An Empirical Inquiry into the Scaling Regimes of Physical Event Intervals

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 ∝ S1.00 (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 ∝ S1.16; above it, the scaling compresses to T ∝ S0.46. 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. 

1. Physical systems rotate, oscillate, and cycle (direct observation)
2. These rotations can be counted (operational definition)
3. The count of rotations provides a measure of sequence (ordering)
4. We conventionally label this count as "time" (linguistic convention)