The Computable Universe Hypothesis

TL;DR

This paper defines computable physical models, explores their properties, and formalizes the computable universe hypothesis, suggesting all physical laws may be inherently computable.

Contribution

It introduces a formal definition of computable physical models and connects it with the computable universe hypothesis, expanding the theoretical framework of physical computability.

Findings

Examples of computable models including discrete, continuous, and probabilistic systems

Formulation of models using type-two effectivity (TTE) on topological spaces

Operations like coarse-graining and statistical ensemble formation are computably formalized

Abstract

When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is discussed, and several examples of computable physical models are given, including models which feature discrete motion, a model which features non-discrete continuous motion, and probabilistic models such as radioactive decay. We show how computable physical models on effective topological spaces can be formulated using the theory of type-two effectivity (TTE). Various common operations on computable physical models are described, such as the operation of coarse-graining and the formation of statistical ensembles. The definition of a computable physical model also allows for a precise formalization of the computable universe hypothesis--the claim that all the laws of physics are computable.