  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)
