In the Holometer experiment, why would one of the split laser beams arriving back at a slightly different time indicate the universe was quantized? 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.
 A: Chris Hogan, University of Chicago. March 1,2009 article in Back Reaction.
The idea underlying Hogan's prediction is that our world might have holographic properties, in which case not all three dimensions of our spacetime would encode really independent degrees of freedom. This conjectured property would become noticeable only at very large distances. A device that was able to measure distances in orthogonal directions at long distances and to high precision could be sensitive to this fundamental limit of encoding details, and be subject to a new kind of uncertainty. Gravitational wave interferometers provide exactly such a device. The holography would show up as noise in the detector.
Gravitational waves create distortions in our space-time that make themselves felt as tiny changes in lengths which are not the same for all three spatial dimensions. Interferometers lead a laser through a beam-splitter that splits the beam into two orthogonal directions into the “arms” of the interferometer, bounce the beam back on mirrors at the end of these arms, and compare the phases of the light when it comes back. This procedure can detect tiny deviations in the arm lengths which will change the phase shift. A common way to enhance the sensitivity of interferometers are “recycling techniques” that basically artificially increase arm lengths by reflecting the beam several times back and forth. GEO600 would be particularly sensitive to the holographic modification of quantum mechanics Hogan is proposing because the laser is reflected through both arms several times, whereas LIGO, VIRGO and TAMA use so called Fabry-Perot arms that reflect the beam in each arm separately. You find a very useful illustration of this difference between LIGO and GEO600 in Peter Shawhan's presentation, slide 19 and 20.
*You may be asking yourself "Gravity is not equal in 3 dimensions"? That is the an aspect of Holographic Universe, a false dimension comes out of it.
