Consequences of a Two-Time Relativistic Bohmian Model

TL;DR

This paper explores a novel relativistic Bohmian model introducing an independent time parameter, revealing new insights into quantum uncertainties, particle motion, and the physical reality of Feynman paths, with implications for the uncertainty principle.

Contribution

It proposes a new relativistic Bohmian framework with an independent time variable, differing from traditional theories by affecting observable motions indirectly.

Findings

Zitterbewegung as a key example of hidden motions

A general law for Zitterbewegung derived

Relativistic revision of the uncertainty principle proposed

Abstract

Effects of a Bohmian type quantum-relativistic theory are explored. The model is obtained by introducing a new and independent time parameter whose relative motions are not directly observable and cause the quantum uncertainties of the physical observables. Unlike the usual de Broglie-Bohm theories, the Quantum Potential does not affect directly the observable motion but determines the one that is relative to the new time variable. It turns out that the Zitterbewegung of a free particle, of which a more general law is obtained, is the key example of these hidden motions and, through it, it seems possible to give physical reality to the Feynman's paths. A relativistic revision of the uncertainty principle also derives from the theory.