Entanglement as a Gravitational Mechanism

We propose that gravitational attraction emerges from networks of quantum entanglement among spacetime degrees of freedom, particularly the entangled virtual-particle pairs that populate the quantum vacuum in quantum field theory (QFT). In this picture, regions of higher entanglement density stitch space together, generating an effective attractive force that manifests macroscopically as gravity. Working within a discrete graph-theoretic framework, we model spacetime as a weighted graph whose nodes carry local mass-energy and whose edge weights encode the mutual information of the vacuum states. Using Ollivier-Ricci curvature (which compares Wasserstein transport distances on local mass measures to the graph metric), we derive the discrete analogue of the Ricci tensor and scalar. Contracting these yields the Einstein tensor $G_{ij}$ . In the continuum limit the graph equations satisfy the Einstein field equations$G_{\mu \nu }=\frac{8\pi G}{c^4}{T}_{\mu \nu }$ ,with the coupling constant fixed by matching to the Newtonian limit. This construction provides a purely quantum-information-theoretic origin for gravity consistent with the QFT vacuum structure and with known results on emergent geometry from random graphs.