Is Bohmian mechanics wrong in the case that space and time are quantized? 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.
 A: does quantized spacetime rule out Bohmian mechanics?
The answer is no. From the loop quantum gravity, the minimum quantum of length is planck
length(pl). To visualise, if 1pl is about a size of tree then the minimum size of a elementary particle is of the order of size of the whole solar system. In no way the position of a particle is discreate, it is always continuos with respect to pl. So the trajectory of a travelling particle is always continuous. And Bohmian mechanics is not ruled out.
In Bohmian mechanis, the trajectory of a particle is govern by the "Path guiding equation" which tells us that the exact path of a particle is well defined by the hidden variables(non-local) of the Bohm's wave function. And there is no conflict with quantized spacetime.
A: The equations of Bohmian mechanics consist of the Schrodinger equation for the overall wavefunction, and a classical trajectory which follows the quantum probability current of that wavefunction. Normally these are differential equations for which space and time are continuous. 
If space and time are instead discrete, there can still be a wavefunction, but its time evolution would consist of a series of discrete unitary transformations, rather than a smooth unitary evolution; and the classical trajectory would have to consist of a series of stochastic (probabilistic, nondeterministic) jumps between classical configurations, rather than a smooth deterministic evolution. 
But there is no barrier here to reproducing the basic features of Bohmian mechanics, and in many cases it would even be possible to embed this discretized system in a continuous one. The real problems for Bohmian mechanics lie elsewhere, such as the assumption of a universal time coordinate, which conflicts with the philosophy (though not necessarily the calculations) of special relativity. 
