Computability and Physical Theories

TL;DR

This paper explores the computability of physical theories, proposing a formal criterion based on whether their predictions are mathematically computable, and examines implications for quantum gravity theories.

Contribution

It introduces a formal definition of computability for physical theories and applies it to quantum gravity, raising questions about the role of algorithms in physical acceptability.

Findings

Indications that some quantum gravity theories may lack computable predictions

Proposes a formal criterion for the computability of physical theories

Discusses the philosophical implications of algorithmic criteria in physics

Abstract

The familiar theories of physics have 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 one approach to a quantum theory of gravity, there are found indications 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.