A unified gravitational and quantum-mechanical space-time structure through a unified origin of inertial and gravitational masses and a discussion of the foundations of special relativity

Abstract

The initial aim is to unify the physics of largest and smallest scales,i.e. gravitation and quantum mechanics. Since inertial mass plays an important role in quantum mechanics and gravitational mass in gravitation, by eliminating the mass term from both theories, we can connect the two theories. This elimination procedure is a thorough discussion of the definition of flatness (hence curvature) in special relativity. The result indicates that actually all electromagnetic and matter waves can be treated on the same footing in a flat 4+1 spacetime. With its time scale all waves have the same velocity (light velocity) and are massless in the 4 + 1 space-time, but, projected on a 3 +1 Lorentz space-time with its time scale, these waves gain mass and behave faster than light. After superposition, they form wave packets and possess inertia. Since we expect this elimination as a restatement of the equivalence principle, the very same act of projection that gives rise to inertia (with inertial mass) should give rise to gravitation (with an equal gravitational mass) as well.