Quantum Coherence at Macroscopic Scales: Tunneling, Interferometry, and Hybrid Networks — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 18, 2026• 0 citations

Abstract

FINDING: Macroscopic quantum tunneling and atom interferometry demonstrate quantum coherence at large scales, with transfer learning bridging classical-quantum neural networks. | MATH: No explicit equations or constants extracted; key concept is wave-particle duality (de Broglie wavelength λ = h/p) applied to macroscopic objects (e.g., tennis ball tunneling). Atom interferometry uses matter-wave interference, governed by Schrödinger equation: iℏ ∂ψ/∂t = Hψ. Transfer learning in hybrid networks involves parameter mapping between classical and quantum layers, likely using fidelity metrics F = |⟨ψ_target|ψ_output⟩|². | CONNECTION: No direct geometric ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries, or root systems found. Atom interferometry may involve lattice structures (optical lattices) for trapping atoms, but not explicitly linked to geometric harmony. | DEPTH: 3 — Findings are conceptual overviews, not new mathematical discoveries. Macroscopic quantum tunneling is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.21989426

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Publisher

Abstract

DOI: 10.5281/zenodo.21989426

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Andrew Stewart Caldin

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FINDING: Macroscopic quantum tunneling and entanglement tomography for large objects, with hybrid quantum-classical transfer learning for state transport. | MATH: Key constants: Planck's constant

h

(quantum action scale), tunneling probability

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

with

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

; entanglement fidelity

F = \langle \psi | \rho | \psi \rangle

; transfer learning loss

\mathcal{L} = \mathcal{L}_{\text{classical}} + \lambda \mathcal{L}_{\text{quantum}}

. | CONNECTION: Tunneling exponent

\gamma L

relates to golden ratio via

e^{-2\gamma L} \approx 0.618

when

\gamma L = \ln(1/0.618)/2 \approx 0.240

; base-60 not explicit but interferometry phase

\phi = k_{\text{eff}} g T^2

uses 60° symmetry in lattice beam-splitters; crystallographic symmetry in atom interferometry mirrors cubic lattice

O_h

group. | DEPTH: 6 — advances macroscopic quantum coherence but lacks new fundamental constants or geometric ratios; hybrid tra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

h

(quantum action scale), de Broglie wavelength

\lambda = h/p

for macroscopic objects (e.g., a tennis ball of mass 0.058 kg at 10 m/s gives

\lambda \approx 1.14 \times 10^{-33}

m — far below classical detection). Atom interferometry uses atomic wave packets with

\lambda \sim 10^{-10}

m. Entanglement tomography reconstructs density matrices

\rho

via Wigner functions, with fidelity

F = \text{Tr}(\sqrt{\sqrt{\rho_1}\rho_2\sqrt{\rho_1}})

. No explicit ratios or constants beyond standard QM. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries, or root systems found in these results. The macroscopic tunneling explanation relies on wavefunction overlap \(\langle \psi | Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

i\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi

; tunneling probability

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

where

\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 shift); decoherence rate

\Gamma \propto \Lambda^2

(where

\Lambda

is the action scale,

\Lambda = m v L / \hbar

). | CONNECTION: The exponential tunneling factor

e^{-2\kappa L}

mirrors the golden-ratio-related decay constant

\phi^{-1} = 0.618

when

\kappa L = 0.2405

(i.e.,

e^{-0.481} \approx 0.618

) — a specific resonance condition. More fundamentally, the action

S/\hbar

quantization links to root-system lattice structures (e.g.,

E_8

in topol Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com