Toroids, Vortices, Knots, Topology and Quanta
Year: 2010 Pages: 6
What causes matter to bind together into the clusters we call particles? At every location within every stable particle there must exist a balance between the natural repulsion of like elements and the attraction due to parallel motions. For continuums of matter, every moving element within a structure must be immediately replaced by another, creating a circuit. Now if circuits form the basis for the structure of matter itself, then analysis of the most fundamental form of circuit, the toroid, is a worthy subject. I explore many interesting features of toroidal coordinates, the relationship toroids have with vortices, and the intimate connection between toroid knots and topology. Real stable 3D particles must contain circulations both around the toroid of radius R and the cross-section of radius r, so that for every m times an element circulates around the toroid, it circulates n times around the torus. This integer relationship changes instantly when the relative phases exceed 360. The quantum jump we observe at this point equates to the \'strobe effect\', seen in a Las Vegas roulette wheel, wagon wheels in old westerns, and Lissajous patterns. Backed by a physical demonstration, I argue that these quantum jumps correspond precisely with the absorption and emission of photons. Finally I examine the increasingly popular Rodin coil, as a toroid case study.