Petals, Tubes and Rings: The Structure of the Four-Direction Orbit

The electron's orbit runs through four spatial directions. Its path has an exact closed form: the product of two turning directions, one turning once while the other turns L times. In one plane of view that path is a rose of petals, in another it is a set of nested rings, and along a third it is a tube. These are views of a single object. For every whole number L from 2 to 8 the orbit is stable. Its petal tips are the vertices of a regular polygon inscribed in a circle, and its crossings of the axis in the end-on view lie exactly at the heights of those vertices, which is the construction chemists know as the Frost circle. Under the proton's own force the electron has stable orbits that fill a hollow tube and show concentric rings when time averaged. There the ratio L is set by the radius, by an exact formula, and at the width that places Lyman-γ at one Bohr radius, the orbit of that radius has L = 2.998, very nearly three cycles through the fourth direction per revolution. The proton's down quark singles out that proton's fourth direction, so an orbit can stand at a right angle to the petal orbit.