Can we measure the Wigner time delay in a photoionization experiment?

No, we cannot! The concept of Wigner time delay was introduced in scattering theory to quantify the delay or advance of an incoming particle in its interaction with the scattering potential. It was assumed that this concept can be transferred to ionization considering it as a half scattering process. In the present work we show, by analyzing the corresponding wave packets, that this assumption is incorrect since the wave function of the liberated particle has to satisfy the incoming-wave boundary condition. We show that the electron released in photoionization carries no imprint of the scattering phase and thus cannot be used to determine the Wigner time delay. We illustrate our conclusions by comparing the numerical results obtained using two different methods of extracting the photoelectron spectra in an attoclock experiment.