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Quantum Physics

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

Authors: Nicolas Gisin
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. Since a finite volume of space can't contain more than a finite amount of information, I argue that the mathematical real numbers are not physically real. 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 that 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. I argue that it is more economical and natural to accept non-determinism with potentialities as a real mode of existence, both for classical and quantum physics.
Comments: 7 pages. Presented at the David Bohm Centennial Symposium, London, Octobre 2017
Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph)
Cite as: arXiv:1803.06824 [quant-ph]
  (or arXiv:1803.06824v1 [quant-ph] for this version)

Submission history

From: Nicolas Gisin [view email]
[v1] Mon, 19 Mar 2018 07:50:38 GMT (15kb)