Tabletop Tests for Quantum Gravity via Gravitational Entanglement Phase — E8 Intelligence Research

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 \(m_1, m_2\) separated by distance \(d\), the interaction Hamiltonian \(H_G = -G m_1 m_2 / d\) generates a phase \(φ = G m_1 m_2 t / d\) in a superposition of paths. The experiment requires \(φ ~ π/2\) for maximal entanglement detection, implying \(m_1 m_2 t / d ~ / G\) — a scale set by the Planck mass squared over \(\). No new constants beyond \(G, , c\) 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 \(α_G/αEM ~ (m_P/m_e)^2 ~ (1.22×10¹⁹/0.511×10^6)^2 ~ 5.7×10⁴⁴\) — 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