The Electron Quantum Orbit

A speculative plot of the quantum orbit of the electron, based on the paper "Electron Geometry". The paper models the electron as a physical quantum of radius 2.035E-19 meter, traversing a selfintersecting toroidal orbit. FIG 1 is a 2D representation of the cross section of a self-intersecting toroidal path. Gamma called the major radius, is the radius from the center of the toroidal path to the center of the circle that forms the toroidal path. Beta called the minor radius, is the radius of the circle that forms the toroidal path. The self-intersection is greatly exaggerated to illustrate the geometry. The electron self-intersection is very small - it is determined by the square of the fine-structure constant alpha. The Compton radius Rc is one leg of a right triangle and is equal to the square root of - . The Compton radius Rc is equal to alpha times the Bohr radius Rb. As shown in the figure, Rb is equal to lengths + . The electron classical radius is equal to alpha times the Compton radius. It is called the inner radius here to give it a unique subscript Ri. As shown in the figure, Ri is equal to lengths - . The inner radius is the minimum radius of the self-intersection. Angle a is used to define quantum movement about the circle, in what is called the poloidal direction. This constitutes one speed component of the quantum. Angle a will be used in the defining formula for the toroidal path. When forming a toroidal geometry, the circle is rotated about the center of the toroidal path, in what is called the toroidal direction. A second quantum speed component will be defined at the major radius . Rb b + g b g b - g Ri b g b FIG 1 r a Rc Done with Maple software: and are values for minor radius and major radius of the electron orbit in meters, from the paper "Electron Geometry". All unit are in base unit of meters, grams and seconds: meter, electron beta, minor toroidal radius meter, electron gamma, major toroidal radius meter, electron Compton radius = meter, Bohr radius The fine structure constant alpha Planck's constant in base units m,g,s Speed of light m/s Electron mass in grams meter, radius of fundamental quantum To plot the quantum orbit, we will speculate as to the components of quantum speed. To arrive at speed Sc for the fundamental quantum at Compton radius Rc, the electron mass is expressed as the equivalent mass of a photon of Compton wavelength and energy hf where h is Planck's constant and f is frequency: m = = m is electron mass, h is Planck's constant, f is frequency = equals the speed of light The speed Sc is the speed of light at radius Rc, the speed component along the circle of radius known as the poloidal direction. At the Compton radius, the speed component in the toroidal direction is zero. We will speculate that the moving quantum exhibits the electron mass at any given radius. For the Bohr radius: = = = This shows the quantum speed at the Bohr radius to be about 137.036 times the speed of light. This may seem unlikely, but it may explain why electrons are impervious to most external forces. The quantum speed at the Bohr radius has two components. One is the speed of light c along the poloidal direction. The other is the speed along the toroidal direction. We will speculate that they combine as the square root of the sum of the squares to result in Sb. The toroidal component then will be the square root of: = = = Following is a plot based on these numbers. The quantum radius is not included in the calculations as it isn't noticable in the plot. here to =1 for plotting. Speed c is normalized here to c=1 for plotting. = 0.999894 gamma scaled for beta equal to 1 Index i sets beta path speed, poloidal, c normalized to 1.0 Index j sets gamma path speed, toroidal, c normalized to 1.0 Torus formula R: Plot definition: For the plot, poloidal angle a runs from 0 thru 2. The toroidal angle is b in the Torus formula. The toroidal angle is angle a multiplied by index j, the speed ratio determined above. Tilted view: Length of vector R, to check radii, radii normalized to beta equal to one. Inner Radius: = 0.000106 = 0.000106 Bohr Radius: = 1.999894 = 1.999894