This chapter covers the early years of quantum theory, a time of guesswork, inspired by problems presented by the properties of atoms and radiation and their interaction. Later, in the 1920s, this struggle led to the systematic theory known as quantum mechanics, the subject of Chapter 5. Quantum mechanics started with the problem of understanding radiation in thermal equilibrium at a non-zero temperature. It was not possible to make progress in applying quantum ideas to atoms without some understanding of what atoms are. The growth of this understanding began with the discovery of radioactivity.

This final chapter discusses spectral distortions of the CMB. We first introduce the relevant collision processes in a universe with photons and non-relativistic electrons: Compton scattering, Bremsstrahlung and double Compton scattering. We derive the corresponding collision terms and Boltzmann equations. For Compton scattering this leads us to the Kompaneets equation for which we present a detailed derivation. We introduce timescales corresponding to these three collision processes and determine at which redshift a given process freezes, i.e., becomes slower than cosmic expansion. We also discuss the generation of a chemical potential in the CMB spectrum by a hypothetical particle decay and by Silk damping of small scale fluctuations. Finally, we study the Sunyaev{Zel’dovich effect of CMB photons which pass through hot cluster gas.