Quantum Tunneling: Exponential Barrier Penetration and Non-Ideal Measurements in QFT — E8 Intelligence Research

Abstract

FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, with the transmission probability governed by exponential decay of the wavefunction inside the barrier; recent QFT work shows "impossible" measurements are mathematically possible but non-ideal. | MATH: Transmission coefficient \(T \approx e^{-2\kappa L}\) for rectangular barrier, where \(\kappa = \sqrt{2m(V_0-E)}/\hbar\); decay length \(\delta = 1/\kappa = \hbar/\sqrt{2m(V_0-E)}\). For arbitrary barrier \(V(x)\), WKB approximation: \(T \approx \exp\left(-2\int_{x_1}^{x_2} \sqrt{2m(V(x)-E)}/\hbar \, dx\right)\). QFT impossibility result: signaling-free measurement operators exist but violate ideal measurement axioms (non-projective, non-local smearing). | CONNECTION: The exponential decay factor \(e^{-2\kappa L}\) is structurally identical to the golden-ratio-related decay in Fibonacci-like recursive barrier stacks — for \(N\) identical barriers, transmission resonances occur when \(kL = n\pi\), a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com