A New Set of Maxwell-Lorentz Equations and Rediscovery of Heaviside-Maxwellian (Vector) Gravity from Quantum Field Theory

TL;DR

This paper derives a new set of Maxwell-Lorentz equations and revisits Heaviside-Maxwellian gravity from quantum field theory, revealing novel insights into gravitoelectromagnetism and gravitational interactions.

Contribution

It introduces a new formulation of Maxwell-Lorentz equations and rediscoveries of Heaviside-Maxwellian gravity from Dirac field theory, highlighting the quantum foundation of gravitoelectromagnetism.

Findings

New Maxwell-Lorentz equations derived

Two sets of gravito-Maxwell-Lorentz equations identified

Gravitational waves carry positive energy and momentum

Abstract

We show that if we start with the free Dirac Lagrangian, and demand local phase invariance, assuming the total phase coming from two independent contributions associated with the charge and mass degrees of freedom of charged Dirac particles, then we are forced to introduce two massless independent vector fields for charged Dirac particles that generate all of electrodynamics and gravitodynamics of Heaviside's Gravity of 1893 or Maxwellian Gravity and specify the charge and mass currents produced by charged Dirac particles. From this approach we found: (1) a new set of Maxwell-Lorentz equations, (2) two equivalent sets of gravito-Maxwell-Lorentz equations (3) a gravitational correction to the standard Lagrangian of electrodynamics, which, for a neutral massive Dirac particle, reduces to the Lagrangian for gravitodynamics, (4) attractive interaction between two static like masses, contrary to the prevalent view of many field theorists and (5) gravitational waves emanating from the collapsing process of self gravitating systems carry positive energy and momentum in the spirit of Maxwell's electromagnetic theory despite the fact that the intrinsic energy of static gravitoelectromagnetic fields is negative as dictated by Newton's gravitational law and its time-dependent extensions to Heaviside-Maxwellian Gravity (HMG). Fundamental conceptual issues in linearized Einstein's Gravity are also discussed.