Derivation of a new multiscale model: I. Derivation of the model for the atomic, molecular and nano material scales

In the present work, a generalized form for the energy equation is derived following the concepts of a new theory called the time of events theory. This theory assumes a dynamic space-time in addition to the static space-time assumed explicitly in the special theory of relativity and implicitly in quantum mechanics. Assuming two spacetimes necessitates the complex space-time. Therefore, the energy equations are rederived assuming a real space-time, represented by the dynamic space-time, and an imaginary space-time represented by the static space-time. An angle θ is assumed between the particle’s world line and the real axis. The θ value depends on the particle’s mass and directly proportional to it. The heavy particles have larger θ , therefore have larger imaginary component, and the reverse is true for the light particles. The energy equations in the complex space-time were written in terms of complex velocities’ squares, each equation is written independently for each particle. Then, the equations are combined to give the final equation for the assembly that is composed of atoms, ions, or molecules. Applying this procedure for the hydrogen atom led to an equation similar to the Schrodinger equation. Based on the above procedure, a general equation for more complicated systems (atoms or molecules) is derived. We find that there is a difference in the leading factors for the electron-electron term from the traditional forms of quantum mechanics. For the case of ions and non-neutral molecules, a different equation is predicted by the current work, due to differences between electrons and protons numbers.