In several theories, space itself is discrete, somewhat in relation to the Planck length, $$l_p = \sqrt{\frac{\hbar G}{c^3}} \simeq 1.616199 \times 10^{-35}\quad m$$ .

More specifically in loop quantum gravity, Carlo Rovelli's 1998 overview paper states the following:

The spin-networks picture of space–time is mathematically precise and physically compelling: nodes of spin networks represent elementary grains of space, and their volume is given by a quantum number that is associated with the node in units of the elementary Planck volume $$V = \left( \frac{\hbar G}{c^3} \right)^{3/2}$$

So, from what I understand of LQG, space has always been discrete. However, mathematically, space being discrete does not imply that time also is (which would mean that spacetime is discrete). A counter example in 2D would be the floor and ceiling functions.

Concerning the OPERA results, let's keep in mind that several explanations have been published which don't allow for supralumnial neutrinos, cf this Universe Today article or this Bad Astronomy article.

I am relatively new here, and I might not have fully answered your question, so feel free to post comments or even modify my answer to improve it. Thanks!

This post imported from StackExchange Physics at 2014-03-17 03:42 (UCT), posted by SE-user ChrisR