Quantum Tunneling and Relativistic Measurement 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; recent work shows "impossible" relativistic measurements are mathematically possible but non-ideal. MATH: - Transmission coefficient: \( T ≈ e-2κ L \), where \( κ = √2m(V_0 - E)/ \) (rectangular barrier, \( E < V_0 \)). - For arbitrary barrier \( V(x) \): WKB approximation \( T ≈ exp[-2/∫x_1x_2 √2m(V(x)-E)\,dx] \). - Decay constant ratio: \( κ L \) dimensionless; critical ratio when \( κ L = 1 \) → \( T ≈ e⁻² ≈ 0.1353 \). - QFT impossibility result (arXiv:2311.13644): nonlocal joint measurements in relativistic QFT produce superluminal signaling unless measurement operators are restricted; the "impossible" case corresponds to a mathematical idealization with zero-wi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com