Newtonian Gravity of Antimatter and Gravitational Needs of Field Quantization: A Path to Renormalizable Gravity

Abstract By incorporating quantum mechanics into gravitational theory through the so-called spacetime geometrization procedure that consists in applying the principle of least action alongside the covariance of quantum mechanical motion equations, we present a model that describes the gravitational behavior of antimatter whose existence is fundamentally rooted in quantum mechanics. The gravity produced by an antimatter macroscopic body, described by continuous quantum mechanical field, shows that it produces attractive Newtonian potential on macroscopic scale. On a microscopic scale, where we cannot use the point-like mass approximation, the work shows that the Newtonian gravity includes an additional term that is inversely proportional to source mass and depending by the shape of the quantum mass density distributions. $$|\psi |$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>ψ</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> </mml:math> . The divergence of gravitational energy for infinitesimal masses, in order to yield finite physical solutions, requires that elementary particles possess a discrete mass spectrum and that the quantization of their fields emerges as a necessary condition for the realization of the physical universe. Furthermore, the quantum mechanical contribution, induced by the energy of the quantum potential on spacetime geometry, which diverges for small masses, can possibly compensate for the divergence in quantum gravity where this contribution is not considered.