Causal Graph Dynamics (CGD): A Minimal, Background-Independent Framework for Emergent Spacetime
Abstract
Abstract We introduce a rigorous, non-perturbative, and strictly background-independent framework for quantum gravity termed Causal Graph Dynamics (CGD). Established models often suffer from structural circularity by introducing primitive metric lengths or uncomputable complexity measures. CGD eliminates these flaws by formulating the universe as a finite Directed Acyclic Graph (DAG) G = (V, E) with explicit boundary conditions. Vertices V represent discrete computational event updates and edges E define asymmetric causal dependencies. By applying a localized, computable polynomial graph Hamiltonian that minimizes local in-out degree differences, we demonstrate that a stable 3+1 dimensional Lorentzian spacetime and fundamental physical constants spontaneously emerge in the infrared continuum limit, driven solely by geometric constraints. Furthermore, we derive the emergence of elementary particles as topological defects and propose a concrete observational signature for cosmic microwave background (CMB) scattering.