As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles. The 4D-embedded dual solutions of the higher dimensional gravitational equation could shed light on origin of physical reality in quantum mechanics, which is to compare with the achievements of the 5D-STM theory. | Communications in Physics, Vol. 26, No. 3 (2016), pp. 209-220 DOI: THE MODERN INDUCED MATTER APPROACH OF GENERAL RELATIVITY FOR QUANTUM MECHANICS VO VAN THUAN† Vietnam Atomic Energy Institute (VINATOM), 59 Ly Thuong Kiet street, Hoan Kiem district, Hanoi, Vietnam NGUYEN THI KIM THOA Physics Faculty, Hanoi National University of Education, 136 Xuan Thuy, Dich Vong Hau, Cau Giay, Hanoi, Vietnam † E-mail: vvthuan@ Received 05 September 2016 Accepted for publication 25 January 2017 Abstract. Wesson and his co-workers developed so-called space-time-matter theory (5D-STM) as a generalization of Kaluza-Klein theory, where the extra-dimension in the 5D space-time is no more compacted, but keeping extended in a macroscopic scale to describe the properties of matter in 4D physics. In a trend of 5D-STM approach (or the induced-matter theory), following a bi-cylindrical model of geometrical dynamics, a recent study has shown that the higher 6Ddimensional gravitational equation leads to bi-geodesic description in an extended time-space symmetry which fits 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. The 4D-embedded dual solutions of the higher dimensional gravitational equation could shed light on origin of physical reality in quantum mechanics, which is to compare with the achievements of the 5D-STM theory. Keywords: time-space symmetry, general relativity, microscopic cosmological model, wave-like solution, Klein-Gordon-Fock equation, physical reality, wave-particle duality. Classification numbers: ; ; . c 2016 Vietnam Academy of Science and Technology 210 THE MODERN INDUCED MATTER APPROACH OF GENERAL RELATIVITY FOR QUANTUM MECHANICS I. INTRODUCTION Following 5D Kaluza-Klein geometrical dynamical theory with extradimension (ED) [1,2], there are two
