Generative Closure and the Emergence of Temporal Order in Relativistic Physics

Recent debates in Foundations of Physics have highlighted a tension between radical relational approaches that eliminate time as a fundamental variable and renewed arguments for preserving an underlying ordinal structure. While Rovelli, Barbour, and Page–Wootters propose that all dynamics can be expressed through timeless correlations, Mozota Frauca and Ellis have recently contended in FoP that physics cannot dispense with the asymmetric “before/after” relation that grounds causal explanation. This paper introduces a physical mechanism by which such ordinal structure can be realised without reinstating absolute time. Each physical event is described as the closure of a lawful relation—the directed completion of an emission–absorption pair that converts open potentiality into realized fact. Every closure involves a finite local generative interval Δτ, defined operationally as the minimal time resolution of the participating clock or detector. The ensemble of these directed closures forms a self-organising partial order whose cumulative growth constitutes the empirical order ordinarily described as time. Using Special Relativity as a case study, the paper shows how worldlines grow tick-by-tick from local clocks, how null connections serve as generative relations, and how energy–mass balance holds across closure cycles. The model predicts that quantum non-local correlations should remain perfect only within a coherence horizon set by Δτ—offering an empirical route to confirm or falsify the generative-layer hypothesis. In this framework, spacetime geometry records what has been realized, while time itself emerges as the topology of ongoing realization.