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 \(E < V_0\)): \[ T \approx \frac{16E(V_0-E)}{V_0^2} e^{-2\kappa a}, \quad \kappa = \frac{\sqrt{2m(V_0-E)}}{\hbar} \] (Exact: \(T = \left[1 + \frac{V_0^2 \sinh^2(\kappa a)}{4E(V_0-E)}\right]^{-1}\)) - WKB approximation for arbitrary barrier \(V(x)\): \[ T \approx \exp\left(-\frac{2}{\hbar}\int_{x_1}^{x_2} \sqrt{2m(V(x)-E)}\, dx\right) \] - 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