# Can a free electron absorb a virtual photon even though it cannot absorb an ordinary photon?

Due to conservation laws a free electron,as I understand it, cannot absorb a photon. But in computing QED probabilities, diagrams are drawn showing emission and absorption of photons by an electron. Also QED requires electrons to exchange photons, which means one emits one and the other absorbs one.

Is this because conservation laws are relaxed for virtual particles?

• @probably_someone: A free electron can emit and re-absorb a virtual photon in a one-loop diagram, without a need for anything else nearby. Apr 28, 2018 at 1:31
• @MichaelSeifert That is correct. I was only thinking at tree-level in my earlier comment. Apr 28, 2018 at 1:33

The four-momentum of any real particle satisifies the relationship $p_\mu p^\mu = -m^2$. This defines a 3-D surface in the 4-D space of all possible four-momenta; this surface is called the mass shell for the particle. A virtual particle, on the other hand, can have any four-momentum vector that you want; a virtual particle is usually "off-shell", because its four-momentum doesn't lie on the mass shell.