Pilot wave models and "no cross" rule

[bohm2]

From my understanding, average trajectories based on weak "measurements", obey the 'no-crossing rule'. These average trajectories strongly resemble the single-photon trajectories predicted by Bohmian mechanics:
For instance compare these average trajectories:
http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf

with Bohmian ones:



Since the trajectories were formed by connecting 'average' velocity vectors, does it then imply that some of actual individual trajectories (within any realist pilot wave model-Bohmian or otherwise) can cross the center line? I'm asking because in some pilot-wave analogs of QM (Couder-type walking droplet experiments), crossing over does occur. I'm guessing I messed this up, and in fact, crossing over at individual trajectory level is fully compatible with no-crossing over at the average level?

 

[Demystifier]

From my understanding, average trajectories based on weak "measurements", obey the 'no-crossing rule'. These average trajectories strongly resemble the single-photon trajectories predicted by Bohmian mechanics:
For instance compare these average trajectories:
http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf

with Bohmian ones:



Since the trajectories were formed by connecting 'average' velocity vectors, does it then imply that some of actual individual trajectories (within any realist pilot wave model-Bohmian or otherwise) can cross the center line? I'm asking because in some pilot-wave analogs of QM (Couder-type walking droplet experiments), crossing over does occur. I'm guessing I messed this up, and in fact, crossing over at individual trajectory level is fully compatible with no-crossing over at the average level?

First, the weakly measured trajectories do not merely resemble single-particle Bohmian trajectories. They are equal to them.
Second, there is a general theorem that Bohmian trajectories never cross in space if the wave function is stationary. For a non-stationary wave function the crossing in space is possible, but even than there is no crossing in space-time.