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

Abstract

FINDING: Quantum cognition models human decision-making under uncertainty using quantum probability amplitudes rather than classical Bayesian probabilities, with context-dependent non-commutative operators. | MATH: Quantum probability: \(P(A|B) \neq P(B|A)\) in general; decision as projection onto Hilbert space basis states; interference term: \(P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta)\), where \(\delta\) is the phase difference between probability amplitudes; non-commutativity: \([\hat{A},\hat{B}] = \hat{A}\hat{B} - \hat{B}\hat{A} \neq 0\) for incompatible decision contexts; social agent model (arXiv:1202.4918) uses Lindblad-type master equation for open quantum systems with interaction Hamiltonian \(H_{int}\) coupling agent states. | CONNECTION: The interference phase \(\delta\) in quantum cognition maps directly to geometric phase — when \(\cos(\delta) = 0.809\) (i.e., \(\delta = 36^\circ\)), the interference term yields the golden ratio conjugate \(0.618\) as a prob Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com