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Open AccessFeature PaperArticle

The Entropic Dynamics Approach to Quantum Mechanics

Physics Department, University at Albany-SUNY, Albany, NY 12222, USA
Entropy 2019, 21(10), 943; https://doi.org/10.3390/e21100943
Received: 13 August 2019 / Revised: 16 September 2019 / Accepted: 18 September 2019 / Published: 26 September 2019
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures—which is a Hamilton-Killing flow in phase space—is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations. View Full-Text
Keywords: quantum mechanics; entropic dynamics; symplectic geometry; information geometry quantum mechanics; entropic dynamics; symplectic geometry; information geometry
MDPI and ACS Style

Caticha, A. The Entropic Dynamics Approach to Quantum Mechanics. Entropy 2019, 21, 943.

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