Bohmian trajectories for Kerr-Newman particles in complex space-time

TL;DR

This paper explores Bohmian trajectories for Kerr-Newman particles in complex space-time using a covariant Stueckelberg theory, revealing multi-valued trajectories, non-radiating extended particles, and potential links to emergent quantum mechanics.

Contribution

It introduces a novel approach combining Kerr-Newman particles with Bohmian mechanics via complex space-time and generalized analytic continuation, leading to new insights into particle behavior.

Findings

Particles are extended and do not radiate.

Multiple Bohmian trajectories arise from GAN.

Particles can have finite electrostatic self energy.

Abstract

Complexified Lienard-Wiechert potentials simplify the mathematics of Kerr-Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known. A covariant theory due to Stueckelberg is used. This paper deviates from the traditional Bohmian interpretation of quantum mechanics since the electromagnetic interactions of Kerr- Newman particles are dictated by general relativity. A Gaussian wave function is used to produce the Bohmian trajectories, which are found to be multi-valued. A generalized analytic continuation (GAN) is introduced which leads to an infinite number of trajectories. These include the entire set of Bohmian trajectories. This leads to multiple retarded times which come into play in complex space-time. If one weights these trajectories by their natural Bohmian weighting factors, then it is found that the particles do not radiate, that they are extended, and that they can have a finite electrostatic self energy, thus avoiding the usual divergence of the charged point particle. This effort does not in any way criticize or downplay the traditional Bohmian interpretation which does not assume the standard electromagnetic coupling to charged particles, but it suggests that a hybridization of Kerr-Newman particle theory with Bohmian mechanics might lead to interesting new physics, and maybe even the possibility of emergent quantum mechanics.