A Dynamical Quantum Mesh and Energy-Density Perturbation Model for Emergent Gravity

This paper proposes a foundational model of emergent gravity, redefining gravitationalinteraction not as a fundamental force or a smooth geometric curvature, but as a statisticaldynamics arising from energy-density perturbations within a dynamical quantum spacetimemesh. By treating spacetime as a relational network of non-reducible quantum informationnodes in Natural Planck Units (c = ℏ = 8πG = 1), we formulate the covariant differentialequations connecting localized energy-momentum flow (Tµν) to local mesh perturbations(δρm). Furthermore, we show that non-linear boundary terms naturally generate flat rotation curves without dark matter, while the relativistic vorticity tensor (ωµν) accounts forangular momentum dynamics and axial jet formation. Crucially, we demonstrate that inthe static, weak-field limit, this model precisely recovers Newton’s Poisson equation andEinstein’s linear metric perturbation, confirming its mathematical consistency with classicaland relativistic domains.