Earlier quoted context omitted.
Single beam of electrons diffracts like single beam of light, but otherwise electrons behave very differently than light: two electron beams interfere with each other, while two light beams do not.
> while two light beams do not [interact] Photons do interact! There is no two-photon vertex, that’s true, since there is no fundamental interaction between two photons. But put four photon/charged particle vertices together and you’ll get the 4-photon box diagram [1], whose contribution is nonzero. [1]: Since I’m not good at painting diagrams in ASCII on HN, here’s a link to the Wikipedia article with the box render…
That's a prediction. Evidence is so far inconclusive.