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MERLIN SCIENCE — T³ Experiment: A Tabletop Path to Quantum Gravity Observation — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 3, 2026• 0 citations
Publisher

Abstract

Here is the narration for today's MERLIN SCIENCE video. The finding, in one clean sentence: A tabletop experiment using matter-wave interferometry, specifically the T-cubed proposal, defines a testable regime where quantum gravity effects should manifest as a measurable phase shift, without introducing any new fundamental constant or equation. The context: We are stuck. Quantum mechanics and general relativity are both spectacularly confirmed, yet they refuse to merge into a single framework. Every attempt to probe the quantum nature of gravity has required astronomical energies or cosmic-scale detectors. The T-cubed experiment offers a different route — a laboratory-scale path that could finally observe the collapse of a quantum superposition under its own gravitational field. The mechanism, at a level you can evaluate: The key is the cubic scaling of the interferometric phase with free-evolution time, T. The phase grows as mass times acceleration times T cubed. This is not new phy Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.23115351

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T³ Experiment: A Tabletop Path to Quantum Gravity Observation — E8 Intelligence Research

Andrew Stewart Caldin

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

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

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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 \(l_P = \sqrt{\hbar G/c^3} \approx 1.616\times10^{-35}\,\text{m}\); Planck mass \(m_P = \sqrt{\hbar c/G} \approx 2.176\times10^{-8}\,\text{kg}\); decoherence rate for gravitationally-induced collapse (Penrose–Diosi): \(\Gamma \sim \Delta E_G/\hbar\), where \(\Delta E_G = \frac{G}{2}\int\!\!\int \frac{[\rho_1(\mathbf{r})-\rho_2(\mathbf{r})][\rho_1(\mathbf{r}')-\rho_2(\mathbf{r}')]}{|\mathbf{r}-\mathbf{r}'|}d^3r\,d^3r'\); Folman T³ experiment: cubic scaling of phase shift \(\Delta\phi \propto T^3\) (where \(T\) is free-fall time), testing equivalence principle at quantum level. | CONNECTION: The ratio \(l_P^2/\lambda_C^2\) (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

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Andrew Stewart Caldin

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Andrew Stewart Caldin

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.com

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Here is the narration for today's MERLIN SCIENCE video. The finding, in one clean sentence: A tabletop experiment using matter-wave interferometry, specifically the T-cubed proposal, defines a testable regime where quantum gravity effects should manifest as a measurable phase shift, without introducing any new fundamental constant or equation. The context: We are stuck. Quantum mechanics and general relativity are both spectacularly confirmed, yet they refuse to merge into a single framework. Every attempt to probe the quantum nature of gravity has required astronomical energies or cosmic-scale detectors. The T-cubed experiment offers a different route — a laboratory-scale path that could finally observe the collapse of a quantum superposition under its own gravitational field. The mechanism, at a level you can evaluate: The key is the cubic scaling of the interferometric phase with free-evolution time, T. The phase grows as mass times acceleration times T cubed. This is not new phy 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 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 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: 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: 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: 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: H^G=−Gm1m2∣x^1−x^2∣ \hat{H}_G = -G \frac{m_1 m_2}{|\hat{x}_1 - \hat{x}_2|} H^G​=−G∣x^1​−x^2​∣m1​m2​​, where the position operators x^i\hat{x}_ix^i​ are in coherent superposition states. The entanglement entropy S=−Tr(ρln⁡ρ)S = -\text{Tr}(\rho \ln \rho)S=−Tr(ρlnρ) of the joint state serves as the witness. The T³ (T-cubed) experiment (Folman) uses a triple-interferometer with time TTT, giving phase shift Δϕ∝Gm2T3/ℏd2\Delta \phi \propto G m^2 T^3 / \hbar d^2Δϕ∝Gm2T3/ℏd2 (where ddd is separation). The decoherence rate scales as Γ∝(Gm2/ℏd2)2τ\Gamma \propto (G m^2 / \hbar d^2)^2 \tauΓ∝(Gm2/ℏd2)2τ, with τ\tauτ the interaction time. | CONNECTION: The phase shift Δϕ\Delta \phiΔϕ contains the ratio Gm2/ℏG m^2 / \hbarGm2/ℏ — a dimensionless coupling Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com