Bohmian Zitterbewegung

TL;DR

This paper introduces a novel Bohmian quantum-relativistic model that generalizes Zitterbewegung from the Klein-Gordon equation, incorporating a new time parameter and revising the uncertainty principle.

Contribution

It presents a new Bohmian framework where quantum uncertainties arise from an independent time parameter, distinct from the observable motion, and extends Zitterbewegung to a relativistic context.

Findings

Zitterbewegung emerges from the generalized model.

Quantum potential influences only the new time variable.

Relativistic revision of the uncertainty principle is proposed.

Abstract

A new Bohmian quantum-relativistic model, in which from the Klein-Gordon equation a generalization of the standard Zitterbewegung arises, is explored. It is obtained by introducing a new independent time parameter, whose relative motions are not directly observable but cause the quantum uncertainties of the observables. Unlike Bohm's original theory, the quantum potential does not affect the observable motion, as for a normal external potential, but it only determines that one relative to the new time variable, of which the Zitterbewegung of a free particle is an example. The model also involves a relativistic revision of the uncertainty principle.