The former leads to a ”microscopic” cosmological model with Hubble expansion. Due to interaction of a Higgs-like cosmological potential, the original time-space symmetry is spontaneously broken, inducing a strong time-like curvature and a weak space-like deviation curve. In the result, the wave-like solution leads to Klein-Gordon-Fock equation which would serve an explicit approach to the problem of consistency between quantum mechanics and general relativity. | Communications in Physics, Vol. 26, No. 2 (2016), pp. 181-192 DOI: KLEIN-GORDON-FOCK EQUATION FROM EINSTEIN GENERAL RELATIVITY VO VAN THUAN† Vietnam Atomic Energy Institute (VINATOM), 59 Ly Thuong Kiet street, Hoan Kiem district, Hanoi, Vietnam † E-mail: vvthuan@ Received 10 March 2016 Accepted for publication 10 September 2016 Abstract. A time-space symmetry based cylindrical model of geometrical dynamics was proposed. Accordingly, the solution of Einstein gravitational equation in vacuum has a duality: an exponential solution and a wave-like one. The former leads to a ”microscopic” cosmological model with Hubble expansion. Due to interaction of a Higgs-like cosmological potential, the original time-space symmetry is spontaneously broken, inducing a strong time-like curvature and a weak space-like deviation curve. In the result, the wave-like solution leads to Klein-Gordon-Fock equation which would serve an explicit approach to the problem of consistency between quantum mechanics and general relativity. Keywords: time-space symmetry, general relativity, microscopic cosmological model, wave-like solution, Klein-Gordon-Fock equation, physical reality, wave-particle duality. Classification numbers: ; ; . I. INTRODUCTION Searching for the consistency between quantum mechanics and general relativity is the most important and long-standing issue of physics. Kaluza and Klein [1, 2] were pioneers to propose a space-like extradimension (ED) which is compacted as a micro circle in relation to general relativity. For the semi-classical approach to quantum mechanics introduced by de Broglie and Bohm [3, 4] the hidden parameters are somehow reminiscent of EDs. However, the evidence for violation of Bell inequalities [5, 6] abandoned the models with local hidden parameters, leaving the door still open to non-local hidden variables. High dimensional superstring models have been developed following Kaluza-Klein
