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

Erkenntnis:1-13 (2019)
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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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Nicolas Gisin
University of Geneva

Citations of this work

Real Numbers Are the Hidden Variables of Classical Mechanics.Nicolas Gisin - 2020 - Quantum Studies: Mathematics and Foundations 7:197–201.
Randomness? What Randomness?Klaas Landsman - 2020 - Foundations of Physics 50 (2):61-104.
Emergence of Time.George F. R. Ellis & Barbara Drossel - 2020 - Foundations of Physics 50 (3):161-190.

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References found in this work

On the Impossible Pilot Wave.J. S. Bell - 1982 - Foundations of Physics 12 (10):989-999.
Time Really Passes.John D. Norton - 2010 - Humana. Mente: Journal of Philosophical Studies 13:23-24.
Time Really Passes.John D. Norton - 2010 - Humana Mente 4 (13).
Physics’ Silence on Time.Yuval Dolev - 2018 - European Journal for Philosophy of Science 8 (3):455-469.

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