Information Load, Mass–Wave Continuum, and Weak–Field Gravity: An Interpretational Bridge Between Quantum Matter and Relativity

This work proposes a phenomenological framework linking quantum localization to weak-field gravitational response through informational load functionals. The central idea is that the degree of spatial localization of a quantum state may be associated with an effective participation factor governing how strongly that state contributes to inertial and gravitational phenomena. Localization is quantified using standard measures such as the inverse participation ratio (IPR), combined with reference scales that render localization dimensionless. A monotonic substrate response function is introduced to map localization load to observable effects. In the weak-field regime, a linear response approximation recovers familiar gravitational scaling relations. The framework does not modify Schrödinger dynamics, introduce new particles, or attempt a full theory of quantum gravity. Instead, it explores whether aspects of gravity normally described geometrically can be reinterpreted as state-dependent informational load. Illustrative empirical connections are discussed using known atomic ionization data to show how varying localization regimes may correspond to different participation factors. These examples are intended as phenomenological consistency checks rather than precision derivations. Scope and Status: This work is exploratory and interpretational. It is intended as a conceptual bridge between quantum and gravitational descriptions, not as a completed fundamental theory. Predictions are restricted to weak-field regimes, and strong-field behavior is left open. Key Points: Treats mass-like behavior as state-dependent participation Uses established localization measures (IPR) Introduces substrate response only phenomenologically Does not invoke gravitons or modify QM equations Suggests testable scaling relations in principle Purpose: The goal is to stimulate discussion on whether gravitational response might be expressible in informational or localization terms, providing an alternative viewpoint on the QM–GR interface.