A Dynamic Relational Network Framework for Discrete Spacetime and Emergent Gravity

This paper proposes a theoretical framework—Relational Theory—based on dynamic relational networks, in which discrete spacetime serves as the fundamental ontology, while continuous geometry and gravity emerge as macroscopic statistical phenomena. This framework unifies the description of matter, spacetime, and gravity, aiming to bridge the theoretical divide between quantum field theory and general relativity, while providing a discrete spacetime physical substrate for the orthodox prob abilistic interpretation of quantum mechanics. The fundamental ontology of the universe is defined as the evolution of a dynamic relational network, where nodes represent fundamental quantum units of space, edges correspond to adjacency relations between units, and matter manifests as complex probability amplitude excitation modes propagating on the network. The framework is built upon two foundational axioms: the matter field undergoes unitary evolution driven by the graph Lapla cian operator, and the network topology dynamically reconfigures in response to the matter energy density, with links undergoing continuous generation and decay, while matter evolution exhibits the discrete alternating character of “annihilation here, creation there.”Under the mean-field continuum limit, the two axioms respectively evolve into a Schr¨odinger equation describing matter propagation in curved space and a link density equation characterizing the response of spacetime geometry to matter distribution. These two sets of equations form a self-consistent feedback mechanism in which matter and spacetime geometry mutually constrain each other. The study demonstrates that grav ity is not a fundamental interaction, but rather a statistical emergent entropic force driven by the inhomogeneous spatial distribution of network link density.This paper further proposes a dynamic relational network interpretation, circumventing the collapse paradox of the Copenhagen interpreta tion, the universe-splitting problem of the many-worlds interpretation, and the non-locality dilemma of hidden variable theories. It provides an underlying topological explanation for wave function evo lution, the measurement problem, and the origin of quantum probability. The laws of black hole thermodynamics and the fundamentals of the holographic principle can all be reasonably explained within this microscopic topological framework. The paper systematically verifies the mathematical self-consistency of the model, distinguishes rigorously derived conclusions from conjectures awaiting verification, and demonstrates the feasible pathways for numerical simulation tests and astronomical observational corroboration.