Quantum Tunneling: Wave-Mechanical Transmission Through Classically Forbidden Barriers — E8 Intelligence Research

FINDING: Quantum tunneling is a wave-mechanical transmission through classically forbidden regions, governed by exponential decay of the wavefunction; "impossible" measurements in QFT are possible but non-ideal, with signaling constraints. | MATH: Transmission coefficient \(T \approx e^{-2\kappa L}\), where \(\kappa = \sqrt{2m(V_0-E)}/\hbar\); barrier penetration integral \(\int_{x_1}^{x_2} \sqrt{2m(V(x)-E)}\,dx/\hbar\) (WKB); for rectangular barrier, \(T = [1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}]^{-1}\). QFT impossibility: measurement operators with spacelike separation violate microcausality unless smeared; non-ideal measurements yield \(P(\text{outcome}) \leq 1 - \epsilon\) with \(\epsilon \sim e^{-d/\xi}\) (exponential suppression with distance). | CONNECTION: The exponential decay \(e^{-2\kappa L}\) is structurally identical to the golden-ratio-related decay in Fibonacci-like recursive systems — specifically, the ratio of successive tunneling amplitudes for a periodic barri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com