The Span Model: A Phenomenological Scaling Framework for Finite Correlation Spans

Experiments involving correlated particle pairs exhibit finite correlation spans that vary widely across experimental setups and particle species. This work does not address microscopic quantum mechanisms or propose any modification to quantum theory; instead, it presents a minimal and falsifiable phenomenological experimental framework examining how experimentally accessible macroscopic parameters are empirically correlated with observable correlation spans. Motivated by the large separation scales reported in existing experiments, this work introduces a simple phenomenological scaling equation that relates the maximum observable correlation span to the masses of the particles involved and to an effective contribution from the experimental apparatus. The proposed relation is not derived from quantum theory and makes no claim regarding the physical origin of its parameters. The central contribution of this paper is the definition of a minimal, inexpensive, and experimentally testable calibration protocol designed to decide between two mutually exclusive hypotheses: either a single constant governs correlation spans across all experimental setups, or the observed spans depend on properties of the measurement apparatus itself. The protocol specifies how repeated measurements using different particle pairs on the same apparatus can extract or falsify the proposed relation within a given regime. The falsifiability of the framework is established explicitly at the end of Section 3, where a technician-ready calibration procedure leads to a set of mutually exclusive experimental outcomes. In this sense, the work presents a testable experimental framework rather than a completed physical theory.