In today’s blog with talk to Dr. Peter Woit, PhD from Princeton University and Senior Lecturer in the Mathematics Department at Columbia University.
David: Over a decade ago, you criticized string theory in Not Even Wrong. Has progress in the field been satisfactory?
Peter: I actually started writing publicly about the problems with string theory almost exactly 20 years ago (see https://arxiv.org/abs/physics/0102051). That article I think has held up very well, with the problems pointed out there just becoming more obvious and more serious since that time. The negative experimental results from the LHC have also had a significant effect. My impression of the situation now is that leading figures in the field have more or less given up hope on the idea of unifying physics using string theory and have moved on to working on other things.
David: I recall one of the criticisms from our discussion 8 years ago was the absence of symmetry principles within string theory. Is the representation theory perspective of your recent quantum textbook related to the importance you see in symmetry principles?
Peter: Yes, one motivation for writing that textbook was to provide an exposition of quantum theory that emphasized the essential role that symmetry principles, expressed mathematically in terms of Lie groups, Lie algebras and their representations, play in the theory.
The fundamental problem of string theory has always been the lack of a non-perturbative formulation of the theory. What is known is a perturbative expansion based on string world-sheets, where symmetry does play a crucial role (conformal invariance on the world-sheet). But all attempts to come up with a full theory have not been successful. The hope has always been that a conjectural "M-theory" satisfying certain duality properties exists, but the search for this has been fruitless. No one has been able to come up with even a promising idea, with one aspect of the problem the lack of any evidence of a fundamental symmetry principle that one could base M-theory on.
David: What do you make of these recent ideas connecting entanglement and space?
Peter: I haven't followed these closely. As far as I can tell, there is nothing in these ideas that addresses the two big questions about the relations of space-time and quantum theory:
1. Unification: what is the relationship between space-time degrees of freedom and the internal symmetry degrees of freedom of the Standard Model?
2. Quantum gravity at short distances: can one find a consistent quantum theory of gravity? By this I mean a quantum theory governing the space-time degrees of freedom which has classical general relativity as an effective theory at large distances, but also a consistent dynamics at short distances.
David: What is quantum theory about? Peter: Quantum theory is our deepest and most fundamental theory of how the physical world works. We have yet to fully understand its structure, which remarkably involves our deepest ideas about mathematics.
David: Thank you Professor!