Search Retrieval Fails for T³ Massive Superposition Decoherence Law — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 24, 2026• 0 citations

Abstract

FINDING: Search results are generic educational videos on quantum superposition (Schrödinger's cat, qubits), not the requested Folman T³ scaling law for massive superposition interferometry. No primary derivation or experimental data retrieved. | MATH: No equations, constants, or scaling laws present in the returned metadata. The T³ (time-cubed) decoherence scaling — typically associated with environmental scattering (e.g., $ \Gamma \propto \Lambda^2 t^3 $ for momentum kicks, where $\Lambda$ is the superposition separation) — is absent from these results. | CONNECTION: None. No golden ratios, base-60, or crystallographic symmetries appear in the educational content. | DEPTH: 1 — The query targeted a specific experimental/theoretical result (Folman's group, massive particle interferometry, T³ scaling) but returned only introductory YouTube lectures. No mathematical content to analyse. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22931338

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Search Retrieval Fails for T³ Massive Superposition Decoherence Law — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 24, 2026• 0 citations

Publisher

Abstract

FINDING: Search results are generic educational videos on quantum superposition (Schrödinger's cat, qubits), not the requested Folman T³ scaling law for massive superposition interferometry. No primary derivation or experimental data retrieved. | MATH: No equations, constants, or scaling laws present in the returned metadata. The T³ (time-cubed) decoherence scaling — typically associated with environmental scattering (e.g., ( \Gamma \propto \Lambda^2 t^3 ) for momentum kicks, where (\Lambda) is the superposition separation) — is absent from these results. | CONNECTION: None. No golden ratios, base-60, or crystallographic symmetries appear in the educational content. | DEPTH: 1 — The query targeted a specific experimental/theoretical result (Folman's group, massive particle interferometry, T³ scaling) but returned only introductory YouTube lectures. No mathematical content to analyse. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22931338

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Search Results Lack Specifics on T³ Decoherence Scaling — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: The search results are generic educational videos on superposition, not the specific T^3 scaling law or Folman experiment. No mathematical derivation, equation, or experimental data on massive superposition decoherence was retrieved. | MATH: None extracted — no equations, constants, or ratios present in the returned sources. | CONNECTION: None — no geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic symmetries appear in the video descriptions. | DEPTH: 1 — The sources are introductory pedagogy, not primary research; they contain zero quantitative content relevant to the T^3 scaling law or interferometric massive superposition. **Precise note:** The T^3 scaling law in quantum interferometry (Folman et al.) refers to the decoherence rate scaling as $\Gamma \propto T^3$ for a massive superposition under certain environmental couplings (e.g., blackbody radiation or gravitational gradient noise). The mathematical core is typically expressed as: Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: The search results are generic educational videos on superposition, not the specific T^3 scaling law or Folman experiment. No mathematical derivation, equation, or experimental data on massive superposition decoherence was retrieved. | MATH: None extracted — no equations, constants, or ratios present in the returned sources. | CONNECTION: None — no geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic symmetries appear in the video descriptions. | DEPTH: 1 — The sources are introductory pedagogy, not primary research; they contain zero quantitative content relevant to the T^3 scaling law or interferometric massive superposition. **Precise note:** The T^3 scaling law in quantum interferometry (Folman et al.) refers to the decoherence rate scaling as $ \Gamma \propto T^3 $ for a massive superposition under certain environmental couplings (e.g., blackbody radiation or gravitational gradient noise). The mathematical core is typically expressed as: Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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\Gamma \propto T^3

for a massive superposition under certain environmental couplings (e.g., blackbody radiation or gravitational gradient noise). The mathematical core is typically expressed as: Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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

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

m_P = \sqrt{\hbar c/G} \approx 2.176 \times 10^{-8}

kg; Planck length

l_P = \sqrt{\hbar G/c^3} \approx 1.616 \times 10^{-35}

m. The proposed experiments (e.g., Ron Folman's T³, matter-wave interferometry) require measuring phase shifts

\Delta \phi \sim (m_1 m_2 G t^3)/(\hbar d^3)

— a cubic time dependence, hence "T-cubed." Decoherence rate for gravitational entanglement:

\Gamma \sim (G m_1 m_2 / \hbar d)^2 \cdot \tau

— dimensionless coupling

\alpha_G = G m_1 m_2 / (\hbar c d) \ll 1

at tabletop scales, yet measurable via entanglement witness. | CONNECTION: The ratio

m_P^2 / (m_1 m_2)

for typical masses (e.g.,

10^{-14}

kg) yields

\sim 10^{12}

— not directly harmonic. However, the T³ phase term contains

t^3

— a cubic symmetry (tetrahedral Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com