We discuss space-time evolution of ultrarelativistic quantum dipole in QED. We show that the space-time evolution can be described, in a certain approximation, by means of a regularized wave function, whose parameters are determined by the process of the dipole creation by a local current. We derive using these wave functions the dipole expansion law, that is found to coincide parametrically in the leading order with the one suggested by Farrar, Frankfurt,Liu and Strikman.