Is there a quantum gravity theory where ''space is discrete''? I have been reading up on some approaches to quantum gravity apart from string theory.  The popular conception of loop quantum gravity is that it says that space is actually physically discrete at some sufficiently small scale, where the lattice spacings are presumably given by the Planck length.
It seems that at least in the case of loop quantum gravity, that this is a misconception and the discreteness is just referring to certain eigenvalues of area in a way which is somewhat familiar from elementary quantum mechanics  (see here for example).
Is there some approach where space is actually a graph or where spacetimes are actually chopped up into lattices such that for example the Universe is a cosmological spacetime which can be chopped up into a lattice?
(I don't mean just doing quantum gravity on a flat lattice by analogy with lattice Yang-Mills theory).
Edit: After some more searching, it looks like this kind of theory tends to go by the name of 'induced gravity' or 'emergent gravity'.  The details of how it all works are about as confused as they are in LQG unfortunately.
 A: Empty space or vacuum cannot be a simple lattice with Planck length spacing, because such a lattice contradicts special relativity.
The idea of a lattice is that it has a smallest length.
But due to special relativity, lengths Lorentz-contract, and can get as small as desired for rapid observers, much smaller than the Planck length, thus invalidating the idea of a smallest length.
So the naive idea that empty space is a lattice must be rejected.
Therefore, all quantum gravity approaches have some kind of fuzzy space at the Planck scale: something happens there that keeps the smallest length the same for all observers, also rapid ones.
Finding a model that maintains minimum length for all observers is one reason that quantum gravity is hard to develop.
A: Tom, I have come up with a highly speculative theory of gravity based on loop quantum gravity that you can download here: An Examination of Gluon Field Excitation as the Initiating Cause of Time Dilation, Gravity and Dark Matter
The basis of the theory is that it is the size of the particulate space of LQG that defines the speed of time, and that adding energy will cause a dilation of the particles and thus a dilation of time.  This provides a clear definition of "spacetime". When looking at the underlying cause of gravity surrounding a planet, gluon field excitation (analogous to the magnetic field surrounding a bar magnet) leads to a dilation of the particulate space of LQG and thus the warping of spacetime and gravity.
As I said above, the theory is highly speculative and based on a number of unproven concepts, but perhaps it will get you thinking.
