Planck length implies lattice structure of space? There is known to be a lower limit on space, which can be derived from the Planck units. It can describe the minimum distance resolvable between two points; but what then would the structure of space look like?
Would it be a lattice, where each point of space, planck length apart on each axis, forms the 3 dimensional space, and space is absolute? Or is it literally just the limiting distance between two arbitrary points? Thoughts? 
 A: Planck length and Planck time (and the other quantities) indicate only a rough space-time-energy scale where we suspect interesting things happen regarding the unification of gravity/GTR with the other three forces.  No one knows yet how those forces unify, or what the structure of space-time-energy really is, or what mass or charge or lepton number etc really are in terms of whatever structure exists.  
We are flat out totally clueless!   
In the past, the 1950s more or less, theoreticians noticed some suggestive numerical similarities between electromagnetism (QED) and the weak nuclear force when extrapolated beyond the beam energies attainable at the time.  The "Fermi constant" figured prominently.   This eventually lead to the ideas of W and Z bosons, and Higgs, and all the rest we take as Standard Model now.  
There was no way the theoreticians of those days could have gone from the Fermi constant and other measured quantities straight to the electroweak theory, but the values known did suggest some sort of convergence or intermingling in a particular fuzzy range of energies and distance scales.  Theorists might have assumed a single type of boson responsible for the weak force, or guessed there'd be more than one.  It wasn't until experiment caught up closer to those Fermi scales, and theory revealed that four-way vertex functions don't work so well in quantum field theory, that a particular model could be held up as describing reality.  As it turned out, reality is not described by Fermi's constant, but by W and Z masses, or well actually not those, but the Higgs.   Fermi is a low energy approximation.
Likewise we have noticed, since a few decades ago, suggestions from the fundamental constants in quantum theory and GTR that something about these theories converges, or shares some sort of infrastructure, at the Planck scale.  We have nothing like a trustworthy model for what is really going on.  Our "Planck" quantities are like Fermi's constant, only a indicator of how far experiment needs to go to show us the truth of physical reality.  Quite likely, we'll find it's a richer, more complex reality than imagined by string theorists, Loop Quantum Gravity, or Finkelstein's Space-Time Code (my favorite horse to bet on), and that all the Planck quantities are nice low-energy approximations.
If you have read about the astrophysics experiments to look for different times of arrivals of low and high frequency radiation from quasars or gamma ray bursts, you know that such differences would indicate something going on with space-time on a smaller scale than we can otherwise measure.  If such a difference is found, it won't imply a lattice structure, or any particular micro-topology, or even help distinguish between various string or LQG ideas.  But it would be great to find such a difference, since theorists expect it, and we'd be very puzzled if no dispersion could be measured at the expected level, although we're not so sure just what to expect.
