Relational Spacetime Dynamics with Finite Update Resolution

Relational Spacetime Dynamics with Finite Update Resolution Abstract:General relativity provides a highly successful geometric description of gravitation, yet the dynamical mechanisms by which physical relations evolve toward self-consistency remain largely implicit. In this work, we propose an axiomatic relational framework that extends the standard description of spacetime dynamics by introducing a finite resolution of relational updates, without discretizing spacetime geometry itself.The framework is based on the assumption that physical evolution proceeds through self-consistent relational updates possessing a minimal dynamical resolution. Within this approach, gravitational effects are interpreted as arising from spatial variations in the local rate of relational evolution, while energy is associated with unresolved relational mismatches between local and environmental configurations. Matter is described as a stabilized non-equilibrium configuration in which such mismatches cannot fully relax.A central consequence of the framework is the natural emergence of relaxation processes, threshold behavior, and effective inertia as outcomes of finite update resolution. Time and spacetime geometry appear as emergent, higher-level descriptions of iterated relational self-consistency rather than as fundamental structures. The proposed approach remains compatible with relativistic causality and offers a unified conceptual interpretation of gravity, energy, and matter within a relational dynamical setting. Notes: This record provides a preprint version for dissemination and priority timestamping. The manuscript corresponds to a version submitted to Foundations of Physics.