In perturbation theory, systems can go through intermediate "virtual states" that normally have energies different from that of the initial and final states. This is because of another uncertainty principle, which relates time and energy.

It isn't classically possible for a charged particle to just emit a photon and remain unchanged (except for recoil) itself. The state with the photon in it has too much energy, assuming conservation of momentum. However, since the intermediate state lasts only a short time, the state's energy becomes uncertain, and it can actually have the same energy as the initial and final states. This allows the system to pass through this state with some probability without violating energy conservation. Some descriptions of this phenomenon instead say that the energy of the system becomes uncertain for a short period of time, that energy is somehow "borrowed" for a brief interval. This is just another way of talking about the same mathematics.