I dont get it. Suppose I have a particle at coordinates (0,0) with some velocity in x-direction. Due to symmetry, the trajectory of a pilot-wave particle has t

I dont get it. Suppose I have a particle at coordinates (0,0) with some velocity in x-direction. Due to symmetry, the trajectory of a pilot-wave particle has to stay on the x-axis, while in QM the heisenberg uncertainty principle results in some momentum in y-direction. Wouldn't you need to add some kind of imperfection to disturb the pilot-wave in order to reproduce the probabilistic results?