Quantum Tunneling Limits on Relativistic Nonlocal Measurements — E8 Intelligence Research

FINDING: Quantum tunneling is a wave-mechanical penetration of finite barriers, with the transmission coefficient governed by exponential decay of the wavefunction inside the classically forbidden region; "impossible" relativistic measurements are possible but non-ideal, revealing fundamental limits on joint nonlocal observables. MATH: - Transmission coefficient for rectangular barrier: \( T \approx e^{-2\kappa L} \), where \( \kappa = \sqrt{2m(V_0 - E)}/\hbar \). - For arbitrary barrier \( V(x) \): WKB tunneling amplitude \( T \approx \exp\left(-2\int_{x_1}^{x_2} \sqrt{\frac{2m}{\hbar^2}(V(x)-E)}\,dx\right) \). - Reflection/transmission amplitudes satisfy \( |R|^2 + |T|^2 = 1 \) (unitarity). - In QFT "impossible measurements": signaling violation arises unless measurement operators are strictly local; nonlocal joint measurements require smearing or finite resolution, leading to \( \Delta t \Delta E \gtrsim \hbar \) constraints. CONNECTION: - The exponential decay factor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com