On the Emergence of Time from Ordered Recurrence

This paper provides an operational and empirically testable definition of time as an emergent property of ordered recurrence. Rather than treating time as a fundamental parameter, the work introduces a Time Definition Index (TDI) that quantifies whether a physical system supports stable temporal ordering based on the coherence and regularity of its recurrent structure. Using independent datasets from atomic clocks and seismic time series, the study shows that temporal ordering does not degrade continuously but instead disappears once ordered recurrence falls below a critical threshold. In such regimes, physical processes may continue, but time as a meaningful index ceases to exist. This work builds directly on the earlier paper “Time, Space, and Quantum Phenomena as Emergent Consequences of Recurrence and Structural Locking,” where a general structural framework was introduced. While the earlier work established recurrence-induced locking as a universal mechanism underlying time, space, and quantum phenomena, the present paper isolates time as a standalone case and provides a minimal, observer-independent operational criterion for its existence. Together, the two papers form a coherent progression: the earlier work outlines the general structural mechanism, while this paper delivers a focused, empirically grounded definition of when and why time itself emerges.