Pseudo-Gravity at Quantum Scales: Role of Quantum Potentials in Spacetime Geometry

The principle of equivalence upon which general relativity is based was extended to the case of quantum potential-driven electrodynamics. It was shown that accelerations can be defined as the gradient of the quantum potential and these accelerations can be locally erased by geometrization of spacetime using a general relativity-based approach. The paper develops spacetime metrics based on the quantum potential for the case of the ground state of the hydrogen atom and show that geodesic accelerations and forces calculated from this metric matched local accelerations and electromagnetic forces that the electron is subjected to. Further, time was found to be contracted, and space expanded, and mass increased, from the perspective of a remote observer, in the presence of the quantum potential. Spacetime perturbations were significant when electrons were confined into a volume having a radius of 10^-15 m. Calculations suggested opportunities for experimental validation of predicted spacetime curvatures in the atom. The spacetime transformation at quantum scales was found to be consistent with the uncertainty principle. It was possible to show that a modified Einstein equation asymptotically approached the electrostatic Poisson equation in the Newtonian limit.