Quantum Spacetime: Emergent Curved Metrics from Relational Separations

In this paper, we propose a novel Quantum Spacetime Theory (QST) that reinterprets spacetime as an emergent structure, challenging the traditional block universe paradigm and aligning with research into emergent spacetime. Using a sphere intersection method, spacetime geometry is constructed from spacelike separations that are inversely proportional to mutual information between quantum subsystems. We show that geometry derived from relational spacelike separations renders a flat metric insufficient, with a curved metric as an inevitable consequence, highlighting spacetime's relational nature. Specifically, the emergent metric exhibits gravitational-like acceleration effects driven by quantum constraints, yielding an inverse-square law $r^{-2}$ with deviations ranging from $r^{-1}$ to $r^{-3}$, consistent with cosmological contexts and post-Newtonian corrections, respectively. Geometric shortcuts for quantum non-locality, aligned with the ER=EPR conjecture, emerge from specific configurations, driven by mutual information between quantum subsystems. Compared to general relativity, our model shares curved spacetime but features observer-dependent metrics emergent from quantum subsystems and a presentist perspective, contrasting eternalist metrics. This quantum-geometric framework advances quantum gravity, with future work focusing on refining the quantum-geometric mapping and exploring cosmological implications.