Can Laplace's formula model a deterministic universe that is irreducibly probabilistic?

2003/07/09 by Bhupinder Singh Anand, Anand, Bhupinder Singh
Computer Science · Mathematics · Physics and Astronomy · #03B10 #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #math.GM #msc:03B10

paper · pdf · doi:10.48550/arxiv.math/0307104

27 pages; an HTML version is available at http://alixcomsi.com/Can_Laplace's_formula.htm

arxiv created 2003/07/09 · openalex publication_date 2003/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If we assume the Thesis that any classical Turing machine T, which halts on every n-ary sequence of natural numbers as input in a determinate time t(n), determines a PA-provable formula, whose standard interpretation is an n-ary arithmetical relation f(x1, ..., xn) that holds if, and only if, T halts, then we can define Laplace's formula recursively such that it can model the state of a deterministic quantum universe that is irreducibly probabilistic.

Citations

• Why we must heed Wittgenstein's "notorious paragraph"
• Some consequences of a recursive number-theoretic relation that is not the standard interpretation of any of its formal representations
• On Computable Numbers, with an Application to the Entscheidungsproblem

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