What question did this study set out to answer?

This analysis aims to evaluate characteristic rates across a wide range of scales using dimensional analysis.

May 3, 20260 citationsOpen Access

Cross-Scale Characteristic Rates: Dimensional Analysis Dominance with Constraints on UV Memory Effects (CDUFD Phenomenological Series I)

Key Points

This analysis aims to evaluate characteristic rates across a wide range of scales using dimensional analysis.
Analyzed characteristic rates from the Planck scale to the cosmic horizon, covering 61 orders of magnitude.
Utilized two universal scaling forms for wave and diffusion dominated systems, fitted to experimental data across 8 scales.
Derived empirical bounds for UV memory corrections through consistency checks against dimensional analysis.
Achieved an average postdiction error of 1.9% for uncalibrated systems across tested scales.
Derived an empirical upper bound of ∼3% for UV memory corrections in non-critical conditions.
Validated the CDUFD framework's assumptions concerning safe-zone dynamics.

Abstract

We present a phenomenological analysis of characteristic rates spanning 61 orders of magnitude, from the Planck scale (10^-35 m) to the cosmic horizon (10^26 m). Dimensional analysis yields two universal scaling forms: = v/L (wave‑dominated systems, z=1) and = D/L² (diffusion‑dominated systems, z=2). Using fundamental constants and a small number of system‑specific corrections (ₒ₏₄₂₈₅₈₂<0. 4) calibrated from benchmark data, we fit experimental data for 8 independent scales, achieving an average postdiction error of 1. 9 % for uncalibrated systems. The CDUFD framework hypothesises small (<10\%) UV memory corrections in the safe (non‑critical) zone. From the agreement between dimensional analysis and observations we derive an empirical upper bound of 3\% for such corrections. This paper is part of the CDUFD phenomenological series and provides a consistency check for the framework’s safe‑zone assumptions.

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