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

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.

10 pages, LaTeX; typos revised, section 3 rearranged into sections 3 and 4, arguments added in section 4, results unchanged

References in corpus (2)

• From Microscopic Gravitational Waves to the Quantum Indeterminism
• Time-space symmetry as a solution to the mass hierarchy of charged lepton generations

Cited by in corpus (1)

• High-order corrections to tauon mass in a microscopic cosmological model