I wanted to mention that even though you have the space foam [little black holes] which are sort of like the Dirac sea of negative particles that fill space, still space is not quantized. There can not be any sudden jumps because of Max Born's four postulates. It has to be that way because otherwise there would be infinite momentum at the jump-off point. [However I am wondering if perhaps a Lipschitz function might fill the needs of the Max Born postulates. It would have a limited derivative even though space would not be continuous. And that might be helpful for the space foam which  seem to mean that space would not be continuous, [even if they are connected by worm holes as mentioned by Alsaleh]] [The original idea of worm holes connecting the quantum foam came from a paper  by Robert Penna]

I also wanted to mention something that was noted by Kelley Ross. That the uncertainty principle does not just mean a limit on what one can know. It requires that things do not have both classical values of position and momentum at the same time because otherwise the electrons would fall into the nucleus. And there are lots of hydrogen atoms in the universe that are not observed.[So it is not just Bell's inequality which shows that things do not have classical values until they interact with something big. Even the very existence of hydrogen atoms shows that.]