Beyond Time V: Closing the Gaps in Emergent Temporality

Abstract: This fifth paper in the Beyond Time series establishes the mathematical foundation for a new model of time as an emergent phenomenon. Building upon the theoretical framework developed in previous installments, it introduces a set of axioms and formal equations that define time not as a fundamental dimension, but as a scalar field (τ\tauτ) arising from entropy-driven, distinguishable state transitions. Time, in this view, emerges only when energy exchange and informational differentiation occur, and vanishes near the physical boundaries defined by the speed of light (ccc) and absolute zero temperature (T0T_0T0). This paper addresses key gaps left open in Beyond Time IV by deriving limit conditions, proposing a Gedankenexperiment, and outlining falsifiable implications. The resulting model repositions time as a local and statistical construct—one that may cease, emerge, or vary based on a system’s thermodynamic behavior.