Stereographical Simulation of the Propagation of the Atomic Orbitals f-3 & f+3 in Spacetime as a Vibrational Wave Over an Ether from Point A to Point B in the “Eternal†Expansion of the Universe

This work is based on a previous published hypothesis which proposed that the solid matter of the universe can be represented as a vibrational wave of energy propagating over an ether or matrix through a mechanism that scrambles the degree of duality in matter: x% localized (solid), y% delocalized (wave). The main purpose of this paper is to present a two dimensional approximation of the three dimensional structure of the shape of the energy distribution of an atomic orbital to propose a mechanism through which the orbital can be transported as a vibration from a point A to point B in the matrix. This process requires cycles or oscillations of mounting-dismounting-remounting in which what travels from point A to point B is the energy forming the orbital and not the solid matter that it can form. The atomic seven dimensional f orbital of hydrogen-like atoms is used as a model to show an analogy to the transformations that it can be submitted to when transported over the matrix. The eight lobes or petals of the f-3 and f+3 sub-orbitals that are allowed by quantum rules to form solidity in matter are approximated with the polar equation r=sin(100*θ). Successive multiplication of the angle θ by the values 101 to 139 generates harmonic structures that here are interpreted as shapes of the orbitals that are not allowed by quantum rules to form solid objects. The initial shape approximated by r=sin(100*θ) is re-generated by r=sin(140*θ). This result suggests that the transportation of the orbitals from point A (r=sin(100*θ)) to point B (r=sin(140*θ) may involve a transition state of forty changes in the structure that cannot form solid matter. Mathematical study of the associated dr/dθ derivatives of each function reveals an underlying order of changes in symmetry and the appearance of a gene-like structure of the mechanism that includes tandem repeats and palindrome sequences. Further discussion considers interpreting the transportation mechanism through templates controlled by quantum coherence and decoherence, and future areas of study.