A more and more common argument one hears from string theorists these days (for one version see a recent anonymous comment posted here) goes more or less like this:
“A fundamental theory shouldn’t be expected to predict things like fermion masses or the standard model gauge group anymore than it should be able to predict the physical properties of the planets. Anyone who expects this is making the same mistake as Kepler, who tried to relate Platonic solids to planet orbits.”
The idea here is that many or even all of the things we don’t understand about the standard model are not fundamental aspects of the theory we should expect to be able to predict. Perhaps they are determined by the details of the history of how we ended up in this particular time and place, just as the properties of the planets were determined by the detailed history of the formation of the solar system.
As far as we can tell, the properties of the standard model hold uniformly throughout the observable universe, so to adopt this point of view one needs to postulate the existence of an unobservable “multiverse” of which we see only one small part. The so-called “landscape” of an unimaginably large number of possible vacuum solutions for string theory provides one realization of such a multiverse.
What are the problems with this idea? First of all, it is not so easy to dismiss out of hand. One can certainly imagine the possibility of the existence of an M-theory (maybe now the “M” is for “Multiverse”) with a local vacuum state that corresponds to our universe, and some dynamics that allows evolution from one universe to another. Perhaps tomorrow night a preprint will appear on arxiv.org containing a simple equation expressing a dynamics such that the possibility of a universe exactly like ours does arise as some part of a solution. Should we believe in such a new theory, whatever it is?
There seem to me to be two possible cases in which such a theory would be compelling. The first would be if the theory made experimentally testable predictions. Perhaps it would have only one solution that agreed completely with current experimental observations. Then the properties of this solution could be used to predict the results of experiments not yet done. If these predictions were accurate, the theory would have strong evidence in its favor.
Even if the theory had so many solutions that one couldn’t readily use it to make predictions, one still might find it compelling due to its “beauty” or “elegance”. If it were based on a very simple equation or idea, the fact that the relatively complex structure of the standard model could be made to fall out of a much simpler equation would again be strong evidence for such a theory. Just how compelling this would be would depend on how much simpler it was than the standard model. If the new equation was more or less as complicated as the equations which determine the standard model, it wouldn’t be compelling at all.
The current state of affairs in particle theory is that many people believe that they are on the road to finding such a compelling theory, but all the evidence is that this is nothing but wishful thinking on their part. There is no viable proposal for an M-theory based on a simple set of equations with a solution corresponding to the real world. This simply does not exist. An easy way to embarass a string theorist who is going on about the beauty of the theory is to ask them to write down a simple set of equations that characterize this beautiful theory. They can’t do it now and I don’t see any reason to believe they ever will be able to in the future.
What string theorists have now is not a single, consistent theory, but a set of several inconsistent fragmentary theories that they hope can be turned into a consistent whole. This circle of ideas is significantly more complicated than the standard model that it is trying to explain.
Even this complex of ideas might be compelling if it could be used to explain one or more not yet understood aspects of the standard model, or if it made new experimental predictions that could be checked. All the evidence of recent years is that this is impossible. If the whole framework makes any sense at all, it appears to predict nothing and explain nothing about the standard model. Not a single one of the parameters of the standard model can be calculated, not a single experimental prediction, at any energy scale, can be made. It is becoming increasingly clear that the circle of ideas known as “M-theory” is completely vacuous.
Strong evidence that this is the case comes from the fact that string theorists have no idea what, if anything, M-theory is supposed to be able to predict. Polchinski and others feel they have demonstrated that M-theory can’t predict the cosmological constant, but can’t come up with anything else it can predict and, increasingly, seem happy to live with the idea of promoting a theory that can’t predict anything. This wholesale abandonment of the scientific method upsets some physicists such as David Gross quite a bit, but more and more people seem to have no problem with this. Frankly I find this all bizarre, disturbing, and becoming ever more so all the time.