Entropic Dynamics, Time and Quantum Theory

TL;DR

This paper derives quantum mechanics using maximum entropy principles, introducing entropic time and variables, providing a statistical interpretation of wave function components, and extending the model to include electromagnetic fields.

Contribution

It presents a novel derivation of quantum theory from entropic principles without classical action assumptions, linking entropy to quantum dynamics.

Findings

Quantum mechanics derived from maximum entropy principles.

Entropic time naturally includes an arrow of time.

Wave function magnitude and phase have statistical interpretations.

Abstract

Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the particles of interest x there exist extra variables y whose entropy S(x) depends on x. The Schr\"odinger equation follows from their coupled dynamics: the entropy S(x) drives the dynamics of the particles x while they in their turn determine the evolution of S(x). In this "entropic dynamics" time is introduced as a device to keep track of change. A welcome feature of such an entropic time is that it naturally incorporates an arrow of time. Both the magnitude and the phase of the wave function are given statistical interpretations: the magnitude gives the distribution of x in agreement with the usual Born rule and the phase carries information about the entropy S(x) of the extra variables. Extending the model to include external electromagnetic fields yields further insight into the nature of the quantum phase.