The Four-Direction Orbit: Width, Tilt, Molecules and the Hidden Rotation

The electron orbits the nucleus in four spatial directions, and the light of a line has the frequency of the orbit's motion in the fourth direction. This paper reports what that orbit does when its conditions change. A nucleus of finite width gives the hydrogen line Lyman-γ at one Bohr radius to 0.13%. The tilt of the orbit into the fourth direction moves the line by only 1.4% between 5° and 85°. The uniform background couples to the electron's orientation through a plane inside our own directions. Around two nuclei the same orbit gives the colours of the four diatomic halogens with one constant, and around a chain of nuclei it moves the line from the ultraviolet toward the visible as the chain grows. A second electron rotating in a hidden plane exchanges energy with the orbit at two sharp resonances and does not lock to it. The paper also records where the orbit does not yet match: the circular orbit with Lyman-γ at one Bohr radius is not the one with hydrogen's binding energy, and the long polyene chains come out too red.