Entropic Gravity via Quantum Causality: A Theoretical Reconstruction of Spacetime Emergence

This paper presents a novel theoretical framework proposing that gravity emerges from quantum entanglement networks rather than existing as a fundamental force. We introduce the concept of a Causal Adjacency Tensor that encodes quantum correlations and demonstrate how spacetime geometry emerges through a two-step process of transformation and coarse-graining. Our approach differs from existing theories (Verlinde's entropic gravity, causal set theory, AdS/CFT) by treating entanglement relations as fundamental rather than spacetime points. We provide concrete mathematical formulations, including a constructive definition of the emergence process via Gaussian smearing kernels, and propose testable predictions for cosmological signatures and laboratory experiments. While speculative, the framework offers a mathematically coherent pathway toward understanding gravity as an information-theoretic phenomenon.