The Computable Universe Hypothesis

Matthew P. Szudzik

doi:10.1142/9789814374309_0025

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arXiv · 1003.5831

The Computable Universe Hypothesis

Matthew P. Szudzik

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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.

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BibTeX RIS

Matthew P. Szudzik. 2010-03-27. The Computable Universe Hypothesis. https://doi.org/10.1142/9789814374309_0025

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