Entanglement‑Based Test of Quantum Gravity with Mesoscopic Matter‑Wave Interferometers — E8 Intelligence Research

FINDING: Tabletop quantum‑gravity experiments aim to detect gravitationally induced entanglement between two mesoscopic masses using matter‑wave interferometry and optomechanical control, thereby testing whether gravity can be described by a quantum field. | MATH: • Gravitational potential energy: \(U_{12}=-\dfrac{G\,m_1m_2}{r}\). • Quantum‑gravity interaction time: \(\tau_{\text{int}}\sim \dfrac{\hbar r}{G m_1 m_2}\). • Condition for observable entanglement: \(\tau_{\text{int}}\lesssim \tau_{\text{decoh}}\). • Planck mass as natural scale: \(m_P=\sqrt{\dfrac{\hbar c}{G}}\); experiments probe masses \(m\ll m_P\) yet large enough that \(Gm^2/\hbar c\) is non‑negligible. | CONNECTION: No direct appearance of golden‑ratio or base‑60 ratios; the relevant geometry is the Euclidean distance \(r\) between masses and the spherical symmetry of the Newtonian potential. | DEPTH: 8 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com