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Other version: http://link.springer.com/10.1007/s10670019001658
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Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real? 

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Published in  Erkenntnis. 2019  
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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Citation (ISO format)  GISIN, Nicolas. Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real?. In: Erkenntnis, 2019. doi: 10.1007/s10670019001658 https://archiveouverte.unige.ch/unige:131921 