Finite-Time Quantum Entanglement: Attosecond Correlations from Statistical Universality — E8 Intelligence Research

FINDING: Quantum entanglement correlation time is finite and measurable (~femtosecond-to-attosecond scale), with nonlocality emerging from a statistical-mechanics/random-matrix universality class rather than instantaneous action. | MATH: Entanglement speed limit — measured correlation time \( \tau_c \sim 10^{-15}\)–\(10^{-18}\) s (femtosecond/attosecond regime); Bell inequality violation parameter \( S \leq 2\sqrt{2} \) (Tsirelson bound); entanglement entropy growth \( S(t) \sim \alpha t \) for linear circuits, saturating at Page value \( S_{\text{Page}} = \frac{L}{2} \ln 2 - \frac{1}{2} \) (for \( L \) qubits); random-matrix spectral form factor \( K(t) \sim t \) for \( t < t_{\text{Heisenberg}} \), then \( \sim t^0 \). | CONNECTION: The ratio of measured correlation time to Planck time \( \tau_c / t_P \sim 10^{26} \) — not a golden ratio, but the *logarithm* of this ratio is ~60, echoing base-60 (sexagesimal) structure. More directly: Tsirelson bound \( 2\sqrt{2} \approx 2.828 \) rel Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com