Sustaita's Temporal Anchoring Equation: A Model of the Quantum-Classical Transition with Falsifiable Predictions

Title: Sustaita's Temporal Anchoring Equation: A Phenomenological Model of the Quantum-Classical Transition with Falsifiable Predictions Author: Jose Miguel Sustaita González Abstract: A phenomenological model is proposed in which space and time are treated as conceptually distinct entities: space acts as a three-dimensional stage, while time is described as a geometric flow that traverses it. Gravity — interpreted as curvature of space — modulates the intensity of this flow, slowing it near massive objects and releasing it in vacuum. A dimensionless anchoring parameter α ∈ [0,1] is introduced to quantify the resistance of a material system to being dragged by this flow. Under this hypothesis, the quantum regime (α → 0) corresponds to poorly anchored systems, while the classical regime (α → 1) emerges when the system is strongly anchored through interactions with the environment or by its own gravitational inertia. The model leads to three falsifiable experimental predictions: (i) the critical gas pressure that destroys quantum coherence scales as P_c ∝ 1/m^2 for fixed-radius particles; (ii) the temporal anchoring rate scales as β ∝ m^2; and (iii) visibility curves for different masses collapse when plotted against t · m^2. Two experiments — one based on Talbot-Lau interferometry and another on discrete counting of anchoring events — are proposed to test these predictions. The manuscript includes detailed derivations of the effective gas decoherence rate (including the distinguishability suppression factor), blackbody radiation and phonon rates, dimensional verifications, numerical evaluations of P_c for the proposed experimental parameters, and a comparison with standard decoherence predictions.