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Tabletop Quantum Gravity: Probing Penrose Collapse with Massive Superposition — E8 Intelligence Research

Andrew Stewart Caldin

Published Sep 20, 2026• 0 citations
Publisher

Abstract

FINDING: Quantum gravity tests are converging on tabletop interferometry experiments probing superposition of massive objects, with Penrose's gravitationally-induced collapse criterion as a central quantitative target. | MATH: Penrose's collapse time τ ≈ ħ/E_G where E_G is gravitational self-energy difference between superposed mass configurations; for a sphere of mass m and radius R, E_G ≈ (4πG/3) m²/R (order-of-magnitude). The Ron Folman "T-cubed" experiment scales with T³ (interferometer time cubed) — a cubic scaling law. No new fundamental constant emerges; G, ħ, c remain the only inputs. | CONNECTION: The T³ scaling echoes cubic lattice symmetry (3D crystallographic point groups, e.g., m-3m) — the experiment's geometry (three orthogonal axes of momentum kicks) mirrors a simple cubic root system (A₃ or B₃). The ratio of gravitational to electromagnetic coupling at Planck scale is ~ (m_P/m_e)² ≈ (2.176×10⁻⁸ kg / 9.109×10⁻³¹ kg)² ≈ 5.71×10⁴⁵ — no golden-ratio link found in the descri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.22853526

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Andrew Stewart Caldin

FINDING: Tabletop experiments for quantum gravity are now feasible using matter-wave interferometry and optomechanical systems, potentially enabling direct observation of quantum gravity effects at accessible scales. | MATH: Key constants: Planck length \( l_P = \sqrt{\hbar G/c^3} \approx 1.616 \times 10^{-35} \, \text{m} \); Planck mass \( m_P = \sqrt{\hbar c/G} \approx 2.176 \times 10^{-8} \, \text{kg} \); Newton's constant \( G \approx 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \); reduced Planck constant \( \hbar \approx 1.0545718 \times 10^{-34} \, \text{J·s} \). Experimental parameters involve superposition size \( \Delta x \), mass \( m \), and coherence time \( t \) such that \( \Delta x \cdot m \cdot t \) approaches Planck scale sensitivity. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries appear in these findings. However, the underlying mathematical structure of quantum gravity ofte Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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FINDING: Quantum gravity tests are converging on tabletop interferometry experiments probing superposition of massive objects, with Penrose's gravitationally-induced collapse criterion as a central quantitative target. | MATH: Penrose's collapse time τ ≈ ħ/E_G where E_G is gravitational self-energy difference between superposed mass configurations; for a sphere of mass m and radius R, E_G ≈ (4πG/3) m²/R (order-of-magnitude). The Ron Folman "T-cubed" experiment scales with T³ (interferometer time cubed) — a cubic scaling law. No new fundamental constant emerges; G, ħ, c remain the only inputs. | CONNECTION: The T³ scaling echoes cubic lattice symmetry (3D crystallographic point groups, e.g., m-3m) — the experiment's geometry (three orthogonal axes of momentum kicks) mirrors a simple cubic root system (A₃ or B₃). The ratio of gravitational to electromagnetic coupling at Planck scale is ~ (m_P/m_e)² ≈ (2.176×10⁻⁸ kg / 9.109×10⁻³¹ kg)² ≈ 5.71×10⁴⁵ — no golden-ratio link found in the descri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum gravity tests are converging on tabletop interferometry experiments probing Planck-scale effects via entanglement and superposition of massive systems. | MATH: Key scales: Planck mass mP=ℏc/G≈2.176×10−8 m_P = \sqrt{\hbar c/G} \approx 2.176 \times 10^{-8} mP​=ℏc/G​≈2.176×10−8 kg; Planck length lP=ℏG/c3≈1.616×10−35 l_P = \sqrt{\hbar G/c^3} \approx 1.616 \times 10^{-35} lP​=ℏG/c3​≈1.616×10−35 m. The proposed experiments (e.g., Ron Folman's T³, matter-wave interferometry) require measuring phase shifts Δϕ∼(m1m2Gt3)/(ℏd3) \Delta \phi \sim (m_1 m_2 G t^3)/(\hbar d^3) Δϕ∼(m1​m2​Gt3)/(ℏd3) — a cubic time dependence, hence "T-cubed." Decoherence rate for gravitational entanglement: Γ∼(Gm1m2/ℏd)2⋅τ \Gamma \sim (G m_1 m_2 / \hbar d)^2 \cdot \tau Γ∼(Gm1​m2​/ℏd)2⋅τ — dimensionless coupling αG=Gm1m2/(ℏcd)≪1 \alpha_G = G m_1 m_2 / (\hbar c d) \ll 1 αG​=Gm1​m2​/(ℏcd)≪1 at tabletop scales, yet measurable via entanglement witness. | CONNECTION: The ratio mP2/(m1m2) m_P^2 / (m_1 m_2) mP2​/(m1​m2​) for typical masses (e.g., 10−14 10^{-14} 10−14 kg) yields ∼1012 \sim 10^{12} ∼1012 — not directly harmonic. However, the T³ phase term contains t3 t^3 t3 — a cubic symmetry (tetrahedral Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Tabletop quantum-gravity tests probe Planck-scale discreteness via matter-wave interferometry and optomechanical superposition, not yet yielding a confirmed equation but constraining collapse models and graviton signatures. | MATH: Planck length lP=ℏG/c3≈1.616×10−35 ml_P = \sqrt{\hbar G/c^3} \approx 1.616\times10^{-35}\,\text{m}lP​=ℏG/c3​≈1.616×10−35m; Planck mass mP=ℏc/G≈2.176×10−8 kgm_P = \sqrt{\hbar c/G} \approx 2.176\times10^{-8}\,\text{kg}mP​=ℏc/G​≈2.176×10−8kg; decoherence rate for gravitationally-induced collapse (Penrose–Diosi): Γ∼ΔEG/ℏ\Gamma \sim \Delta E_G/\hbarΓ∼ΔEG​/ℏ, where ΔEG=G2∫ ⁣ ⁣∫[ρ1(r)−ρ2(r)][ρ1(r′)−ρ2(r′)]∣r−r′∣d3r d3r′\Delta E_G = \frac{G}{2}\int\!\!\int \frac{[\rho_1(\mathbf{r})-\rho_2(\mathbf{r})][\rho_1(\mathbf{r}')-\rho_2(\mathbf{r}')]}{|\mathbf{r}-\mathbf{r}'|}d^3r\,d^3r'ΔEG​=2G​∫∫∣r−r′∣[ρ1​(r)−ρ2​(r)][ρ1​(r′)−ρ2​(r′)]​d3rd3r′; Folman T³ experiment: cubic scaling of phase shift Δϕ∝T3\Delta\phi \propto T^3Δϕ∝T3 (where TTT is free-fall time), testing equivalence principle at quantum level. | CONNECTION: The ratio lP2/λC2l_P^2/\lambda_C^2lP2​/λC2​ (Planck length squared over Compton wavelength squared) appears in gravitationally-induced entanglement rates — nume Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Tabletop experiments propose direct quantum-gravity observation via matter-wave interferometry and optomechanics, with the T-cubed experiment (Folman) as a specific proposal; no new fundamental constant or equation emerges, but a testable regime is defined. MATH: The key scaling is the **T³ (T-cubed) phase accumulation** in matter-wave interferometry: phase ∝ (mass) × (acceleration) × T³, where T is the free-evolution time. For quantum gravity signatures, the relevant energy scale is the **Planck mass** mP=ℏc/G≈2.176×10−8 kg m_P = \sqrt{\hbar c/G} \approx 2.176 \times 10^{-8} \, \text{kg} mP​=ℏc/G​≈2.176×10−8kg, and the gravitational self-energy term in Penrose's collapse criterion: ΔE=G2∫∫ρ(r)ρ(r′)∣r−r′∣ d3r d3r′ \Delta E = \frac{G}{2} \int \int \frac{\rho(\mathbf{r})\rho(\mathbf{r}')}{|\mathbf{r}-\mathbf{r}'|} \, d^3r \, d^3r' ΔE=2G​∫∫∣r−r′∣ρ(r)ρ(r′)​d3rd3r′ (Newtonian gravitational self-energy difference between superposed mass distributions). The decoherence time predicted is τ∼ℏ/ΔE \tau \sim \hbar / \Delta E τ∼ℏ/ΔE. 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
FINDING: Quantum gravity experiments are transitioning from theoretical speculation to tabletop-scale tests probing the quantum nature of spacetime via superposition of massive systems. MATH: The core experimental framework relies on the quantum superposition of a mass m m m in two spatial locations separated by Δx \Delta x Δx, generating a gravitational phase shift Δϕ=Gm2ΔtℏΔx \Delta \phi = \frac{G m^2 \Delta t}{\hbar \Delta x} Δϕ=ℏΔxGm2Δt​ (for two masses in superposition, per Bose–Marletto–Vedral proposal). The decoherence timescale for gravitational entanglement is τ∼ℏΔxGm2 \tau \sim \frac{\hbar \Delta x}{G m^2} τ∼Gm2ℏΔx​. Penrose's criterion for gravitationally-induced collapse: EG=Gm2Δx E_G = \frac{G m^2}{\Delta x} EG​=ΔxGm2​ compared to ℏ/τ \hbar/\tau ℏ/τ. CONNECTION: The ratio Gm2ℏc \frac{G m^2}{\hbar c} ℏcGm2​ (gravitational coupling) is dimensionless and tiny (~10−4510^{-45}10−45 for protons), but the experimental geometry uses harmonic oscillator frequencies and lattice-like trap spacings — the optimal Δx \Delta x Δx often scale Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum gravity remains experimentally untested; proposed tabletop tests (matter-wave interferometry, optomechanics) probe Planck-scale effects via superposition of massive objects, with no confirmed mathematical discovery yet. MATH: No new equations or constants extracted. Relevant framework: Planck mass mP=ℏc/G≈2.176×10−8 kg m_P = \sqrt{\hbar c/G} \approx 2.176 \times 10^{-8} \, \text{kg} mP​=ℏc/G​≈2.176×10−8kg, Planck length ℓP=ℏG/c3≈1.616×10−35 m \ell_P = \sqrt{\hbar G/c^3} \approx 1.616 \times 10^{-35} \, \text{m} ℓP​=ℏG/c3​≈1.616×10−35m. Proposed test scales: superposition separation Δx∼ℓP2/3λC1/3 \Delta x \sim \ell_P^{2/3} \lambda_C^{1/3} Δx∼ℓP2/3​λC1/3​ (where λC \lambda_C λC​ 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∝Gm1m2/r H \propto G m_1 m_2 / r H∝Gm1​m2​/r yields entanglement e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Tabletop experiments for quantum gravity are now feasible using matter-wave interferometry and optomechanical systems, potentially enabling direct observation of quantum gravity effects at accessible scales. | MATH: Key constants: Planck length lP=ℏG/c3≈1.616×10−35 m l_P = \sqrt{\hbar G/c^3} \approx 1.616 \times 10^{-35} \, \text{m} lP​=ℏG/c3​≈1.616×10−35m; Planck mass mP=ℏc/G≈2.176×10−8 kg m_P = \sqrt{\hbar c/G} \approx 2.176 \times 10^{-8} \, \text{kg} mP​=ℏc/G​≈2.176×10−8kg; Newton's constant G≈6.67430×10−11 m3kg−1s−2 G \approx 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} G≈6.67430×10−11m3kg−1s−2; reduced Planck constant ℏ≈1.0545718×10−34 J⋅s \hbar \approx 1.0545718 \times 10^{-34} \, \text{J·s} ℏ≈1.0545718×10−34J⋅s. Experimental parameters involve superposition size Δx \Delta x Δx, mass m m m, and coherence time t t t such that Δx⋅m⋅t \Delta x \cdot m \cdot t Δx⋅m⋅t approaches Planck scale sensitivity. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries appear in these findings. However, the underlying mathematical structure of quantum gravity ofte Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com