# Why does an positive absorbtion coefficient imply impossibility of population inversion?

In "Radiative Processes in Astrophysics" from Rybicki and Lightman there is a chapter called "6.9 The impossibility of a synchrotron maser in vacuum":

They prove that there can not be a synchrotron maser in vacuum. I understand the very little mathematics, which basically consists in showing that $\alpha_\nu$ – the absorption coefficient – is positive for this special case. But why does a positive absorption coefficient imply the impossibility of population inversion?