Derivation of Klein-Gordon-Fock equation from General relativity in a time-space symmetrical model

TL;DR

This paper demonstrates that Einstein's gravitational equations in a symmetrical time-space model can lead to the Klein-Gordon-Fock equations, bridging quantum mechanics and general relativity through a bi-cylindrical geometrical framework.

Contribution

It introduces a bi-cylindrical geometrical model where Einstein's equations produce Klein-Gordon-Fock equations, suggesting a new approach to unify quantum mechanics with general relativity.

Findings

Einstein equations lead to bi-geodesic descriptions in symmetrical time-space.

Geodesic solutions are mathematically equivalent to Klein-Gordon-Fock equations.

The model provides a potential pathway for quantum-gravity unification.

Abstract

Following a bi-cylindrical model of geometrical dynamics, in the present study we show that Einstein gravitational equation leads to bi-geodesic description in an extended symmetrical time-space which fit Hubble expansion in a "microscopic" cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, as the squared Dirac equations of leptons and as a sub-solution with pseudo-axion. This result would serve an explicit approach to consistency between quantum mechanics and general relativity.