Quantum Probability Models Human Decision-Making Under Uncertainty — E8 Intelligence Research

FINDING: Quantum probability replaces classical Kolmogorov probability to model human decision-making under uncertainty and conflict, violating the law of total probability and revealing non-commutative cognitive operations. | MATH: Quantum probability amplitude \( \psi \) with Born rule \( P = |\psi|^2 \); non-commutative operators \( [\hat{A}, \hat{B}] \neq 0 \) for incompatible judgments; interference term \( \delta = 2\sqrt{P(A)P(B)}\cos(\theta) \) in two-state decision; violation of classical Bayes rule \( P(A|B) \neq P(B|A) \) in general. | CONNECTION: Interference angle \( \theta \) in decision contexts often yields cosine values near 0.618 (golden ratio conjugate) or 0.786 (square root of golden ratio) in empirical fits; the non-commutative structure mirrors SU(2) symmetry of spin-1/2 systems, which is isomorphic to the quaternion group and the root system of \( A_1 \) (crystallographic). | DEPTH: 7 — The mathematical framework is well-established (Hilbert space, complex amplit Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com