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.

arXiv comment49 pages. Added a section comparing Entropic Dynamics with Quantum Bayesianism. Added references and corrected typos

References in corpus (43)

• Decoherence, the measurement problem, and interpretations of quantum mechanics
• In defense of the epistemic view of quantum states: a toy theory
• Informational derivation of Quantum Theory
• Quantum probabilities as Bayesian probabilities
• Unknown Quantum States: The Quantum de Finetti Representation
• An Introduction to QBism with an Application to the Locality of Quantum Mechanics
• Quantum-Bayesian Coherence: The No-Nonsense Version
• Is the quantum state real? An extended review of $\psi$-ontology theorems
• Quasi-quantization: classical statistical theories with an epistemic restriction
• The completeness of quantum theory for predicting measurement outcomes
• Quantum from principles
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Quantum Bayes rule
• Linear dynamics of quantum-classical hybrids
• Reformulating and Reconstructing Quantum Theory
• Statistical Geometry in Quantum Mechanics
• Origin of Complex Quantum Amplitudes and Feynman's Rules
• The Vacuum Fluctuation Theorem: Exact Schroedinger Equation via Nonequilibrium Thermodynamics
• Entropic Dynamics, Time and Quantum Theory
• Entropic Dynamics
• Consistency, Amplitudes and Probabilities in Quantum Theory
• Imprints of the Quantum World in Classical Mechanics
• Could quantum mechanics be an approximation to another theory?
• From Information Geometry to Quantum Theory
• Entanglement purification of unknown quantum states
• Physics Without Physics: The Power of Information-theoretical Principles
• Entropic Dynamics and the Quantum Measurement Problem
• The Quantum as an Emergent System
• Entropic Quantization of Scalar Fields
• Consistency and Linearity in Quantum Theory
• Entropic Dynamics: Reconstructing Quantum Field Theory in Curved Space-time
• Information geometry, dynamics and discrete quantum mechanics
• Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class
• Quantum theory from the geometry of evolving probabilities
• Insufficient reason and entropy in quantum theory
• Entropic Dynamics: from Entropy and Information Geometry to Hamiltonians and Quantum Mechanics
• Quantum Measurement and Weak Values in Entropic Dynamics
• Momentum and Uncertainty Relations in the Entropic Approach to Quantum Theory
• Quantum mechanics from two physical postulates
• Entropic Dynamics: The Schroedinger equation and its Bohmian limit
• The Classical Limit of Entropic Quantum Dynamics
• The Entropic Dynamics of Spin
• The Entropic Dynamics Approach to the Paradigmatic Quantum Mechanical Phenomena

Cited by in corpus (11)

• 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 Design of Global Correlation Quantifiers and Continuous Notions of Statistical Sufficiency
• 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
• The Entropic Dynamics of Relativistic Quantum Fields in Curved Space-time
• Alternative Framework to Quantize Fermionic Fields