Trading drift and fluctuations in entropic dynamics: quantum dynamics as an emergent universality class

TL;DR

This paper demonstrates that various entropic dynamics models, differing in microscopic fluctuations, all lead to the same emergent quantum behavior, unifying different quantum interpretations within a universality class.

Contribution

It introduces a family of entropic dynamics models that vary microscopic fluctuations but share the same macroscopic quantum behavior, including a limit resembling Bohmian mechanics.

Findings

Different ED models converge to the same Schrödinger dynamics.

Suppression of fluctuations yields a Bohmian-like evolution.

Heisenberg uncertainty remains invariant across models.

Abstract

Entropic Dynamics (ED) is a framework that allows the formulation of dynamical theories as an application of entropic methods of inference. In the generic application of ED to derive the Schroedinger equation for N particles the dynamics is a non-dissipative diffusion in which the system follows a "Brownian" trajectory with fluctuations superposed on a smooth drift. We show that there is a family of ED models that differ at the "microscopic" or sub-quantum level in that one can enhance or suppress the fluctuations relative to the drift. Nevertheless, members of this family belong to the same universality class in that they all lead to the same emergent Schroedinger behavior at the "macroscopic" or quantum level. The model in which fluctuations are totally suppressed is of particular interest: the system evolves along the smooth lines of probability flow. Thus ED includes the Bohmian or causal form of quantum mechanics as a special limiting case. We briefly explore a different universality class -- a non-dissipative dynamics with microscopic fluctuations but no quantum potential. The Bohmian limit of these hybrid models is equivalent to classical mechanics. Finally we show that the Heisenberg uncertainty relation is unaffected either by enhancing or suppressing microscopic fluctuations or by switching off the quantum potential.