Hydrogen Atom in the Cosmic Microwave Background

The cosmic microwave background covers the entire universe, which suggests the absence of ay closed system, except the universe itself. In this paper, I consider the effect of the cosmic microwave background on the hydrogen atom, which must be very small, otherwise, changes in energy levels would have been measurable. But how small is small? This I compute by considering a system in an environment or bath. I derived the bath's, (in this case the CMB) effect on the hydrogen atom in the Feynman-Vernon approach to an open system. The effect is small and quantified in terms of a correction to the hydrogen atom that breaks time-reversal symmetry, as expected of memory effects. This is significant. There are imperceptible changes in the state of the hydrogen atom, which means that the pervasive CMB must have similar small effects on other atoms, thus breaking time-reversal symmetry in all physical systems.