Gen Rel is an amazingly accurate theory of spacetime geometry whever it is applicable, where it doesnt break down and fail to compute.
Where it is applicable it predicts very fine differences in angles and times out to many decimal places. People have tried for decades to improve on it, or to test it and find it wrong out at the 6th decimal place. But they havent succeeded yet.
But Gen Rel famously has places where it blows up and predicts infinities, in other words it is flawed. It has singularities.
this has been the case with other classical theories and it has been found that if you can QUANTIZE a classical theory it will often extend the applicability and get rid of places where it breaks down.
So a big aim of quantizing Gen Rel is to get rid of the classical singularities. mainly the "bigbang" and "blackhole" singularities.
The main reason why LQG is so active these days is that it appears to have removed Gen Rel singularities. the main reason Martin Bojowald is a key LQG figure is that he has been in the forefront in this and has gathered a considerable group of people who are working on this.
the first break came in 2001 when MB removed the bigbang classical singularity in a certain case.
To get the history since then, just go to arxiv.org and get the list of all Bojowald papers since 2001. the people active in this field are the people who have co-authored papers with Bojowald, and you can click on their names and find all the papers they have published independently.
the blackhole singularity is being removed just now, starting at end 2004 and very much at the present. a bojo paper on that came out this month (March 2005)
When a classical singularity is removed then you can run the model THROUGH where it used to be. the machine no longer blows up or stalls at that point. So you can explore BEYOND the classical singularity and that is interesting. It is expected that one way to check LQG is to look for traces in the cosmic microwave background of what LQG predicts about the bigbang that is different from classical Gen Rel, different because of it having removed the singularity.
So that is a very important feature of LQG, the fact that it doesnt encounter these irritating singularities in Gen Rel that have bothered people so long.
If you want a non-math way to think about it, focus on the uncertainty of a quantum theory. For the universe or a black hole to collapse all the way to a point would just be too certain, wouldnt it? Too definite for real nature to allow
. So it doesnt happen. At a certain indeterminate very high density there is a "bounce" according to the math (a time-evolution difference equation model) and contraction turns into expansion. And conditions for inflation are automatically generated.
the early universe in Loop Quantum Cosmology
Bojo, Goswami, Maartens, Singh
a black hole mass threshhold from non-singular quantum gravitational collapse
if you glance at these papers you will not see anything about thinking of space as divided up into little bits, or grains
because that is not what real LQG is about,
but you will get a taste of what is going on with the overcoming of the Gen Rel singularities at bigbang and blackhole.