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.