All the pop-sci articles I've read have a description of the set-up similar to this:
It uses a pair of laser interferometers placed close to one another, each sending a one-kilowatt beam of light through a beam splitter and down two perpendicular arms, 40 meters each. The light is then reflected back into the beam splitter where the two beams recombine. If no motion has occurred, then the recombined beam will be the same as the original beam. But if fluctuations in brightness are observed, researchers will then analyze these fluctuations to see if the splitter is moving in a certain way, being carried along on a jitter of space itself.
I have emboldened the sections I'm having trouble with. If the universe was discretised, why would that result in the splitter moving? Bounce two balls off a wall made of discrete lego blocks and they'll return to your hands at the same time. The lego blocks in the wall, or the pixels in a digital image, are discrete, but don't move.
As a side note: I could understand if they varied the distance for one of the split laser beams and found that the intensity of the recombined laser always varied at some integer multiple of a constant*Planck_length, but this is not their procedure. (I assume there's a reason that this wouldn't work?)
I apologise for my lack of knowledge or if this question is tiringly uninformed.