Objective uncertainty relation with classical background in a statistical model

TL;DR

This paper demonstrates that within a statistical model based on Hamilton-Jacobi theory, the fluctuations of trajectories satisfy an objective reciprocal uncertainty relation, which implies the standard quantum uncertainty principle.

Contribution

It introduces an objective uncertainty relation derived from a classical statistical model that reproduces quantum uncertainty without observer dependence.

Findings

Fluctuations of trajectories satisfy a reciprocal uncertainty relation.

The relation is objective and independent of observation.

It implies the standard quantum mechanical uncertainty relation.

Abstract

We show within a statistical model of quantization reported in the previous work based on Hamilton-Jacobi theory with a random constraint that the statistics of fluctuations of the actual trajectories around the classical trajectories in velocity and position spaces satisfy a reciprocal uncertainty relation. The relation is objective (observation independent) and implies the standard quantum mechanical uncertainty relation.