On the Possibility of Nonlinearities and Chaos Underlying Quantum Mechanics

Abstract

Some of the so-called imponderables and counterintuitive puzzles associated with the Copenhagen interpretation of quantum mechanics appear to have alternate, parallel explanations in terms of nonlinear dynamics and chaos. These include the mocking up of exponetial decay in closed systems, possible nonlinear extensions of Bell's inequalities, spontaneous symmetry breaking and the existence of intrinsically preferred internal oscillation modes (quantization) in nonlinear systems, and perhaps even the production of diffraction-like patterns by "order in chaos." The existence of such parallel explanations leads to an empirical, quasi-experimental approach to the question of whether or not there might be fundamental nonlinearities underying quantum mechanics. This will be contrasted with recent more theoretical approaches, in which nonlinear extensions have been proposed rather as corrections to a fundamentally linear quantum mechanics. Sources of nonlinearity, such as special relativity and the measurement process itself, will be investigated, as will possible implications of nonlinearities for entanglement and decoherence. It is conceivable that in their debates both Einstein and Bohr could have been right -- for chaos provides the fundamental determinism favored by Einstein, yet for practical measurements it requires the probabilistic interpretation of the Bohr school.