A Statistical Framework for the Emergenceof Spacetime and Gravity

We present a fundamentally statistical and background-independent framework where spacetime and gravity emerge from the collective behavior of quantum information clusters. The system’s dynamics are governed by the minimization of an Informational Free Energy, giving rise to a dual-natured force. This framework derives a long-range attraction consistent with gravity, provides a mechanism for singularity avoidance, and defines the full metric tensor gµν from statistical correlations. We validate the model through extensive 3D N-body simulations, first confirming a robust scaling law for its scalar component, where the emergent potential U scales with the number of clusters N as U ∝ N^α with α = 1.9925 ± 0.0069. Subsequently, we successfully validate the full tensor framework, confirming the emergence of a consistent relativistic geometry—including frame-dragging and gravitational time dilation—directly from the system’s underlying statistical properties.<br>