Nonlinear Dynamics and Quantum Mechanics: Bell’s Theorem Meets Correlated Statistics

Abstract

A number of the paradoxes encountered in the Copenhagen interpretation of quantum mechanics have apparent resolutions through parallels based in nonlinear dynamics and chaos theory. An overview of these is presented, with Bell’s theorem treated in somewhat greater detail. In these conferences (both “Quantum Theory: Reconsiderations of Foundations” and “Foundations of Probability and Physics”) Bell’s theorem has already been attacked by a number of authors in a number of ways, but here I demonstrate that the so‐called “classical” (or hidden variables) side of the derivation of Bell‐type inequalities is flawed because it is usually based on standard, non‐correlated statistics. When correlated statistics (including nonextensive thermodynamics) is considered, the classical upper limit on correlations is raised, overlapping with quantum predictions using entangled states. Thus, many of the Bell‐type experiments are rendered moot in ruling out “local reality.” Nonlinear dynamics/chaos could well provide a bridge between the determinism of Einstein and the probability of the Bohr school. Possible nonlinear underpinnings for quantum mechanics could also have implications lowering the plausibility of quantum computing.