Question

It's a truism that in science it is at least as important to state the reasons why a theory or idea might be wrong, as to state the reasons why it is might be correct. For example, early renormalization methods made experimental predictions that were very accurate, but the inventor's famously worried for decades about the conceptual problems of divergences; and many of their papers/articles/books on the subject include a long discussion about how acutely worried they were that their method for handling divergences was deeply flawed somehow.

My intention with this post is not to engage any user in a debate about whether string theory is true or not. I think anyone who takes string theory seriously should be happy to acknowledge as clearly as possible all the potential theoretical issues/problems with the theory.

Therefore I would like to ask, what are the major theoretical problems which would lead a reasonable person to be worried that string theory is not an accurate theory? I am excluding the fact that string theory has made no (major) predictions that have been confirmed, I am only interested in conceptual and theoretical ideas which might discredit the theory.

Please keep all answers to one issue per post.

Answer 1

I don't know any reason to suspect string theory may be incorrect, but the closest analogy to renormalisation infinities is the fact that we only know string theory as a perturbation series from a fixed background, plus a collection of non-perturbative dualities that relate different versions. By rights there should be a better formulation from which all the perturbative string theories can be derived directly. M-theory is a name sometimes used in this connection but we still don't know what it is.

Even if string theory were not a theory of physics there would be good reason from the mathematics to think that such a formulation exists because otherwise all the relationships between the different string theories would be just creepy coincidences. There really has to be some underlying framework that explains them.

I think this is comparable in some ways with the original view of renormalisation which made people question the original perturbative formulations of quantum field theories. Once non-perturbative formulations such as lattice gauge theory emerged they were able to understand renormalisation as a scaling behaviour related to critical points in the theory and things were better understood.

String theory has other problems such as the need to understand how a vacuum can be selected that explains low energy particle physics and the cosmological constant. We also need to understand better what happens to spacetime in string theory at Planckian energies. These problems are often highlighted because they are the reason why string theory cannot yet make any testable predictions, but I don't think they can be resolved properly until the underlying principles of the theory are known. So that is the key issue to resolve first.