Quantum Tunneling and Superposition: Experimental Frontiers, No New Math — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 19, 2026• 0 citations

Abstract

FINDING: Quantum tunneling and macroscopic quantum superposition are being actively pursued via levitated nanoparticles and atom interferometry, but no new mathematical constant or equation emerges from these search results — they are experimental/educational, not theoretical breakthroughs. | MATH: No new equations or constants extracted. Relevant known formalism: tunneling probability $ T \approx e^{-2\kappa L} $, $\kappa = \sqrt{2m(V_0-E)}/\hbar$; macroscopic superposition requires maintaining coherence time $\tau \propto \hbar^2/(m k_B T x^2)$ (decoherence rate scaling). Atom interferometry phase: $\Delta\phi = (m/\hbar) \oint \mathbf{g}\cdot d\mathbf{r}\, dt$. | CONNECTION: None directly stated. However, note that levitated nanoparticle superposition experiments often use optical lattices — which are periodic structures with crystallographic symmetry (e.g., 1D lattice spacing $d = \lambda/2$ — ratio 0.5, not golden). No 0.382/0.618/0.786/1.618/2.618 or base-60 appears in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23465085

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Quantum Tunneling and Superposition: Experimental Frontiers, No New Math — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 19, 2026• 0 citations

Publisher

Abstract

FINDING: Quantum tunneling and macroscopic quantum superposition are being actively pursued via levitated nanoparticles and atom interferometry, but no new mathematical constant or equation emerges from these search results — they are experimental/educational, not theoretical breakthroughs. | MATH: No new equations or constants extracted. Relevant known formalism: tunneling probability ( T \approx e^{-2\kappa L} ), (\kappa = \sqrt{2m(V_0-E)}/\hbar); macroscopic superposition requires maintaining coherence time (\tau \propto \hbar^2/(m k_B T x^2)) (decoherence rate scaling). Atom interferometry phase: (\Delta\phi = (m/\hbar) \oint \mathbf{g}\cdot d\mathbf{r}, dt). | CONNECTION: None directly stated. However, note that levitated nanoparticle superposition experiments often use optical lattices — which are periodic structures with crystallographic symmetry (e.g., 1D lattice spacing (d = \lambda/2) — ratio 0.5, not golden). No 0.382/0.618/0.786/1.618/2.618 or base-60 appears in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23465085

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

, with tunneling probability

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

where

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

. Atom interferometry relies on the de Broglie wavelength

\lambda = h/mv

. No novel constants or dimensionless ratios emerge from the search summaries. CONNECTION: No explicit geometric harmony ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic symmetries appear in the findings. However, the levitated nanoparticle superposition experiments inherently involve trapping potent 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 \sim e^{-2\gamma d}

(WKB), superposition timescale

\tau \sim \hbar/\Delta E

, decoherence rate

\Gamma \sim \Lambda^2

(where

\Lambda

is the environmental coupling). Levitated nanoparticle mass

m \sim 10^6

–

10^8

amu, superposition separation

\Delta x \sim 10^{-8}

–

10^{-7}

m. | CONNECTION: None directly stated. However, macroscopic tunneling and superposition inherently involve wavefunction phase

\phi = kx - \omega t

, which in periodic potentials (crystal lattices) yields Bloch states with quasimomentum — a lattice symmetry link (translational symmetry, reciprocal lattice vectors

G = 2\pi n/a

). No golden ratio or base-60 ap 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

, de Broglie wavelength

\lambda = h/(mv)

, and superposition principle

|\psi\rangle = \sum c_i |i\rangle

. Tunneling probability via WKB:

T \approx \exp\left(-2\int_{x_1}^{x_2} \sqrt{2m(V(x)-E)}/\hbar \, dx\right)

. | CONNECTION: None directly stated. However, atom interferometry paths encode phase differences

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

— a geometric phase (Aharonov-Bohm type), which is a symmetry of the action, not a golden-ratio or base-60 link. Levitated nanoparticle superpositions involve phonon modes — lattice-like vibrational spectra, but no crystallographic symmetry Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com