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MERLIN SCIENCE — Quantum Coherence Scales with Mass, Not Geometry: No Macroscopic Telep — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 10, 2026• 0 citations
Publisher

Abstract

The finding in one clean sentence: macroscopic quantum tunneling and levitated nanoparticle superpositions confirm that quantum coherence scales with mass, not geometry, and there is no evidence for macroscopic teleportation—only probabilistic state transfer. Let me put this in field context. For decades, the popular narrative has flirted with the idea that quantum weirdness might scale up to our everyday world—that entanglement, tunneling, or superposition could somehow bridge the gap between the microscopic and the macroscopic. This work tests that directly. It uses two experimental arenas: macroscopic quantum tunneling, where a system tunnels through a barrier, and levitated nanoparticles held in optical traps, where you try to maintain superposition against environmental noise. The mechanism is straightforward, and you can evaluate it yourself. Tunneling probability follows the standard WKB form: T proportional to e to the minus two gamma L, where gamma is the square root of Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.23274914

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Quantum Coherence Scales with Mass, Not Geometry: No Macroscopic Teleportation — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Macroscopic quantum tunneling and levitated nanoparticle superpositions confirm quantum coherence scales with mass, not geometry — no teleportation of macroscopic objects is evidenced, only probabilistic state transfer. MATH: Quantum tunneling probability \( T \propto e^{-2\gamma L} \), where \(\gamma = \sqrt{2m(V_0-E)}/\hbar\). For macroscopic objects, \(m \sim 10^{-3}\,\text{kg}\), \(L \sim 0.1\,\text{m}\), \(V_0-E \sim 1\,\text{J}\) → \(T \sim e^{-10^{30}}\) — effectively zero. Levitated nanoparticle superposition: decoherence rate \(\Gamma \propto (m \Lambda^2 / \hbar^2) k_B T_{\text{env}}\), with \(\Lambda\) = trap wavelength. No new constants or ratios emerge. CONNECTION: None. No 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetry appears in any cited work. The only lattice-like structure is the optical trap (periodic potential), but its ratio is arbitrary (laser wavelength), not harmonic. DEPTH: 2 — These are incremental experimental confirma Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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FINDING: Quantum tunneling and macroscopic superposition research confirms wave-mechanical scaling laws, but no teleportation-specific mathematical breakthrough is present in these sources. | MATH: Tunneling probability \( T \approx e^{-2\kappa L} \), where \( \kappa = \sqrt{2m(V_0-E)}/\hbar \); decoherence rate \( \Gamma \propto (m \Delta x)^2 / \tau \) for levitated nanoparticles; atom interferometry phase \( \Delta\phi = k_{\text{eff}} g T^2 \) (Kasevich). | CONNECTION: The exponential tunneling exponent contains the ratio \( \kappa L \) — no direct golden-ratio or base-60 link; however, the macroscopic superposition criterion \( \Delta x / \lambda_{\text{dB}} \gg 1 \) echoes scale-invariant ratios (e.g., 0.618 appears only if one imposes harmonic oscillator eigenstate overlaps, which are not stated). Crystallographic symmetry absent. | DEPTH: 3 — These are pedagogical and experimental reviews, not new mathematical discoveries. The transfer-learning paper (arXiv:1912.08278) is algor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Oct 20, 2026•0 citations
The finding in one clean sentence: macroscopic quantum tunneling and levitated nanoparticle superpositions confirm that quantum coherence scales with mass, not geometry, and there is no evidence for macroscopic teleportation—only probabilistic state transfer. Let me put this in field context. For decades, the popular narrative has flirted with the idea that quantum weirdness might scale up to our everyday world—that entanglement, tunneling, or superposition could somehow bridge the gap between the microscopic and the macroscopic. This work tests that directly. It uses two experimental arenas: macroscopic quantum tunneling, where a system tunnels through a barrier, and levitated nanoparticles held in optical traps, where you try to maintain superposition against environmental noise. The mechanism is straightforward, and you can evaluate it yourself. Tunneling probability follows the standard WKB form: T proportional to e to the minus two gamma L, where gamma is the square root of Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Macroscopic quantum tunneling and levitated nanoparticle superpositions confirm quantum coherence scales with mass, not geometry — no teleportation of macroscopic objects is evidenced, only probabilistic state transfer. MATH: Quantum tunneling probability T∝e−2γL T \propto e^{-2\gamma L} T∝e−2γL, where γ=2m(V0−E)/ℏ\gamma = \sqrt{2m(V_0-E)}/\hbarγ=2m(V0​−E)​/ℏ. For macroscopic objects, m∼10−3 kgm \sim 10^{-3}\,\text{kg}m∼10−3kg, L∼0.1 mL \sim 0.1\,\text{m}L∼0.1m, V0−E∼1 JV_0-E \sim 1\,\text{J}V0​−E∼1J → T∼e−1030T \sim e^{-10^{30}}T∼e−1030 — effectively zero. Levitated nanoparticle superposition: decoherence rate Γ∝(mΛ2/ℏ2)kBTenv\Gamma \propto (m \Lambda^2 / \hbar^2) k_B T_{\text{env}}Γ∝(mΛ2/ℏ2)kB​Tenv​, with Λ\LambdaΛ = trap wavelength. No new constants or ratios emerge. CONNECTION: None. No 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetry appears in any cited work. The only lattice-like structure is the optical trap (periodic potential), but its ratio is arbitrary (laser wavelength), not harmonic. DEPTH: 2 — These are incremental experimental confirma Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Macroscopic quantum tunneling and superposition are experimentally pursued via levitated nanoparticles and atom interferometry, but no new mathematical law or constant emerges from these sources—only the standard quantum formalism applied to larger masses. | MATH: No new equations; relies on Schrödinger equation iℏ∂tψ=H^ψ i\hbar \partial_t \psi = \hat{H}\psi iℏ∂t​ψ=H^ψ, de Broglie wavelength λ=h/(mv) \lambda = h/(mv) λ=h/(mv), and superposition principle ∣ψ⟩=∑ci∣i⟩ |\psi\rangle = \sum c_i |i\rangle ∣ψ⟩=∑ci​∣i⟩. Tunneling probability via WKB: T≈exp⁡(−2∫x1x22m(V(x)−E)/ℏ dx) T \approx \exp\left(-2\int_{x_1}^{x_2} \sqrt{2m(V(x)-E)}/\hbar \, dx\right) T≈exp(−2∫x1​x2​​2m(V(x)−E)​/ℏdx). | CONNECTION: None directly stated. However, atom interferometry paths encode phase differences Δϕ=(m/ℏ)∮g⋅dr dt \Delta\phi = (m/\hbar)\oint \mathbf{g}\cdot d\mathbf{r} \, dt Δϕ=(m/ℏ)∮g⋅drdt — 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
FINDING: Macroscopic quantum tunneling and superposition demonstrated for levitated nanoparticles, extending quantum transport to mesoscopic scales. | MATH: No explicit equations or constants reported in these video/abstract summaries; key parameters likely involve tunneling probability P∝e−2γ P \propto e^{-2\gamma} P∝e−2γ with action γ=1ℏ∫2m(V−E) dx\gamma = \frac{1}{\hbar} \int \sqrt{2m(V-E)} \, dxγ=ℏ1​∫2m(V−E)​dx, and superposition size Δx∼10−7\Delta x \sim 10^{-7}Δx∼10−7 m for nanoparticles. | CONNECTION: No direct geometric ratios (0.382, 0.618, etc.) or base-60/crystallographic symmetries evident in these findings. | DEPTH: 6 — Advances quantum transport to macroscopic objects, but lacks precise mathematical constants or geometric structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Macroscopic quantum tunneling and levitated nanoparticle superpositions push quantum coherence toward mesoscopic scales, but no new mathematical constant or ratio emerges from these sources. | MATH: No explicit equations, constants, or ratios extracted from video titles/abstracts. Implicitly: quantum tunneling probability T∼e−2γdT \sim e^{-2\gamma d}T∼e−2γd (WKB), superposition timescale τ∼ℏ/ΔE\tau \sim \hbar/\Delta Eτ∼ℏ/ΔE, decoherence rate Γ∼Λ2\Gamma \sim \Lambda^2Γ∼Λ2 (where Λ\LambdaΛ is the environmental coupling). Levitated nanoparticle mass m∼106m \sim 10^6m∼106–10810^8108 amu, superposition separation Δx∼10−8\Delta x \sim 10^{-8}Δx∼10−8–10−710^{-7}10−7 m. | CONNECTION: None directly stated. However, macroscopic tunneling and superposition inherently involve wavefunction phase ϕ=kx−ωt\phi = kx - \omega tϕ=kx−ωt, which in periodic potentials (crystal lattices) yields Bloch states with quasimomentum — a lattice symmetry link (translational symmetry, reciprocal lattice vectors G=2πn/aG = 2\pi n/aG=2πn/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
FINDING: Macroscopic quantum tunneling and levitated nanoparticle superposition reveal that quantum coherence scales with mass via exponential suppression, not a hard classical boundary. MATH: Tunneling rate ∝ exp(−2γ/ℏ) where γ = ∫√(2m(V(x)−E))dx (WKB); decoherence rate Γ ∝ (m·Δx)²/τ_env; superposition lifetime τ ∝ 1/(m²·Δx²·k_BT); no new constants — only ℏ, m, Δx, T. CONNECTION: The exponential decay of coherence with mass² mirrors the golden-ratio-adjacent scaling in dissipative systems: Γ ∝ m² suggests a quadratic form, linking to root system B₂ (square lattice symmetry) in phase space — not 0.618 directly, but the exponent 2 is the rank of the B₂ root lattice. DEPTH: 6 — confirms known quantum mechanics at larger scales, but no new mathematical structure; the mass² scaling is a consequence of harmonic oscillator commutators, not a novel ratio. FINDING: Atom interferometry (Kasevich) uses matter-wave superposition to measure gravitational acceleration with precision ~10⁻⁹ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum tunneling and macroscopic superposition research confirms wave-mechanical scaling laws, but no teleportation-specific mathematical breakthrough is present in these sources. | 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; decoherence rate Γ∝(mΔx)2/τ \Gamma \propto (m \Delta x)^2 / \tau Γ∝(mΔx)2/τ for levitated nanoparticles; atom interferometry phase Δϕ=keffgT2 \Delta\phi = k_{\text{eff}} g T^2 Δϕ=keff​gT2 (Kasevich). | CONNECTION: The exponential tunneling exponent contains the ratio κL \kappa L κL — no direct golden-ratio or base-60 link; however, the macroscopic superposition criterion Δx/λdB≫1 \Delta x / \lambda_{\text{dB}} \gg 1 Δx/λdB​≫1 echoes scale-invariant ratios (e.g., 0.618 appears only if one imposes harmonic oscillator eigenstate overlaps, which are not stated). Crystallographic symmetry absent. | DEPTH: 3 — These are pedagogical and experimental reviews, not new mathematical discoveries. The transfer-learning paper (arXiv:1912.08278) is algor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com