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Quantum Tunneling Limits on Joint Nonlocal Quantum Measurements — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 22, 2026• 0 citations
Publisher

Abstract

FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, with a transmission coefficient exponentially suppressed by barrier width and height; "impossible" QFT measurements are possible but non-ideal, revealing fundamental limits on joint nonlocal observables. MATH: Transmission coefficient \(T \approx e^{-2\kappa L}\), where \(\kappa = \sqrt{2m(V_0-E)}/\hbar\). For a rectangular barrier: \(T = \left[1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}\right]^{-1}\). In the semiclassical (WKB) limit: \(T \approx \exp\left(-\frac{2}{\hbar}\int_{x_1}^{x_2} \sqrt{2m(V(x)-E)}\,dx\right)\). The "impossible measurement" result (arXiv:2311.13644) shows that ideal joint nonlocal measurements in non-relativistic QM would violate no-signaling; only approximate (non-ideal) measurements are consistent, with error bounds scaling as \(\epsilon \sim \hbar / \Delta t\) for spacelike separations. CONNECTION: The exponential decay \(e^{-2\kappa L}\) is structurally identica Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.23553647

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FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, with a transmission coefficient exponentially suppressed by barrier width and height; "impossible" QFT measurements are possible but non-ideal, revealing fundamental limits on joint nonlocal observables. MATH: Transmission coefficient (T \approx e^{-2\kappa L}), where (\kappa = \sqrt{2m(V_0-E)}/\hbar). For a rectangular barrier: (T = \left[1 + \frac{V_0^2 \sinh^2(\kappa L)}{4E(V_0-E)}\right]^{-1}). In the semiclassical (WKB) limit: (T \approx \exp\left(-\frac{2}{\hbar}\int_{x_1}^{x_2} \sqrt{2m(V(x)-E)},dx\right)). The "impossible measurement" result (arXiv:2311.13644) shows that ideal joint nonlocal measurements in non-relativistic QM would violate no-signaling; only approximate (non-ideal) measurements are consistent, with error bounds scaling as (\epsilon \sim \hbar / \Delta t) for spacelike separations. CONNECTION: The exponential decay (e^{-2\kappa L}) is structurally identica Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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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≈e−2κL T \approx e^{-2\kappa L} T≈e−2κL, where κ=2m(V0−E)/ℏ \kappa = \sqrt{2m(V_0 - E)}/\hbar κ=2m(V0​−E)​/ℏ. - For arbitrary barrier V(x) V(x) V(x): WKB tunneling amplitude T≈exp⁡(−2∫x1x22mℏ2(V(x)−E) dx) T \approx \exp\left(-2\int_{x_1}^{x_2} \sqrt{\frac{2m}{\hbar^2}(V(x)-E)}\,dx\right) T≈exp(−2∫x1​x2​​ℏ22m​(V(x)−E)​dx). - Reflection/transmission amplitudes satisfy ∣R∣2+∣T∣2=1 |R|^2 + |T|^2 = 1 ∣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 ΔtΔE≳ℏ \Delta t \Delta E \gtrsim \hbar ΔtΔE≳ℏ constraints. CONNECTION: - The exponential decay factor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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