SUMMARY
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 6D-dimensional gravitational equation leads to bi-geodesic description in an extended timespace symmetry which ?ts 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.