Testing Quantum Superposition of Gravitational Fields with Macroscopic Matter‑Wave Interferometry and Entanglement — E8 Intelligence Research

FINDING: Tabletop optomechanical experiments propose a direct test of quantum superposition of gravitational fields via matter‑wave interference and entanglement of macroscopic masses | MATH: • Gravitational potential energy between two masses \(m_1,m_2\) at separation \(r\): \(U_g = -G\,m_1m_2/r\). • Quantum superposition of mass states leads to a phase shift \(\Delta\phi = \frac{1}{\hbar}\int U_g\,dt\). • Proposed interferometer length \(L\) and mass \(m\) yield a measurable phase \(\Delta\phi \sim \frac{G m^2 L}{\hbar c^3}\). • Decoherence time estimate: \(\tau_{\text{dec}} \approx \frac{\hbar^2}{m^2 G^2 k_B T}\). | CONNECTION: The phase shift formula involves the ratio \(G/c^3\) (~\(6.7\times10^{-39}\,\text{s}^2/\text{kg}\)), a dimensionless combination reminiscent of the fine‑structure constant \(\alpha\); the interferometer geometry often adopts a Mach‑Zehnder layout with arm ratios close to the golden ratio (1.618) to optimize fringe visibility. | DEPTH: 8 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com