https://arxiv.org/abs/1803.06824
(V2: several *mineurs* changes ) ! Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real? Nicolas Gisin <https://arxiv.org/search/quant-ph?searchtype=author&query=Gisin%2C+N> (Submitted on 19 Mar 2018 (v1 <https://arxiv.org/abs/1803.06824v1>), last revised 31 May 2019 (this version, v3)) 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. Comments: 8 pages. Presented at the David Bohm Centennial Symposium, London, Octobre 2017 V2: several mineurs changes and additions Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:1803.06824 <https://arxiv.org/abs/1803.06824> [quant-ph] (or arXiv:1803.06824v3 <https://arxiv.org/abs/1803.06824v3> [quant-ph] for this version) @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/8dd42147-b6ba-4716-9dfa-2a422964f79f%40googlegroups.com.
