Attractive Heaviside-Maxwellian (Vector) Gravity from Special Relativity and Quantum Field Theory

Abstract: Adopting two independent approaches (a) Lorentz-invariance of physical laws and (b) local phase invariance of quantum field theory applied to the Dirac Lagrangian for massive electrically neutral Dirac particles, we rediscovered the fundamental field equations of Heaviside Gravity (HG) of 1893 and Maxwellian Gravity (MG), which look different from each other due to a sign difference in some terms of their respective field equations. However, they are shown to represent two mathematical representations of a single physical theory of vector gravity that we name here as Heaviside-Maxwellian Gravity (HMG), in which the speed of gravitational waves in vacuum is uniquely found to be equal to the speed of light in vacuum. We also corrected a sign error in Heaviside's speculative gravitational analogue of the Lorentz force law. This spin-1 HMG is shown to produce attractive force between like masses under static condition, contrary to the prevalent view of field theorists. Galileo's law of universality of free fall is a consequence of HMG, without any initial assumption of the equality of gravitational mass with velocity-dependent mass. We also note a new set of Lorentz-Maxwell's equations having the same physical effects as the standard set - a byproduct of our present study.