advertised are quantum consistent. They explode upon quantization. I still
    dont know what to do about this, besides many months of work.

  13. Jean-Paul says:

    You described the book without any comments on its quality — very diplomatic.
    So is it a good book? A possible best-seller?

  14. Thomas Larsson says:


    What you say about spinors and connections is technically correct, but why don’t you think that this is beautiful? Mathematical beauty is usually connected with symmetry, and groups (and infinitesimally Lie algebras) are the language of symmetry.

    You can regard differential geometry (DG) as the representation theory of the group of diffeomorphisms. All objects of interest in DG, like tensor fields, connections, exterior and covariant derivatives, etc., have a natural formulation in diffeomorphism group language. This is obvious, since DG is about well-defined objects, and an object is well-defined precisely when it transforms as a representation under arbitrary coordinate transformations.

    You are of course free to think that DG is trivial or ugly. However, you cannot coherently argue that DG is beautiful and that diffeomorphism group representations are not, because the former is a special case of the latter.

    A major insight of conformal field theory is that in addition to the classical reps relevant to 1D DG (primary and secondary fields), there are also quantum or lowest-energy reps, with energy = L_0: Verma modules, Fock modules, minimal models, etc. These quantum reps are directly applicable to the physics of 2D phase transitions, and also play an important role in string theory; the special role of D=26 follows immediately from the Virasoro algebra.

    Algebras of diffeomorphisms and gauge transformations admit similar quantum representations also in higher dimensions. I have tried to educate the physics community about this remarkable fact for several years, so far in vain. People unwilling to learn are simply not susceptible to edification.

  15. a says:

    From a phenomenological point of view the AdS/CFT duality means that the Randall-Sundrum model is the same thing as “walking technicolor”. So, it is curious that almost no phenomenologist likes to work on technicolor (because disfavored by precision electroweak tests), while its dual Randall-Sundrum version attracted a lot of attention. Luckily LHC will start in a few years, allowing us to restart doing real physics.

  16. woit says:


    No clue whether it will be a best-seller. Intellectually, I think it’s a better book than many recent ones of the same genre, because there’s less gee-whiz evangelizing for very speculative ideas that probably don’t work. In this case the author only does a bit of this, and mostly only for her own work. Every scientist should have the right to write something overly optimistic about their own work for the general public, and I think anyone reading such a thing does so well aware that people tend to have an exaggerated opinion of how wonderful their own children are. About ideas like supersymmetry and string theory, Randall is even-handed, saying the jury is out and explaining what some of the severe problems with these ideas are.

    The book is written so as to be in principle understandable by someone with no knowledge at all of math or physics, which is a worthy goal, but I’m not sure how realistic this is. Some simple ideas are explained in great detail, with several different analogies and related stories. I confess to having skipped most of this, since it wasn’t aimed at me, and it’s hard to tell how effective these parts of the book will be. I just finished my own book, and spent a lot of time thinking about how to explain some sophisticated ideas to as wide a range of people as possible, without using equations. In my case I decided to mostly avoid analogies and just give the clearest short explanation I could come up with. People with more background hopefully will get something out of these explanations, people with less will find some paragraphs baffling, but hopefully just move on to the next paragraph.

    The danger with writing a long explanation, with lots of analogies is that people can get lost in these things, and if not chosen very carefully the analogies can do more harm than good. They can confuse people who focus on the wrong part of the analogy and miss the point, or convince people they understand a concept when all they’ve learned is that X is like Y, where they know what Y is, but still don’t have a clue as to what it is about X that is like Y. Anyway, I can’t really tell how well Randall succeeds at communicating these ideas to someone who starts not knowing much at all about this stuff, for that you need to hear from a different reviewer.

  17. rrtucci says:

    I don’t like analogies too much either; but, physics/math figures (including graphs), I consider vital. (e.g. Penrose’s latest book is brimming with figures) Pedro, how many figures will your book have? Even before you answer, I will ask my next question: Do you think such a paltry number of figures is enough? If it’s still possible, I think you should add a few more.

  18. woit says:

    Hmm, the book has a few figures, but not enough. How did you know?

    Actually I’m about to start dealing with the figures next week, will take your excellent advice to think about smuggling in more.

    The figures in Penrose’s book are truly amazing, definitely one of the best parts of his book. He’s an excellent draftsman, did them himself I hear. Just thinking about the amount of work that went into them scares me.

  19. plato says:

    He’s an excellent draftsman, did them himself I hear.

    With his tessellations and influence of Escher one understands why I think.

  20. basho. says:


    I have been a reader of your blog for some time (as a graduate student in particle physics).

    Recently, I began writing too.

    I won’t be writing for some time due to other commitments.

    However, I would like it if you read a few things I had written in the past.



  21. Arun says:

    I just wonder why he feels so threatened by a book by the ignorant catering to an undemanding audience.

  22. D R Lunsford says:

    It’s utter horseshit.

    Markarian 205. WMAP. Connect the dots.


  23. Shantanu says:

    I just browsed through this book at a nearby bookstore and in the
    acknowledgements Lee smolin has been thanked.

  24. Nigel says:

    Just read Warped Passages and think it brilliant. Especially where Lisa writes on page 295 that ‘even if string theory is correct, we are unlikely to find the many additional particles it predicts. The energy of current experiments is sixteen orders of magnitude too low. … because the string length is so tiny and the string tension is so high, we won’t see any evidence to support string theory at the energies achievable in accelerators, even if the string description is correct.’

    In addition, she admits the fact that not only are these speculations impossible to test convincingly, they are also extremely vague because there are many variations of the extra-dimensional theories. She remarks on page 456: ‘We now know that extra-dimensional setups can come in any number of shapes and sizes. They could have warped extra dimensions, or they could have extra large dimensions; they might contain one brane or two branes; they might contain particles in the bulk and other particles confined to branes. … Which, if any, of these ideas describes the real world?’

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