Gisin, Nicolas (2019) Indeterminism in Physics, Classical Chaos and Bohmian Mechanics.\\ Are Real Numbers Really Real? Erkenntnis. ISSN ISSN 01650106

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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 socalled 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 finiteinformation numbers. This alternative classical mechanics is nondeterministic, 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  

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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/s10670019001658  
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 01650106  
URI:  https://philsciarchivedev.library.pitt.edu/id/eprint/18278 
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