From Entropic Dynamics to Quantum Theory

TL;DR

This paper derives non-relativistic quantum theory from an information-theoretic framework using entropic dynamics, linking statistical geometry with quantum evolution and explaining core quantum features statistically.

Contribution

It introduces a novel derivation of quantum mechanics from entropic inference principles, emphasizing the role of statistical manifolds and geometry in quantum dynamics.

Findings

Derives Schrödinger equation from energy conservation in entropic dynamics

Explains the wave function phase as a statistical feature

Provides a quantum analogue of the gravitational equivalence principle

Abstract

Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration space and the corresponding probability distributions constitute a statistical manifold. The dynamics follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. A welcome feature is that the entropic dynamics notion of time incorporates a natural distinction between past and future. The statistical manifold is assumed to be a dynamical entity: its curved and evolving geometry determines the evolution of the particles which, in their turn, react back and determine the evolution of the geometry. Imposing that the dynamics conserve energy leads to the Schroedinger equation and to a natural explanation of its linearity, its unitarity, and of the role of complex numbers. The phase of the wave function is explained as a feature of purely statistical origin. There is a quantum analogue to the gravitational equivalence principle.