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

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Listed:
  • Leilei Shi
  • Xinshuai Guo
  • Jiuchang Wei
  • Wei Zhang
  • Guocheng Wang
  • Bing-Hong Wang

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)

Suggested Citation

  • Leilei Shi & Xinshuai Guo & Jiuchang Wei & Wei Zhang & Guocheng Wang & Bing-Hong Wang, 2023. "A Theory of Complex Adaptive Learning and a Non-Localized Wave Equation in Quantum Mechanics," Papers 2306.15554, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2306.15554
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    References listed on IDEAS

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    1. Shi, Leilei, 2006. "Does security transaction volume–price behavior resemble a probability wave?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 419-436.
    2. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    3. Shi, Leilei & Wang, Binghong & Guo, Xinshuai & Li, Honggang, 2021. "A price dynamic equilibrium model with trading volume weights based on a price-volume probability wave differential equation," International Review of Financial Analysis, Elsevier, vol. 74(C).
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