Bohmian mechanics assumes that particle trajectories are continuous. Also, it claims the random outcome of certain experiments (like the double-slit experiment) to be due to the random initial particle positions at the beginning of the universe.
However, there are some conjectures that space and time are quantized at the plank scale. Look at this link for example: https://www.scientificamerican.com/article/is-time-quantized-in-othe/
If we assume that such conjectures are true and space and time are quantized, doesn't this rule out Bohmian mechanics? Isn't this in conflict with the continuity of trajectories? More importantly, if the initial particle positions are quantized with a minimum distance between possible positions, I think it would be very unlikely that their random distribution would be the same as the outcome of experiments. My reason is that the evolution of trajectories is chaotic and if we cannot make the distances between possible initial positions arbitrarily small, the future would be so different for different initial distributions such that the experiment will not occur at all for all of the initial distributions except the one which has been realized (maybe even the humans would exist only for this initial distribution).
Am I true? My field is not physics and I might have made a mistake in my argument, I'm just curious.