A Theory of Complex Adaptive Learning and a Non-Localized Wave Equation in Quantum Mechanics

TL;DR

This paper develops a unified theoretical framework linking complex adaptive systems, quantum mechanics, and finance through a non-localized wave equation, revealing universal interaction laws and a new understanding of quantum entanglement.

Contribution

It introduces a non-localized wave equation in quantum mechanics based on complex adaptive learning principles, connecting quantum entanglement with complex systems and finance.

Findings

Quantum entanglement is an interactively coherent state.

Interaction invariance exists across quantum mechanics and finance.

Quantum entanglement is non-separable, steerable, and energy-consuming.

Abstract

Complex adaptive learning is intelligent. It is adaptive, learns in feedback loops, and generates hidden patterns as many individuals, elements or particles interact in complex adaptive systems (CAS). CAS highlights adaptation in life and lifeless complex systems cutting across all traditional natural and social sciences disciplines. However, discovering a universal law in CAS and understanding the underlying mechanism of distribution formation, such as a non-Gauss distribution in complex quantum entanglement, remains highly challenging. Quantifying the uncertainty of CAS by probability wave functions, the authors explore the inherent logical relationship between Schr\"odinger's wave equation in quantum mechanics and Shi's trading volume-price wave equation in finance. Subsequently, the authors propose a non-localized wave equation in quantum mechanics if cumulative observable in a time interval represents momentum or momentum force in Skinner-Shi (reinforcement-frequency-interaction) coordinates. It reveals that the invariance of interaction as a universal law exists in quantum mechanics and finance. The theory shows that quantum entanglement is an interactively coherent state instead of a consequence of the superposition of coherent states. As a resource, quantum entanglement is non-separable, steerable, and energy-consumed. The entanglement state has opposite states subject to interaction conservation between the momentum and reversal forces. Keywords: complex adaptive systems, complex adaptive learning, complex quantum systems, non-localized wave equation, interaction conservation, interactively coherent entanglement PACS: 89.75.-k (Complex Systems); 89.65.Gh (Economics, Econophysics, Financial Markets, Business and Management); 03.65.Ud (Entanglement and Quantum Nonlocality)