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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.|ψ|. 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.
Highlights
General Relativity, a form of spacetime geometrization, is derived by utilizing two fundamental conditions: the equivalence of inertial and gravitational masses, and the principle of least action [1]
It is true that the equivalence of inertial and gravitational masses corresponds to imposing the covariance of the classical equations of motion in curved spacetime In this sense, General Relativity can be conceptualized as the geometrization of classical spacetime arising from the principle of least action, together with the classical
This essentially means that spacetime geometry is influenced by the energy of the quantum potential, which has no equivalent in classical physics
Summary
General Relativity, a form of spacetime geometrization, is derived by utilizing two fundamental conditions: the equivalence of inertial and gravitational masses, and the principle of least action [1]. Analogously to the general relativity procedure, by imposing the covariance of (3) in curved spacetime we can utilize the minimum action principle to obtain the geometry of spacetime subject to the quantum physics This approach is based on the fact that the equivalence of gravitational and inertial mass in classical General Relativity can be replaced by the condition of covariance of classical equations of motion in curved spacetime. In the case of macroscopic matter or antimatter that appears macroscopically spinless regardless of the spin of its elementary constituents, the non-relativistic limit of the KGE (2) can be applied to bodies with nonzero rest mass in the low-velocity regime In this context, the wavefunction (2) can be used in (17) and (12). Performing the (non-relativistic) weak gravity limit of (12) with quantum mechanical mass densities || m+||2 and || m−||2 we obtain the Newtonian forces for both matter and antimatter states.
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