Exact form of the generalized Lorentz force in Fock's nonlinear relativity

TL;DR

This paper derives the exact form of the Lorentz force within Fock's nonlinear relativity, revealing a gravitational-type force component that depends on universe radius or Planck energy, highlighting electromagnetism-gravity analogies.

Contribution

It provides the complete, exact Lorentz force law in Fock's nonlinear relativity, including a novel gravitational-type component absent in previous formulations.

Findings

Identifies a gravitational-type Lorentz force in FNLR

Shows the force depends on universe radius or Planck energy

Force is independent of electromagnetic fields

Abstract

This work completes a serie of two papers devoted to the extension of the fundamental laws of electrodynamics in the context of Fock's nonlinear relativity (FNLR). Indeed, after having established in the previous study the exact generalizations of both Maxwell's equations and Dirac magnetic monopole, we present here the remaining exact Lorentz force. As in k-Minkowski spacetime, two different nature contributions appear in the corresponding equation of motion where the new effect is interpreted as the gravitational-type Lorentz force. This common point separately induced by the radius of the universe in our case or Planck energy in other works, reinforces once more the analogy between electromagnetism and gravity in two different scientific approaches. As a relative difference, it is very important to highlight that more homogeneity characterizes our results where each effect is exclusively generated by mass or charge but not both at the same time. Even more, the new effect emerges as the result of the triple effect of R-deformation, mass and the square of velocities but completely independent of electromagnetic field.