Momentum and Uncertainty Relations in the Entropic Approach to Quantum Theory

TL;DR

This paper explores the entropic approach to quantum theory, showing that momentum is a statistical property of probability distributions rather than an intrinsic particle property, and derives related uncertainty relations.

Contribution

It introduces four notions of momentum within the entropic dynamics framework and establishes their relations and uncertainty principles, highlighting the statistical nature of momentum.

Findings

Momentum is a statistical concept in ED.

Derived relations among four different momentum notions.

Established uncertainty relations for these momentum concepts.

Abstract

In the Entropic Dynamics (ED) approach to quantum theory the particles have well-defined positions but since they follow non differentiable Brownian trajectories they cannot be assigned an instantaneous momentum. Nevertheless, four different notions of momentum can be usefully introduced. We derive relations among them and the corresponding uncertainty relations. The main conclusion is that momentum is a statistical concept: in ED the momenta are not properties of the particles; they are attributes of the probability distributions.