Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

TL;DR

This paper presents Entropic Dynamics as a novel framework deriving Quantum Mechanics from principles of entropy and information geometry, emphasizing the epistemic nature of the wave function and its phase.

Contribution

It introduces a geometric approach linking entropic inference to quantum dynamics, unifying Riemannian, symplectic, and complex structures in phase space.

Findings

Derivation of quantum phase space geometry from information geometry

Identification of constraints that lead to quantum dynamics

Connection between gauge symmetry, charge quantization, and wave function phases

Abstract

Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single-valuedness of wave functions.