Lemonade from the Landscape

There's a piece by Michael Dine in Physics Today this month with the ambitious title "String theory in the era of the Large Hadron Collider, thus combining two of my very favorite topics... I was going to give it a pass, but I was surprised to discover that it's freely available-- most of their articles are behind a subscription wall-- and as long as it's linkable, I might as well say something about it.

The bulk of it is stuff that anybody with a passing familiarity with high-energy physics has heard before. Unification of forces, blah, blah, quantum gravity, blah, blah, only game in town. It's a well-done capsule summary of the state of the theory, but it's not terribly new.

The title appears to promise some sort of connection between string theory and the soon-to-be-started-up LHC, so you might be hoping for something good about string phenomenology. Alas, it's just another piece on the "Landscape," which as always comes off as a desperate attempt to make lemonade from all the sour citrus fruit that nature has handed to string theorists.

A quick (and slightly snarky) summary of the "landscape" issue, for those who haven't heard it before: The term refers to a problem that comes out of the process of trying to use string theory to unify the fundamental forces and account for the fundamental particles. As you know, even if you're not named "Bob," string theory is based on the observations that it's possible to describe all of the fundamental particles observed in physics using a model that is mathematically identical to that which describes the vibrations of a piece of elastic string. Different vibrations correspond to different types of particles, and this allows you to describe everything that we see in terms of a single mathematical object.

It's a very appealing idea, but there are a couple of minor catches. In order for this to work, the "strings" have to be vibrating in ten or eleven dimensions. That's not a problem mathematically, but it's a little hard to explain why we don't see the extra five or six dimensions that ought to be there. This can be fixed by "rolling up" the dimensions so that the univers doesn't extend very far in those directions, and thus we can't detect their existence, which leads to some faintly cumbersome mathematics, but also isn't a huge problem.

What is a problem is that there turn out to be an awful lot of possible ways to "roll up" those dimensions. And those different formulations of string theory each give slightly different values of the physical constants, and slightly different sets of extra particles that haven't been detected yet. Which means that, while string theory lets you describe all the particles we see in terms of a single mathematical object, it doesn't give you a unique description of the universe that we see, but rather a whole set of different possible descriptions.

Well, what exactly does "an awful lot" mean? Maybe it's not that bad, right? "An awful lot," in this context means something in excess of 10¹⁰⁰ possible models. Different people use different numbers-- Dine eventually settles on 10⁵⁰⁰, but it really doesn't matter, as the lowest number I've seen anybody use is 10⁶⁰, which is laughably gigantic. This gargantuan number of possible models is referred to as the "Landscape" of possible theories, for reasons that really don't matter.

There are a number of different approaches that can be taken at this point. If you're Peter Woit, you throw up your hands, and start denouncing the whole field as nonsense. Most people working in or near the field note that this is hardly the only thing that we don't understand about the theory, and keep working on the other areas where string theory is generating useful physics, and hope that the eventual resolution of other problems will take care of the Landscape business. But if you're one of a smallish community of Landscape aficionadoes, you, well, try to make lemonade. And that's what Dine's piece is about.

The Landscape business is a Good Thing in his presentation, because it turns out that there are a few things that are hard to do in string theory. Recent observations tell us that the expansion of the universe is accelerating, which is described by a "cosmological constant." The observed value of this constant is very small, which is good because it allows stars and galaxies to form, and thus give rise to us, but it's kind of a hassle theoretically speaking, because it's difficult to construct a string model that gives a cosmological constant of the size that we see. If you were to pick a theory at random out of the Landscape, odds are that the constant would be a lot bigger. Like, 10¹⁰⁰ times bigger. So it's a little tough to see why our universe should have such an oddly tiny value of the cosmological constant.

This is where Dine, and Leonard Susskind, and a bunch of other people attempt to turn the Landscape problem from a bug into a feature. It's great that there are all these bazillions of possible models, they say, because we can imagine that they're all out there somewhere as different universes. And if they all exist, it's inevitable that there should be one that happens to be just like ours, which is good, because we know we exist.

This is a somewhat snarky summary-- though not nearly as snarky as what you'll get from Peter Woit-- but I have a hard time taking this stuff seriously. I'm not in the camp of people that feel that the lack of a single unique theory of everything arising from string theory signals the utter worthlessness of the enterprise-- to the contrary, I've never been particularly bothered by the particle unification problem in the first place. So you need to specify a bunch of arbitrary parameters in order to get the right value out of the model. Big deal.

(I find the case put forward by Sean Carroll to be more persuasive-- that string theory is interesting because it might provide a way to reconcile quantum mechanics and general relativity. That would be worthwhile-- according to Sean, and I'll take his word for it-- whether it manages to descibe all the particle stuff in a unique way or not. I still don't care that much, but it seems like a more sensible reason to me than complaints about the large number or free parameters in the Standard Model.)

The problem I have with Landscapeology is precisely because I'm not all that worked up about uniqueness. Which makes it seem particularly loopy for people to start going off on this huge kick about multiverses and Anthropic Principles and all the rest. You've got serious physicists running around jabbering about this sort of stoned dorm-room bull session material in response to a problem that doesn't seem like that much of a problem to me.

Dine's article is notable for taking this sort of thing to an extreme that I hadn't seen before, which is to claim that the Landscape business might be the key to making predictions that will be confirmed by the LHC. The approach that he is cautiously optimistic about, and the headline writers are more gung-ho about, is to try to look at the parts of the Landscape that match the broad features of our universe, and make statistical predictions. That is, it might turn out that those models that give cosmological constants of the right general magnitude also tend to have some other feature in common-- most of them have a particular extra symmetry, or predict the existence of a certain class of particles. Then, since we're most likely to be living in a universe of one of the more common types, you could "predict" that that general form of extra symmetry, or those general types of extra particles will be observed at the LHC. You wouldn't be able to say anything about their masses or properties, necessarily, but you could give a vague idea of what would be more likely.

This strikes me as kind of a thin reed to be grasping at, let alone touting as a great feature of your theory. Even assuming that it's possible to do this kind of statistical assessment on an unimaginably large number of very poorly understood theories, this is the kind of "prediction" that I associate with economics, not physics. And, of course, I can't help noting that we're evidently already in a fairly unlikely universe, given the trouble with finding models that reproduce the cosmological constant. Theorists have apparently already lost a 10¹⁰⁰-to-1 bet-- do you really want to go double-or-nothing on the theory that the "principle of mediocrity" has got to work out one of these days?

In the end, I find this whole line of argument pretty unfortunate, because as far as I can tell it's pretty peripheral to the actual interesting questions of the string theory enterprise (which would be things like its use for quantum gravity, and as a calculational technique for situations like the RHIC experiments). In some ways, it strikes me as being rather like arguments over the various interpretations of quantum mechanics-- it's interesting enough in a philosophical sort of way, but it really doesn't make any concrete predictions, or have any concrete applications. It may be that somebody, down the road, will find a way to do something useful with it, but until then, it's not worth spending all that much effort on.

And yet, this ends up getting more press than areas in which actual progress is being made. And, for that matter, more popular attention than whole fields of physics that are producing fascinating and concrete results all the time. It's kind of maddening, really.