In the transition from "basic" quantum theory to quantum field theory, both in the derivation of the Gordon-Klein and of the Dirac-equations, there is a big problem with solutions with negative energies. Can anyone explain me why this is being considered a big problem in the first place (it seems obvious to textbook authors). After all, energy is anyhow only determined up to a constant. And electrons within atoms are generally assigned negative energies. This is probably one of those stupid questions with obvious answers which people just forget to mention. The more grateful I would be for an answer.