Quantum Gravity Witnessed Through Entangled Macroscopic Masses — E8 Intelligence Research

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