Consequences of a two-time relativistic Bohmian model

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 quantum uncertainties of the physical observables. Unlike the usual de Broglie–Bohm theories, the Quantum Potential does not directly affect 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 is also derived from the theory.