CHAPTER 1: Computability and Physical Theories
With Robert Geroch (Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA).
The familiar theories of physics share the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature — one based on the issue of whether or not the physically measurable numbers predicted by the theory are computable in the mathematical sense. Applying this formulation to an approach to quantum theory of gravity, indications imply that there may exist no such algorithms in this case. Finally, we discuss the issue of whether the existence of an algorithm to implement a theory should be adopted as a criterion for acceptable physical theories.
