In explaining such phenomena as the redshift and even the fact that we can see stars and planets, the effect of wave packet spreading (WPS) of the photon wave function is not taken into account. Probably the main reason is a belief that WPS is not important since a considerable WPS would blur the images more than what is seen. However, WPS is an inevitable consequence of quantum theory and moreover this effect is also known in classical electrodynamics. So it is not sufficient to just say that a considerable WPS is excluded by observations. One should try to estimate the importance of WPS and to understand whether our intuition is correct or not. We explicitly demonstrate that a standard relativistic quantum-mechanical calculation shows that spreading in the direction perpendicular to the photon momentum is very important and cannot be neglected. Hence the physics of the above phenomena is not well understood yet. Possible approaches for solving the problem are discussed.