This is one of those "existential doubts" that most likely have a trivial solution which I can't see. Veltman says in the Diagrammatica book: Although the reasoning makes perfect sense for a Hilbert space spanned by momentum states, intuitively it doesn't make sense to me, because a translated particle cannot correspond to the same state "physically speaking" (i.e. the same ray in Hilbert space). How is that possible? Another question: does this hold for non-relativistic quantum mechanics as well? At a glance, it seems so. Thanks.