Quantum Tunneling and Nonlocal Measurements: Relativity's Quantum Limits — E8 Intelligence Research

FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, with the transmission coefficient governed by exponential decay of the wavefunction inside the classically forbidden region; "impossible" quantum measurements in QFT are shown to be possible but non-ideal, revealing a fundamental tension between relativity and joint nonlocal measurements. MATH: - Transmission coefficient for a rectangular barrier (height \(V_0\), width \(a\), particle energy \(E < V_0\)): \[ T ≈ 16E(V_0-E)/V_0^2 e-2κ a, κ = {√2m(V_0-E)}{} \] (Exact: \(T = [1 + V_0^2 ^2(κ a)/4E(V_0-E)]⁻¹\)) - WKB approximation for arbitrary barrier \(V(x)\): \[ T ≈ exp(-2/∫x_1x_2 √2m(V(x)-E)\, dx) \] - For the QFT "impossible measurements" result: the non-ideal measurement operators are positive operator-valued measures (POVMs) with finite norm, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com