Information Measures for Inferring Quantum Mechanics

Abstract

Starting from the Hamilton-Jacobi equation describing a classical ensemble, one may infer a quantum dynamics using the principle of maximum uncertainty. That procedure requires an appropriate measure of uncertainty: Such a measure is constructed here from physically motivated constraints. It leads to a unique single parameter extension of the classical dynamics that is equivalent to the usual linear quantum mechanics.

arXiv comment11 pages; Further refinements: Final Journal version

References in corpus (3)

• Schrodinger equation from an exact uncertainty principle
• Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schrödinger Equations
• An Information-Theoretic Link Between Spacetime Symmetries and Quantum Linearity

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• Objective uncertainty relation with classical background in a statistical model
• Jensen-Shannon Divergence and Non-linear Quantum Dynamics
• Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable
• A Physical Axiomatic Approach to Schrodinger's Equation
• Variational Principle for Stochastic Mechanics Based on Information Measures
• Information and Particle Physics
• The large nonlinearity scale limit of an information-theoretically motivated nonlinear Schrodinger equation
• Nonlinear Quantum Cosmology
• Understanding quantization: a hidden variable model
• Information-theoretic corrections to black hole area quantisation?