Quantum Complementarity, Tunneling Times, and Universal Entanglement Dynamics — E8 Intelligence Research

FINDING: MIT double-slit reprise with single photons confirms Bohr complementarity; 2025 Nature study on quantum tunneling suggests no superluminal signal; hybrid quantum circuits show entanglement dynamics governed by universal statistical laws. | MATH: Complementarity: \(P(x) = |ψ_1(x) + ψ_2(x)|^2 = |ψ_1|^2 + |ψ_2|^2 + 2Re(ψ_1^*ψ_2)\) — interference term vanishes under which-path information. Tunneling: phase time \(τ_φ = \, dφ/dE\) (no superluminal group velocity violation; Hartman effect bounded by \(τ_φ → const\) for opaque barriers). Hybrid circuits: entanglement entropy \(S ~ c ln L\) (critical) vs \(S ~ L\) (volume law); phase transition at measurement rate \(p_c\) — universal scaling exponents from random-matrix ensembles (GUE/GOE). | CONNECTION: The interference term \(2Re(ψ_1^*ψ_2)\) is a cosine modulation — its visibility \(V = 2√I_1 I_2/(I_1+I_2)\) maps to \(cos(δ)\) where \(δ\) is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com