[tsimionescu]

That's not really a good counter - Planck units are not a discretization. Space-time is continuous in all quantum models, two objects can very well be 6.75 Planck lengths away from each other. The math of QM or QFT actually doesn't work on a discretized spacetime, people have tried.

[tsimionescu]

I should add one thing here: no theory that is consistent with special relativity can work on a discretized spacetime, because of the structure of the Lorrentz transform. If a distance appears to be 5 Planck units to you, it will appear to be 2.5 Planck units to someone moving at half the speed of light relative to you in the direction of that distance.