A Dynamic Relational Network Framework for Discrete Spacetime and Emergent Gravity

Published June 3, 2026 | Version v1

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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.

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