Given a source of electrons, like from an electron gun. Physicists call these freely traveling particles and often use a Gaussian wave packet to represent them with the group velocity being precisely defined as the velocity of the center of the packets. But if we do not measure the position of the particle then we have no idea where the "center of the packet" is and if we do measure the position of the particle then the wave function, because of dispersion, becomes an expanding spherical wave with basically a zero or undefined group velocity. So does nature really know about traveling, well-defined wave packets? Thanks in advance.