Discovery of Four Space Dimensions in a Sphere for Electronic Orbitals in a Neon Shell

Abstract

For the first time we discover four space dimensions in a sphere, namely two periphery points, two semicircular arcs, two hemispherical surfaces, and two spherical solids. When these four geometric elements are compared with electronic orbitals in a neon shell, we draw a conclusion that while 2s orbitals are spherical, three types of 2p orbitals in the X, Y, and Z directions are different in the number of space dimensions. These anisotropic 2p orbitals prompt us to modify Schrödinger’s equation to reflect these fine space gradients. Within the atomic sphere, electrons are transforming from one dimension to another following the rule of calculus implemented by circular functions rather than position movement. An electron may exist in the physical shape of a point, an arc, a surface, or a solid. Eight electrons in the neon shell are undergoing various harmonic oscillations that form a continuous octet cycle. This motion feature is derived from a four-dimensional space harmonic oscillation equation coupled with a one-dimensional time harmonic oscillation equation in synthesis of the modified Schrödinger’s equation. Substantial amount of evidence can be found in organic chemistry where a carbon atom has an anisotropic electron configuration of 2s2px2py2pz. By furnishing a fresh and fundamental spacetime worldview, the quaternity theory may change the direction of quantum mechanics from discrete linear algebra toward continuous dynamic calculus in the future.