Quantum Gravity Entanglement Tests: Frameworks, No New Math — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 2, 2026• 0 citations

Abstract

FINDING: Multiple experimental proposals (Penrose-Folman T³, Marletto-Vedral, Bose et al.) aim to test quantum gravity via gravitationally-induced entanglement, but no mathematical discovery is presented — only experimental frameworks. MATH: No new equations or constants emerge from these search results. The core theoretical basis remains the linearized gravity coupling: $ \hat{H}_{\text{int}} = -\frac{G m_1 m_2}{d} \hat{\sigma}_z^{(1)} \hat{\sigma}_z^{(2)} $ (for spin-1/2 test masses), yielding entanglement witness via Bell-inequality violation. The T³ experiment (Folman) uses triple-well interference with time $ T^3 $ scaling in phase accumulation: $ \Delta \phi \propto G m^2 T^3 / \hbar d^3 $. No new dimensionless constants or ratios are derived. CONNECTION: No explicit geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618) appears. However, the T³ scaling hints at cubic symmetry — the $ T^3 $ term corresponds to a third-order time crystal lattice, reminiscent of cubic cr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22245800

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Quantum Gravity Entanglement Tests: Frameworks, No New Math — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 2, 2026• 0 citations

Publisher

Abstract

FINDING: Multiple experimental proposals (Penrose-Folman T³, Marletto-Vedral, Bose et al.) aim to test quantum gravity via gravitationally-induced entanglement, but no mathematical discovery is presented — only experimental frameworks. MATH: No new equations or constants emerge from these search results. The core theoretical basis remains the linearized gravity coupling: ( \hat{H}_{\text{int}} = -\frac{G m_1 m_2}{d} \hat{\sigma}_z^{(1)} \hat{\sigma}_z^{(2)} ) (for spin-1/2 test masses), yielding entanglement witness via Bell-inequality violation. The T³ experiment (Folman) uses triple-well interference with time ( T^3 ) scaling in phase accumulation: ( \Delta \phi \propto G m^2 T^3 / \hbar d^3 ). No new dimensionless constants or ratios are derived. CONNECTION: No explicit geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618) appears. However, the T³ scaling hints at cubic symmetry — the ( T^3 ) term corresponds to a third-order time crystal lattice, reminiscent of cubic cr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22245800

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FINDING: Tabletop experiments propose direct observation of quantum gravity via entanglement of macroscopic masses, with the core mathematical framework being the quantum superposition of gravitational fields and the resulting entanglement witness. | MATH: The key equation is the gravitational interaction Hamiltonian between two masses in superposition: $\hat{H}_G = -G \frac{m_1 m_2}{|\hat{x}_1 - \hat{x}_2|}$ , where the position operators $\hat{x}_i$ are in coherent superposition states. The entanglement entropy $S = -\text{Tr}(\rho \ln \rho)$ of the joint state serves as the witness. The T³ (T-cubed) experiment (Folman) uses a triple-interferometer with time $T$ , giving phase shift $\Delta \phi \propto G m^2 T^3 / \hbar d^2$ (where $d$ is separation). The decoherence rate scales as $\Gamma \propto (G m^2 / \hbar d^2)^2 \tau$ , with $\tau$ the interaction time. | CONNECTION: The phase shift $\Delta \phi$ contains the ratio $G m^2 / \hbar$ — a dimensionless coupling Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Tabletop experiments propose direct observation of quantum gravity via entanglement of macroscopic masses, with the core mathematical framework being the quantum superposition of gravitational fields and the resulting entanglement witness. | MATH: The key equation is the gravitational interaction Hamiltonian between two masses in superposition: $ \hat{H}_G = -G \frac{m_1 m_2}{|\hat{x}_1 - \hat{x}_2|} $, where the position operators $\hat{x}_i$ are in coherent superposition states. The entanglement entropy $S = -\text{Tr}(\rho \ln \rho)$ of the joint state serves as the witness. The T³ (T-cubed) experiment (Folman) uses a triple-interferometer with time $T$, giving phase shift $\Delta \phi \propto G m^2 T^3 / \hbar d^2$ (where $d$ is separation). The decoherence rate scales as $\Gamma \propto (G m^2 / \hbar d^2)^2 \tau$, with $\tau$ the interaction time. | CONNECTION: The phase shift $\Delta \phi$ contains the ratio $G m^2 / \hbar$ — a dimensionless coupling Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Andrew Stewart Caldin

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Testing Quantum Gravity via Tabletop Mass Entanglement — E8 Intelligence Research

Andrew Stewart Caldin

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Oct 13, 20260 citations

\hat{H}_G = -G \frac{m_1 m_2}{|\hat{x}_1 - \hat{x}_2|}

, where the position operators

\hat{x}_i

are in coherent superposition states. The entanglement entropy

S = -\text{Tr}(\rho \ln \rho)

of the joint state serves as the witness. The T³ (T-cubed) experiment (Folman) uses a triple-interferometer with time

T

, giving phase shift

\Delta \phi \propto G m^2 T^3 / \hbar d^2

(where

d

is separation). The decoherence rate scales as

\Gamma \propto (G m^2 / \hbar d^2)^2 \tau

, with

\tau

the interaction time. | CONNECTION: The phase shift

\Delta \phi

contains the ratio

G m^2 / \hbar

— a dimensionless coupling 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

m

in two spatial locations separated by

\Delta x

, generating a gravitational phase shift

\Delta \phi = \frac{G m^2 \Delta t}{\hbar \Delta x}

(for two masses in superposition, per Bose–Marletto–Vedral proposal). The decoherence timescale for gravitational entanglement is

\tau \sim \frac{\hbar \Delta x}{G m^2}

. Penrose's criterion for gravitationally-induced collapse:

E_G = \frac{G m^2}{\Delta x}

compared to

\hbar/\tau

. CONNECTION: The ratio

\frac{G m^2}{\hbar c}

(gravitational coupling) is dimensionless and tiny (~

10^{-45}

for protons), but the experimental geometry uses harmonic oscillator frequencies and lattice-like trap spacings — the optimal

\Delta x

often scale 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} \, \text{kg}

, Planck length

\ell_P = \sqrt{\hbar G/c^3} \approx 1.616 \times 10^{-35} \, \text{m}

. Proposed test scales: superposition separation

\Delta x \sim \ell_P^{2/3} \lambda_C^{1/3}

(where

\lambda_C

is Compton wavelength) — from Bose–Marletto–Vedral entanglement criterion. No golden-ratio or base-60 structure appears in the cited abstracts. CONNECTION: None explicit. However, the Bose–Marletto–Vedral test relies on gravitational entanglement of two masses — a bipartite quantum correlation. If gravity is quantum, the interaction Hamiltonian

H \propto G m_1 m_2 / r

yields entanglement e 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} \, \text{kg}

, and the gravitational self-energy term in Penrose's collapse criterion:

\Delta E = \frac{G}{2} \int \int \frac{\rho(\mathbf{r})\rho(\mathbf{r}')}{|\mathbf{r}-\mathbf{r}'|} \, d^3r \, d^3r'

(Newtonian gravitational self-energy difference between superposed mass distributions). The decoherence time predicted is

\tau \sim \hbar / \Delta E

. No new dimensionless constants; the fine-structure consta Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

H_{\text{int}} = -G m_1 m_2 / |\mathbf{r}_1 - \mathbf{r}_2|

, with quantum superposition of positions

|\psi\rangle = \frac{1}{\sqrt{2}}(|L\rangle + |R\rangle)

for each mass; the entanglement witness is the phase

\phi = \frac{G m_1 m_2 t}{\hbar d}

(where

d

is separation,

t

interaction time). Key constants:

G \approx 6.674 \times 10^{-11} \, \text{m}^3\text{kg}^{-1}\text{s}^{-2}

\hbar \approx 1.054 \times 10^{-34} \, \text{J·s}

. No new ratio emerges; the test is binary: gravity is quantum (entanglement) or classical (no entanglement). | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) appears in the experimental design. However, the superposition states

|L\rangle, |R\rangle

form a two-level sy Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com