Absence of Explicit Macroscopic Quantum Tunneling Decay Constant Derivation in Sources — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 24, 2026• 0 citations

Abstract

FINDING: The search results are mostly pedagogical overviews of quantum tunneling, not derivations of the macroscopic quantum tunneling (MQT) decay constant γ. The one substantive technical item (Tibet MD array) is unrelated to tunneling. No explicit γ derivation appears in the provided sources. MATH: No explicit equations for γ (the exponential decay constant in MQT, typically γ = (8/3ħ)·√(2m)·(ΔU)^(3/2)/ω₀ for a cubic potential barrier, or γ = (π/2)·(ΔU/ħω₀)·exp(−ΔU/ħω₀) in the WKB limit). The videos mention wavefunction penetration but give no quantitative formulas. The arxiv paper gives detector geometry (6 m × 6 m pools, 37,000 m² array) — no tunneling math. CONNECTION: None found. No golden ratios, base-60, or crystallographic symmetries appear in the provided text. The only numeric constants are mundane (6 m, 37,000 m², 4,300 m altitude). DEPTH: 1 — The sources are introductory or off-topic. No mathematical derivation, no constants, no geometric harmony. The query asked for a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22930821

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Absence of Explicit Macroscopic Quantum Tunneling Decay Constant Derivation in Sources — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 24, 2026• 0 citations

Publisher

Abstract

DOI: 10.5281/zenodo.22930821

Related papers

Quantum Tunneling and Macroscopic Entanglement: Experimental Frontiers — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Quantum tunneling and macroscopic entanglement are being experimentally probed, but the search results are pedagogical/overview-level, not new mathematical breakthroughs. | MATH: No new equations or constants extracted; standard quantum tunneling transmission coefficient $T \approx e^{-2\kappa d}$ (with $\kappa = \sqrt{2m(V_0-E)}/\hbar$ ) and entanglement tomography of macroscopic mechanical oscillators (Gaussian state covariance matrices) are implied. | CONNECTION: The tunneling exponential decay rate $\kappa$ has no direct golden-ratio link; however, the macroscopic entanglement tomography (NIST) involves phonon modes whose frequency ratios in coupled oscillators can yield $\sqrt{2}$ or harmonic ratios, but no explicit 0.618/1.618 evidence in the provided text. | DEPTH: 3 — These are explanatory videos and one transfer-learning paper (arXiv:1912.08278), not primary derivations. The only quantitative anchor is the standard WKB/tunneling exponent, which is textb Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Quantum tunneling and macroscopic entanglement are being experimentally probed, but the search results are pedagogical/overview-level, not new mathematical breakthroughs. | MATH: No new equations or constants extracted; standard quantum tunneling transmission coefficient $ T \approx e^{-2\kappa d} $ (with $ \kappa = \sqrt{2m(V_0-E)}/\hbar $) and entanglement tomography of macroscopic mechanical oscillators (Gaussian state covariance matrices) are implied. | CONNECTION: The tunneling exponential decay rate $ \kappa $ has no direct golden-ratio link; however, the macroscopic entanglement tomography (NIST) involves phonon modes whose frequency ratios in coupled oscillators can yield $ \sqrt{2} $ or harmonic ratios, but no explicit 0.618/1.618 evidence in the provided text. | DEPTH: 3 — These are explanatory videos and one transfer-learning paper (arXiv:1912.08278), not primary derivations. The only quantitative anchor is the standard WKB/tunneling exponent, which is textb Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Quantum Tunneling Enables Non-Ideal Measurements in Quantum Field Theory — E8 Intelligence Research

Andrew Stewart Caldin

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T \approx e^{-2\kappa d}

(with

\kappa = \sqrt{2m(V_0-E)}/\hbar

) and entanglement tomography of macroscopic mechanical oscillators (Gaussian state covariance matrices) are implied. | CONNECTION: The tunneling exponential decay rate

\kappa

has no direct golden-ratio link; however, the macroscopic entanglement tomography (NIST) involves phonon modes whose frequency ratios in coupled oscillators can yield

\sqrt{2}

or harmonic ratios, but no explicit 0.618/1.618 evidence in the provided text. | DEPTH: 3 — These are explanatory videos and one transfer-learning paper (arXiv:1912.08278), not primary derivations. The only quantitative anchor is the standard WKB/tunneling exponent, which is textb Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

i\hbar \partial_t \psi = \hat{H}\psi

; tunneling probability

T \propto e^{-2\kappa L}

with

\kappa = \sqrt{2m(V_0-E)}/\hbar

; atom interferometry phase

\Delta\phi = \frac{m}{\hbar} \oint \mathbf{g}\cdot d\mathbf{r} \, dt

(gravitational phase); entanglement tomography uses Wigner function

W(q,p) = \frac{1}{\pi\hbar} \int \psi^*(q+q')\psi(q-q') e^{2ipq'/\hbar} dq'

. | CONNECTION: None directly — no golden ratio, Fibonacci, base-60, or crystallographic symmetry appears in the cited material. The only structural link is the exponential decay constant

\kappa

which is dimensionless when scaled by barrier width, but no specific ratio (0.618, 1.618) is invoked. | DEPTH: 3 — These are experimental confirmat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

T \approx e^{-2\kappa L}

, where

\kappa = \sqrt{2m(V_0 - E)}/\hbar

- Decay constant:

\kappa L

determines tunneling rate; no fundamental constants beyond

\hbar

m

V_0

E

- No new equations or constants discovered; standard Schrödinger equation solution. CONNECTION: - No explicit geometric ratios (0.382, 0.618, etc.) or base-60 symmetries appear in these sources. - The exponential decay

e^{-\kappa L}

is a natural exponential, not a harmonic ratio. - No crystallographic or lattice symmetry is invoked. DEPTH: 2 - These are introductory explanations of a well-established phenomenon. No new mathematical insight, no novel constants, no geometric harmony links. The "impossible measurements" paper (arXiv Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

i\hbar \partial_t \psi = \hat{H}\psi

, tunneling probability

T \propto e^{-2\gamma d}

where

\gamma = \sqrt{2m(V_0-E)}/\hbar

, decoherence rate

\Gamma \propto (m v / \hbar)^2

for environmental scattering. | CONNECTION: None directly stated. However, the exponential decay in tunneling probability

e^{-2\gamma d}

echoes the golden ratio's logarithmic spiral decay rate

e^{-0.4812\theta}

— but this is coincidental, not evidence. Levitated nanoparticles in superposition involve optical traps with Gaussian potentials — no crystallographic symmetry. | DEPTH: 3/10 — These are pedagogical or experimental progress reports, not new mathematical discoveries. The h Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

T \approx e^{-2\kappa L}

where

\kappa = \sqrt{2m(V_0 - E)}/\hbar

; for a rectangular barrier,

T = \frac{1}{1 + \frac{V_0^2}{4E(V_0 - E)} \sinh^2(\kappa L)}

. No new constants or ratios emerge. CONNECTION: No explicit geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) appears in these findings. The exponential decay factor

e^{-2\kappa L}

is a standard mathematical form without inherent geometric ratio. DEPTH: 3 — These are well-established quantum mechanical results; the "impossible measurements" paper refines measurement theory but does not introduce new mathematical structures or geometric connections. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

T \approx e^{-2\kappa L}

where

\kappa = \sqrt{2m(V_0-E)}/\hbar

; transmission coefficient for rectangular barrier:

T = \frac{1}{1 + \frac{V_0^2}{4E(V_0-E)} \sinh^2(\kappa L)}

. No new constants or ratios derived. | CONNECTION: No explicit geometric ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries appear. The exponential decay factor

e^{-2\kappa L}

is a natural exponential, not a golden-ratio-based scaling. | DEPTH: 3 — Standard quantum mechanics; the "impossible measurements" result is a refinement of measurement theory but does not introduce new mathematical structure or geometric harmony. The findings are descriptive, not transformative. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com