2018/03/19 by Nicolas Gisin · 1 voice · 48 citations
Computer Science · Mathematics · Physics and Astronomy · #Classical physics #Computability, Logic, AI Algorithms #De Broglie–Bohm theory #Indeterminism #Interpretations of quantum mechanics #Mathematical and Theoretical Analysis #Mathematical formulation of quantum mechanics #Minority interpretations of quantum mechanics #Quantum #Quantum Mechanics and Applications #Quantum chaos #Real number #Terminology #physics.hist-ph #quant-ph
paper · pdf · open access · doi:10.1007/s10670-019-00165-8
published in Erkenntnis 86(6), 1469-1481 (Springer Science+Business Media) · 8 pages. Presented at the David Bohm Centennial Symposium, London, Octobre 2017 V2: several mineurs changes and additions
openalex created_date 2018/03/29 · arxiv created 2019/05/31 · openalex publication_date 2019/10/23 · arxiv updated 2021/11/04 · openalex updated_date 2026/08/05
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is ``random numbers'', as their series of bits are truly random. I propose an alternative classical mechanics, which is empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality.