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Indeterminism in Physics, Classical Chaos and Bohmian Mechanics.\\ Are Real Numbers Really Real?

Gisin, Nicolas (2019) Indeterminism in Physics, Classical Chaos and Bohmian Mechanics.\\ Are Real Numbers Really Real? Erkenntnis. ISSN ISSN 0165-0106

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Abstract

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.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Gisin, NicolasNicolas.Gisin@unige.ch0000-0003-0788-3494
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Physics > Classical Physics
Specific Sciences > Computation/Information
General Issues > Philosophers of Science
Depositing User: Prof. Nicolas Gisin
Date Deposited: 18 Oct 2020 02:50
Last Modified: 18 Oct 2020 02:50
Item ID: 18278
Journal or Publication Title: Erkenntnis
Publisher: Springer
DOI or Unique Handle: https://doi.org/10.1007/s10670-019-00165-8
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Physics > Classical Physics
Specific Sciences > Computation/Information
General Issues > Philosophers of Science
Date: 23 October 2019
ISSN: ISSN 0165-0106
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/18278

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