Chapter 46: The Hydrogen Spectrum

The hydrogen atom emits and absorbs light at discrete wavelengths, not a continuum. In Category τ, these spectral lines are the direct fingerprint of quantised co-rotor modes on T²: only integer winding numbers are permitted, so only discrete energy differences can be radiated. This chapter derives the energy-level formula, the Rydberg spectral formula, the named series (Lyman, Balmer, Paschen), and the fine structure and Lamb shift corrections. Every spectral line is a transition between U(1) holonomy modes on τ².