[Paper Review] On the Possibility of Nonlinearities and Chaos Underlying Quantum Mechanics

Wm. C. McHarris|ArXiv.org|Oct 27, 2006

Quantum Mechanics and Applications16 references3 citations

TL;DR

This paper explores the hypothesis that nonlinear dynamics and chaos could underlie quantum mechanics, offering alternative explanations for phenomena like exponential decay, quantization, and diffraction patterns. It proposes that chaos provides deterministic foundations (aligning with Einstein's view) while preserving probabilistic measurement outcomes (Bohr's interpretation), suggesting a unified framework for long-standing quantum puzzles.

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.

Motivation & Objective

• To investigate whether nonlinear dynamics and chaos could resolve interpretational puzzles in quantum mechanics.
• To explore how chaos might provide a deterministic basis for quantum phenomena, reconciling Einstein's determinism with Bohr's probabilistic interpretation.
• To examine the role of nonlinearity in fundamental processes like measurement, entanglement, and decoherence.
• To propose empirical, quasi-experimental approaches to test for underlying nonlinearities in quantum systems.

Proposed method

• Analyzing closed systems to model exponential decay using nonlinear dynamics, challenging the standard quantum mechanical treatment.
• Extending Bell's inequalities through nonlinear frameworks to assess their implications for nonlocality and hidden variables.
• Studying spontaneous symmetry breaking and intrinsic oscillation modes in nonlinear systems to explain quantization.
• Investigating how 'order in chaos' can produce diffraction-like patterns, mimicking quantum interference.
• Examining sources of nonlinearity, including special relativity and the measurement process, as potential origins of quantum behavior.
• Comparing empirical, phenomenological approaches to nonlinear extensions with purely theoretical corrections to linear quantum mechanics.

Experimental results

Research questions

• RQ1 Can nonlinear dynamics explain exponential decay in closed quantum systems without relying on standard quantum postulates?
• RQ2 Do nonlinear extensions of Bell's inequalities reveal new insights into nonlocality and hidden variables?
• RQ3 Can spontaneous symmetry breaking and intrinsic oscillation modes in nonlinear systems account for the emergence of quantized states?
• RQ4 Can diffraction-like patterns arise from deterministic chaotic systems, offering a classical analog to quantum interference?
• RQ5 To what extent can chaos reconcile Einstein's determinism with Bohr's probabilistic interpretation of measurement?

Key findings

• Nonlinear dynamics can reproduce exponential decay in closed systems, offering an alternative to the standard quantum mechanical treatment.
• Nonlinear extensions of Bell's inequalities may provide new pathways to test nonlocality and hidden variable theories.
• Spontaneous symmetry breaking in nonlinear systems can lead to intrinsic, preferred oscillation modes that resemble quantized energy levels.
• Deterministic chaotic systems can generate diffraction-like patterns, suggesting a classical mechanism for wave-like interference.
• Chaos provides a framework where fundamental determinism (Einstein) coexists with practical probabilistic measurement (Bohr), resolving a long-standing interpretational tension.
• The measurement process and special relativity may serve as sources of nonlinearity that underlie quantum behavior, suggesting deeper physical origins.