InterJournal Complex Systems, 612
Status: Submitted
Manuscript Number: [612]
Submission Date: 21102
Bell's Theorem is Invalid for Cellular Automata, or Demonstrating EPR effects on a One-Dimensional (Non-Quantum) CA
Author(s): Plamen Petrov

Subject(s): CX.04, CX.09, CX.07

Category: Article

Abstract:

In the mid 1950s Edward Fredkin proposed the idea that our Universe is a cellular automaton (CA). For a long time, Fredkin's idea has not been taken seriously mainly because it was thought that CAs (as purely local and deterministic models) are not able to demonstrate quantum mechanical effects due to the well-known theorem/inequality proven by J. S. Bell in 1964. In the present paper, we demonstrate that Bell's inequality is invalid for cellular automata by giving a concrete example of a one-dimensional (non-quantum) CA that clearly violates it. Thus, we prove that (at least, from a purely mathematical point of view) there is no problem for Fredkin's idea with regard to Bell's theorem. In fact, it turns out to be just the opposite: the very presence of EPR effects in mathematical models like CAs strongly suggests that we live in a perfectly deterministic Universe.

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