Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

• Published in: Annalen der Physik Vol. 531; no. 3
• Main Author: Caticha, Ariel
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.03.2019
• Subjects: entropic inference; Entropy (Information theory); foundations of quantum mechanics; Geometry; information physics; Quantum mechanics; Quantum physics; Quantum theory; Wave functions
• ISSN: 0003-3804; 1521-3889
• DOI: 10.1002/andp.201700408

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. The derivation of dynamics as an application of the method of maximum entropy hinges on identifying evolving constraints that capture the relevant physical information. Considerations from information geometry lead to a phase space geometry that combines Riemannian, symplectic, and complex structures. The Entropic Dynamics that preserves these structures is Quantum Mechanics. The argument casts new light on the connection between gauge symmetry, charge quantization, and the single‐valuedness of wave functions.