Quantum Tunneling and the Limits of Joint Nonlocal Measurements — E8 Intelligence Research

FINDING: Quantum tunneling is a wave-mechanical penetration of finite barriers, with transmission probability governed by exponential decay of the wavefunction inside the barrier; "impossible" QFT measurements are shown to be possible but non-ideal, revealing a fundamental tension between relativity and joint nonlocal measurements. MATH: - Tunneling transmission coefficient (WKB approximation): \( T \approx e^{-2\gamma} \), where \( \gamma = \frac{1}{\hbar} \int_{x_1}^{x_2} \sqrt{2m(V(x)-E)} \, dx \) - For a rectangular barrier of height \(V_0\) and width \(a\): \( T = \frac{1}{1 + \frac{V_0^2 \sinh^2(\kappa a)}{4E(V_0-E)}} \), with \( \kappa = \sqrt{2m(V_0-E)}/\hbar \) - Exponential suppression factor: \( e^{-2\kappa a} \) — the core "impossibility" barrier. - QFT "impossible measurements" (arXiv:2311.13644v2): signaling between space-like separated regions is avoided only if measurement operators are strictly local; nonlocal joint measurements violate microcausalit Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com