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: \(P(x) = |\psi_1(x) + \psi_2(x)|^2 = |\psi_1|^2 + |\psi_2|^2 + 2\text{Re}(\psi_1^*\psi_2)\) — interference term vanishes under which-path information. Tunneling: phase time \(\tau_\phi = \hbar \, d\phi/dE\) (no superluminal group velocity violation; Hartman effect bounded by \(\tau_\phi \to \text{const}\) for opaque barriers). Hybrid circuits: entanglement entropy \(S \sim c \ln L\) (critical) vs \(S \sim L\) (volume law); phase transition at measurement rate \(p_c\) — universal scaling exponents from random-matrix ensembles (GUE/GOE). | CONNECTION: The interference term \(2\text{Re}(\psi_1^*\psi_2)\) is a cosine modulation — its visibility \(V = 2\sqrt{I_1 I_2}/(I_1+I_2)\) maps to \(\cos(\delta)\) where \(\delta\) is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com