Rube Goldberg’s Instruction Manual

Since string theory first became popular in 1984-5, attempts to connect it to particle physics have suffered from various problems. One of the most severe of these goes under the name of “moduli stabilization”. Six dimensional Calabi-Yau manifolds come in families, parametrized by “moduli”. The dimensions of these moduli spaces can be of order 100 or so.

Naively it might appear that string theories are characterized by a choice of a topological class of Calabi-Yaus (no one knows if the number of these is finite or infinite), and then a choice of each of the 100 or so parameters that fix the size and shape of the Calabi-Yau. According to the standard string theory ideology, this is not the right way to think, instead there is really only one string theory, with different moduli values corresponding to different states. The moduli parameters are supposed to be dynamical elements of the theory, not something parametrizing different theories.

The problem with this is that if you promote the moduli to dynamical fields, they naively correspond to massless fields, and thus give new long-range forces. So you have to explain away why we don’t see 100 or so different kinds of long-range forces, and the experimental bounds on such forces are very good. Some kind of dynamics must be found that will “stabilize moduli”, giving them a non-trivial potential. The moduli fields will then be fluctuations about the minima of this potential. If the quadratic piece of the potential is large enough, their mass will be high enough to have escaped observation.

One needs a potential with non-trivial minima, and has to ensure that the dynamics is not such that the moduli will run off to infinity. In recent years, ways of achieving this have been found that typically involve “flux compactifications”, i.e. choosing non-trivial fluxes through the topologically non-trivial holes in the Calabi-Yau. On the one hand, this seems to provide a long-standing solution to the problem of how to stabilize the Calabi-Yau, on the other hand, it appears that there is an exponentially large number of possible minima. This is the origin of the “Landscape” and the associated claims of 10500 or more possible vacuum states for string theory.

The constructions involved are famously exceedingly complex and ugly, with Susskind referring to them as “Rube Goldberg machines”, and one of their creators, Shamit Kachru, the “Rube Goldberg architect”. Very recently a new Reviews of Modern Physics article by Kachru and Douglas called Flux Compactification has appeared. It can be thought of as a manual describing how to construct and count these Rube Goldberg machines.

Many string theorists had long hoped that whatever method was found to stabilize moduli would have only a small number of solutions. Then, in principle one would get only a small number of possible models of particle physics for each topological class of Calabi-Yaus. If the number of these was finite and not too large (the known number of constructions is something like 105-106), then to see if string theory could make contact with particle physics, one would just have to do a moderately large number of calculations, check them against the real world, and hope that one matched. If it did, it would then be highly predictive.

The existence of the flux compactifications with stabilized moduli described in the Douglas-Kachru article has convinced many string theorists that this old dream is dead. Some have tried to claim that this is a good thing, that the exponentially large number of states allows the existence of ones with anomalously small cosmological constants, and thus an anthropic explanation of its value. The problem then becomes one of how to ever extract any prediction of anything from string theory. Small CCs are achieved by very delicate cancellations, and it appears to be a thoroughly calculationally intractable problem to even identify a single state with small enough CC.

Many string theorists are now claiming that this is not really a big deal. So what if there are lots and lots of string theory vacua, it’s just like the fact that there are lots and lots of 4d QFTs! For arguments of this kind, see recent comment threads here and here. There’s something fishy about this argument, since discussion of flux compactifications has from the beginning focused on whether it is possible to use them to make predictions, whereas no one ever was worrying about whether (renormalizable) QFTs were predictive or not.

The source of the problem lies in the combination of the large numbers of string theory vacua with their Rube Goldberg nature. Consistent 4d QFTs are characterized by a limited set of data (gauge groups, fermion and scalar representations, coupling constants), and it has turned out that among the simplest possible choices of such data lies the Standard Model. String theorists commonly describe the Standard Model as “ugly”, but it is among the simplest possible 4d QFTs, and is extremely simple and beautiful compared to something like the flux compactification constructions. One could hope that while flux compactifications are inherently rather complicated, one of the simpler ones might correspond to the real world. As far as I know there’s no evidence at all for this, such a hope appears to have nothing behind it besides pure wishful thinking. Some string theorists like Douglas and Kachru don’t seem to think this is possible, focussing instead on statistical counts of more and more complicated flux compactifications, hoping to find not a simple one that will work, but a statistical enhancement of certain complicated ones that would pick them out.

4d QFT is a predictive framework not because the number of possible such QFTs is small, but because our universe is described extremely accurately by one of a small number of the simplest of such QFTs. A few experiments are sufficient to pick out the right QFT, and then an infinity of predictions follow.

Is the QFT framework falsifiable? One could imagine that things had worked out differently, that instead of the Standard Model predictions being confirmed, each time a new experimental result came in, one could only get agreement with experiment by adding new fields and interactions to the model. It might very well be that the QFT framework could not be falsified, since one could always evade falsification by adding complexity. This happens very often with wrong ideas: they start with a simple model, experimental results disagree with this, but can be matched by making the model more complicated. As new experiments are done, if the original idea is wrong, it doesn’t get simply falsified, but the increasing complexity of the models needed to match experiment sooner or later causes people to give up on the whole idea.

This is very much what has happened with string theory. The simple models that got people excited about the idea of string theory unification don’t agree with experiment, with the moduli stabilization problem just one example. It appears one can solve the problem, but it’s a Pyrrhic victory: one is forced into working with a class of models so vast and so complicated that one can get almost anything, and never can extract any real predictions.

Douglas and Kachru do address the question of whether one can ever hope to get predictions out of this class of models, but their answer is that they can’t think of any plausible way of doing so. They mention various things that people have tried, but none of these ideas seem to work. The best hope was that counting vacua with different supersymmetry breaking scales would lead to a statistical prediction of this scale, but this has not worked out for reasons that they describe. In the end they conclude:

For the near term, the main goal here is not really prediction, but rather to broaden the range of theories under discussion, as we will need to keep an open mind in confronting the data.

This acknowledges that no predictions from this framework seem to be possible, and that continuing work in this area just keeps producing yet wider and wider classes of these Rube Goldberg machines. They are suggesting basically giving up not on string theory, which would be the usual scientific conclusion in this circumstance, but instead to for now give up on the theorist’s traditional goal of making testable predictions. They advocate not giving up on string theory no matter how bad things look, instead just continuing as before, hoping against hope that an experimental miracle will occur. Maybe astronomers will find evidence for cosmic superstrings, maybe the LHC will see strings or something that matches up with characteristics of one of the Rube Goldberg models. There’s not the slightest reason to believe this will happen other than wishful thinking, which has now been promoted to a new program for how to do fundamental science.

Update: Via Lubos, for those who don’t know what a Rube Goldberg machine is, two examples are here and here.