The Entropic Dynamics approach to Quantum Mechanics

Abstract

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 the 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.

49 pages. Added a section comparing Entropic Dynamics with Quantum Bayesianism. Added references and corrected typos

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Cited by in corpus (10)

• Entropy, Information, and the Updating of Probabilities
• Entropic dynamics on Gibbs statistical manifolds
• Approach to Data Science with Multiscale Information Theory
• Quantum Mechanics Based on an Extended Least Action Principle and Information Metrics of Vacuum Fluctuations
• Quantum Scalar Field Theory Based on the Extended Least Action Principle
• Entropic Density Functional Theory
• The Entropic Dynamics of Spin
• Spin Theory Based on the Extended Least Action Principle and Information Metrics: Quantization, Entanglement, and Bell Test With Time Delay
• Alternative Framework to Quantize Fermionic Fields
• The Entropic Dynamics of Relativistic Quantum Fields in Curved Space-time