Quantum Cognition: Hilbert‑Space Interference Explains Decision‑Making Deviations from Classical Probability — E8 Intelligence Research

**FINDING:** Quantum cognition models human decision making with Hilbert‑space probability amplitudes, producing observable interference effects that deviate from classical Kolmogorovian probabilities. **MATH:** - State vector |ψ⟩ ∈ ℂⁿ representing a mental state. - Projectors P_A, P_B for mutually exclusive choices A, B (P_A + P_B = I). - Classical probability P(A) = ⟨ψ|P_A|ψ⟩ is replaced by the **Born rule** with possible **interference term**: \[ P(A\ \text{or}\ B)=\underbrace{|\langle A|\psi\rangle|^{2}+|\langle B|\psi\rangle|^{2}}_{\text{classical sum}} + 2\,\Re\!\big[\langle\psi|A\rangle\langle B|\psi\rangle\big] . \] - In the "order‑effect" experiments the probability of answering Q₁ then Q₂ is \[ P(Q_{2}=y|Q_{1}=x)=\|P_{Q_{2}=y}P_{Q_{1}=x}|\psi\rangle\|^{2}, \] which is generally **non‑commutative**: \(P_{Q_{2}}P_{Q_{1}}\neq P_{Q_{1}}P_{Q_{2}}\). - The **quantum‑Bayesian update** after a measurement uses Lüders rule: \[ |\psi'\rangle=\frac{P_{Q_{1}=x}|\p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com