A Theory of Complex Adaptive Learning Based on a Subject's Intelligent Trading Probability Wave Equation

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 (CASs). It is uncertain and crucial in life and inanimate complex systems. However, it is challenging to simulate and reveal its mechanism. Quantifying the uncertainty by probability waves in CASs, the authors attempt to extract a law of complex adaptive learning from a subject's intelligent trading volume-price probability wave equation in the financial markets, apply it to inanimate complex quantum systems that obey the law and have innovative two-worlds interpretations of the quantum entanglement debated for nearly a century. It says particles possess an intelligence-like property in interactive coherence and violate Newton's laws if cumulative quantity or volume in a time interval represents momentum in complex adaptive quantum systems. It concludes that quantum entanglement is not a superposition of two coherent states as mainstream Copenhagen interprets. It is a coherent state in interaction between two opposite, adaptive, and complementary forces. The two intelligent powers keep an invariance of interaction and generate particles' interactively coherent entanglement with two opposite properties in a bipartite complex adaptive quantum system, suggesting industrialized production of quantum entanglement available. Keywords: complex adaptive systems, complex adaptive learning, intelligence-like particle, intelligent probability wave, two-world interpretation, 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)