Entropic Dynamics approach to the classical limit of Quantum Mechanics: decoupling of the centerof mass motion for a mesoscopic particle

Abstract

In the Entropic Dynamics (ED) approach, quantum mechanics is derived from the principles of entropic inference and information geometry. The ED approach differs from other interpretations by making a clear commitment to distinguishing which variables are ontic (real) and which are epistemic. The classical limit for the center of mass (CM) coordinate is achieved for a large number of particles, M →∞, while Planck’s constant ℏ remains finite. Typically, the emergence of the classical limit requires decoherence through interactions with the external environment. In this work, we investigate whether the classical behavior of the CM coordinate in a mesoscopic system can instead be achieved through internal decoherence resulting from interactions of the CM with the particles of the system itself. Within the framework of entropic dynamics, we study how correlations between a system's center of mass and its internal coordinates impact this transition. We look at mesoscopic systems placed in both uniform and non-uniform gravitational potentials using probabilistic forms of the Hamilton–Jacobi equation. In uniform fields, the center of mass remains independent of internal coordinates, maintaining quantum coherence. Meanwhile, non-uniform potentials create coupling that induces decoherence, leading to classical behavior. These results show correlation-induced information loss as a natural process for the quantum-to-classical transition and clarify how entropic dynamics provide a coherent, information-theoretic link between quantum and classical realms.