Quantum Tunneling Limits Measurement Locality via Non-Ideal Barrier Penetration — E8 Intelligence Research

FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, with recent QFT work showing "impossible" measurements are possible but non-ideal, revealing a fundamental limit on measurement locality. MATH: - Tunneling transmission coefficient (WKB approximation): \( T \approx e^{-2\gamma} \), where \( \gamma = \frac{1}{\hbar}\int_{x_1}^{x_2} \sqrt{2m(V(x)-E)} \, dx \) — exponential decay in barrier width. - For a rectangular barrier of height \( V_0 \) and width \( a \): \( T = \left[ 1 + \frac{V_0^2 \sinh^2(\kappa a)}{4E(V_0-E)} \right]^{-1} \), with \( \kappa = \sqrt{2m(V_0-E)}/\hbar \). - QFT impossibility result (arXiv:2311.13644): nonlocal joint measurements in non-relativistic QM produce superluminal signaling unless the measurement is "ideal" (projective, with vanishing variance in the measured observable). The mathematical constraint is that the measurement operator must commute with all spacelike-separated observables — a condition that fails

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com