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Nature

Experimental evidence for non-exponential decay in quantum tunnelling

Steven R. Wilkinson, C. F. Bharucha, Martin C. Fischer, Kirk W. Madison, Patrick R. Morrow, Qian Niu, Bala Sundaram, Mark G. Raizen

Published Jun 1, 1997• 232 citations
Publisher
DOI
10.1038/42418

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Quantum Tunneling Enables Non-Ideal "Impossible" QFT Measurements — E8 Intelligence Research

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FINDING: Quantum tunneling is a wave-mechanical phenomenon enabling barrier penetration, with recent work showing "impossible" measurements in QFT are possible but non-ideal. MATH: - Tunneling probability \( T \approx e^{-2\kappa L} \), where \( \kappa = \sqrt{2m(V_0 - E)}/\hbar \) (decay constant). - For a rectangular barrier: \( T = \frac{1}{1 + \frac{V_0^2}{4E(V_0-E)} \sinh^2(\kappa L)} \). - No explicit constants or ratios (0.382, 0.618, etc.) appear in the provided sources. CONNECTION: - No direct geometric harmony (golden ratio, base-60, crystallographic symmetry) is evident in these findings. - The wavefunction's exponential decay \( e^{-\kappa L} \) is a natural exponential, not a harmonic ratio. DEPTH: 3 - The findings are standard quantum tunneling pedagogy; no new mathematical structure or geometric link is revealed. The "impossible measurements" paper (arXiv:2311.13644) is a theoretical nuance, not a breakthrough in constants or symmetries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Quantum Tunneling Wins 2025 Nobel: Macroscopic Quantum Reality Proven — E8 Intelligence Research

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FINDING: The 2025 Nobel Prize in Physics centers on experimental proof that quantum mechanics governs macroscopic phenomena — specifically quantum tunneling and the "quantumness" of reality — with Google's Quantum AI and MIT single-photon experiments as corroborating evidence. | MATH: No new fundamental equation is presented in the titles/descriptions; the core mathematics remains the Schrödinger equation \( i\hbar \frac{\partial}{\partial t}|\psi\rangle = \hat{H}|\psi\rangle \), with tunneling probability \( T \approx e^{-2\kappa L} \) where \( \kappa = \sqrt{2m(V_0-E)}/\hbar \). The MIT single-photon experiment confirms the Born rule \( P = |\langle \phi | \psi \rangle|^2 \). | CONNECTION: The tunneling exponent \( e^{-2\kappa L} \) is a decaying exponential — its characteristic decay length \( 1/\kappa \) has no inherent ratio to 0.618 or 1.618. However, the *macroscopic* tunneling demonstrated (likely in superconducting qubits or Josephson junctions) involves phase coherence, where Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Time dependent quantum tunnelling

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FINDING: Quantum tunneling is a wave-mechanical phenomenon enabling barrier penetration, with recent work showing "impossible" measurements in QFT are possible but non-ideal. MATH: - Tunneling probability 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 (decay constant). - For a rectangular barrier: T=11+V024E(V0−E)sinh⁡2(κL) T = \frac{1}{1 + \frac{V_0^2}{4E(V_0-E)} \sinh^2(\kappa L)} T=1+4E(V0​−E)V02​​sinh2(κL)1​. - No explicit constants or ratios (0.382, 0.618, etc.) appear in the provided sources. CONNECTION: - No direct geometric harmony (golden ratio, base-60, crystallographic symmetry) is evident in these findings. - The wavefunction's exponential decay e−κL e^{-\kappa L} e−κL is a natural exponential, not a harmonic ratio. DEPTH: 3 - The findings are standard quantum tunneling pedagogy; no new mathematical structure or geometric link is revealed. The "impossible measurements" paper (arXiv:2311.13644) is a theoretical nuance, not a breakthrough in constants or symmetries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: The 2025 Nobel Prize in Physics centers on experimental proof that quantum mechanics governs macroscopic phenomena — specifically quantum tunneling and the "quantumness" of reality — with Google's Quantum AI and MIT single-photon experiments as corroborating evidence. | MATH: No new fundamental equation is presented in the titles/descriptions; the core mathematics remains the Schrödinger equation iℏ∂∂t∣ψ⟩=H^∣ψ⟩ i\hbar \frac{\partial}{\partial t}|\psi\rangle = \hat{H}|\psi\rangle iℏ∂t∂​∣ψ⟩=H^∣ψ⟩, with tunneling probability 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. The MIT single-photon experiment confirms the Born rule P=∣⟨ϕ∣ψ⟩∣2 P = |\langle \phi | \psi \rangle|^2 P=∣⟨ϕ∣ψ⟩∣2. | CONNECTION: The tunneling exponent e−2κL e^{-2\kappa L} e−2κL is a decaying exponential — its characteristic decay length 1/κ 1/\kappa 1/κ has no inherent ratio to 0.618 or 1.618. However, the *macroscopic* tunneling demonstrated (likely in superconducting qubits or Josephson junctions) involves phase coherence, where Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com