An Empirical Inquiry into the Scaling Regimes of Physical Event Intervals

Abstract This paper undertakes a humble, first-principles inquiry into the relationship between the size of physical systems (S) and their characteristic event intervals (T). We define an event interval operationally as the time between distinguishable state changes, allowing for a consistent comparison across diverse physical domains. We compiled a dataset of 40 systems spanning 61 orders of magnitude and, through a methodological filtering process, focused our primary analysis on a subset of 28 "physics-native" systems, excluding those with primarily biological or anthropogenic timescales. Our analysis of this physics-only dataset reveals a remarkably linear scaling relationship, T ∝ S^1.00 (R²=0.95), across the full range of physical scales. However, a more detailed, statistically-validated analysis reveals a two-regime model with a transition at the stellar-to-galactic boundary (~10⁹ m). Below this transition, the scaling is T ∝ S^1.16; above it, the scaling compresses to T ∝ S^0.63. This two-regime model is statistically preferred over a single power law (ΔAIC > 15). We present these purely observational findings as a call for further research into the physical mechanisms that may govern this transition in the universe's event-scaling architecture. Addendum: On the Nature of "Time" in This Framework Addendum: On the Nature of Time and Rotation In the spirit of first-principles inquiry, we clarify an important conceptual distinction. Throughout this paper, we use "T" to denote the characteristic interval between events, specifically, rotational or oscillatory periods for most systems in our dataset. We acknowledge that calling this quantity "time" presupposes the existence of time as an independent dimension. From a more fundamental perspective, what we measure are rotations, oscillations, and cycles. The counting of these cycles is what we operationally define as "time." Whether this relationship reveals something fundamental about the nature of time itself—or whether "time" is simply our label for counted rotations—remains an open philosophical and physical question. This paper documents the empirical relationship between system size and rotational period without making ontological claims about the nature of time. Physical systems rotate, oscillate, and cycle (direct observation) These rotations can be counted (operational definition) The count of rotations provides a measure of sequence (ordering) We conventionally label this count as "time" (linguistic convention) Therefore, our equation R ∝ S^α (where R represents rotational/oscillation period) describes a relationship between the spatial scale of a system and the duration of its characteristic cycle—without presupposing what "time" fundamentally is. This distinction is critical. We are not claiming to have discovered a "law of time." We are claiming to have discovered a scaling relationship between size and rotation across physical systems. Whether this relationship reveals something about the nature of time itself, or whether it reveals that "time" is an emergent property of rotation and counting, remains an open question for further investigation. We adopt this more cautious framing to avoid prematurely importing theoretical constructs into what is intended as a purely empirical, first-principles inquiry.