Of course they travel, or at least they have a wave function in momentum space which makes it possible to calculate the probability that we will find it at a ce

Of course they travel, or at least they have a wave function in momentum space which makes it possible to calculate the probability that we will find it at a certain point further away at a later time. And we have very good ideas. Quantum Mechanics is not something mysteriously handwaving mumbo jumbo. It is used every day to make very precise predictions.