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Tabletop Probes of Quantum Gravity: Untested Planck-Scale Superposition Experiments — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 31, 2026• 0 citations
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Abstract

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 \( m_P = \sqrt{\hbar c/G} \approx 2.176 \times 10^{-8} \, \text{kg} \), 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

DOI
10.5281/zenodo.22190669

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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: Quantum gravity may be testable via tabletop matter-wave/optomechanical interferometry, probing the quantum superposition of gravitational fields at mesoscopic scales. | MATH: The core observable is the gravitational entanglement phase — for two masses m1,m2m_1, m_2m1​,m2​ separated by distance ddd, the interaction Hamiltonian HG=−Gm1m2/dH_G = -G m_1 m_2 / dHG​=−Gm1​m2​/d generates a phase ϕ=Gm1m2t/ℏd\phi = G m_1 m_2 t / \hbar dϕ=Gm1​m2​t/ℏd in a superposition of paths. The experiment requires ϕ∼π/2\phi \sim \pi/2ϕ∼π/2 for maximal entanglement detection, implying m1m2t/d∼ℏ/Gm_1 m_2 t / d \sim \hbar / Gm1​m2​t/d∼ℏ/G — a scale set by the Planck mass squared over ℏ\hbarℏ. No new constants beyond G,ℏ,cG, \hbar, cG,ℏ,c appear; the test is purely quantum-informational (entanglement witness) rather than energy-based. | CONNECTION: The ratio of gravitational to electromagnetic coupling at the Planck scale is αG/αEM∼(mP/me)2∼(1.22×1019/0.511×106)2∼5.7×1044\alpha_G/\alpha_{EM} \sim (m_P/m_e)^2 \sim (1.22\times10^{19}/0.511\times10^6)^2 \sim 5.7\times10^{44}αG​/αEM​∼(mP​/me​)2∼(1.22×1019/0.511×106)2∼5.7×1044 — not a golden ratio, but the experimental thre 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: 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
FINDING: Tabletop experiments propose direct quantum-gravity tests via entanglement of two masses, probing the quantum nature of the gravitational field. | MATH: The core observable is the gravitational interaction Hamiltonian Hint=−Gm1m2/∣r1−r2∣ H_{\text{int}} = -G m_1 m_2 / |\mathbf{r}_1 - \mathbf{r}_2| Hint​=−Gm1​m2​/∣r1​−r2​∣, with quantum superposition of positions ∣ψ⟩=12(∣L⟩+∣R⟩) |\psi\rangle = \frac{1}{\sqrt{2}}(|L\rangle + |R\rangle) ∣ψ⟩=2​1​(∣L⟩+∣R⟩) for each mass; the entanglement witness is the phase ϕ=Gm1m2tℏd \phi = \frac{G m_1 m_2 t}{\hbar d} ϕ=ℏdGm1​m2​t​ (where d d d is separation, t t t interaction time). Key constants: G≈6.674×10−11 m3kg−1s−2 G \approx 6.674 \times 10^{-11} \, \text{m}^3\text{kg}^{-1}\text{s}^{-2} G≈6.674×10−11m3kg−1s−2, ℏ≈1.054×10−34 J⋅s \hbar \approx 1.054 \times 10^{-34} \, \text{J·s} ℏ≈1.054×10−34J⋅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⟩,∣R⟩ |L\rangle, |R\rangle ∣L⟩,∣R⟩ form a two-level sy Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com