Testing Quantum Gravity via Gravity-Mediated Entanglement — E8 Intelligence Research

FINDING: Quantum gravity may be testable via gravity-mediated entanglement between two masses, without needing Planck-scale energies; the key is quantum information-theoretic verification of the gravitational field's non-classicality. | MATH: The core criterion is the generation of entanglement entropy \( S = -\mathrm{Tr}(\rho \log \rho) > 0 \) between two initially separable mechanical oscillators (masses \( m_1, m_2 \)) coupled only by the Newtonian potential \( V_G = -G m_1 m_2 / r \). The interaction Hamiltonian in the quantum regime is \( H_{\text{int}} = \hbar g (\hat{a}_1 + \hat{a}_1^\dagger)(\hat{a}_2 + \hat{a}_2^\dagger) \), with coupling \( g \propto G m_1 m_2 / (\hbar d^3) \cdot \text{(zero-point amplitudes)} \). The entanglement witness is typically the logarithmic negativity \( E_N = \log_2 \| \rho^{T_A} \|_1 > 0 \), or a Bell-inequality violation parameter \( S_{\text{Bell}} > 2 \). The experimental scale: masses ~\(10^{-14}\) kg, separation ~\(10^{-4}\) m, requiring \( g Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com