Reply to Comment on "Nonlinear quantum effects in electromagnetic radiation of a vortex electron" by A. Karnieli, R. Remez, I. Kaminer, et al.

We argue that while the experiment of Remez et al. is interesting and its conclusions may well be correct, neither the original paper nor the recent comment by Karnieli et al.[arXiv:2102.13345] fully discusses and rules out all alternative classical hypotheses that could have led to the same wide azimuthal distributions, ascribed to Bohmian-like quantum nature of an electron packet. On the contrary, there exists a family of classical effects that could also have resulted in the measured distributions and that were neither discussed nor even mentioned by the authors. Such alternative hypotheses include {\it (i)} effects of the beam sizes, of its angular divergence, of the temporal coherence of the radiation process, which is also related to how the wave zone is defined, and {\it (ii)} influence of the grating shape and of its material -- the effects that are known to be of crucial importance for Smith-Purcell radiation from non-relativistic electrons. In order to prove a hypothesis, all its alternatives must be checked and proved to be inconsistent with the measurements. In our opinion, this was not properly done in the discussed paper and in the comment. Finally, we propose to repeat the experiment and to measure diffraction radiation from a thin metallic semi-plane or a strip. In this case, the aforementioned classical effects play a much smaller role and the results of such measurements would have higher credibility.