CDT, which could be called Lego Path gravity, is a very simple and, in its own terms, remarkably successful approach to quantum spacetime dynamics. The recent Loll paper, called The Emergence of Spacetime, or Quantum Gravity on your Desktop, is something to read if you want to keep tabs on current CDT work. http://arxiv.org/abs/0711.0273 There are two basic ideas: the Legoblock idea Use a huge number of identical spacetime building blocks----little chunks of 4D looking like higherdimension pyramids or more precisely higherdimension tetrahedrons. Every shape of geometry can be approximated with these spacetime "Legoblocks" depending on how they are stuck together. There is no surrounding space. the Path Integral idea A spacetime is like a path, or history of evolution, between the geometry that space has at the start and at the finish. What the spacetime does is fill in: showing how the geometry evolves. It shows all the intermediate shapes. It is like the path in a Feynman path integral. In this case, a path thru the land of all possible spatial geometries. One should be able to calculate a probability or amplitude for each way that geometry can evolve---for each path. In fact, following Feynman's example one can just write down a GRAVITATIONAL PATH INTEGRAL plugging in the Einstein-Hilbert where the action term belongs. IF ONE CAN DO THE INTEGRAL then one should be able to calculate all sorts of things straightforwardly---expectation values, amplitudes to get from here to there ==================== For concreteness, have a look at Loll's review paper. The gravitational path integral is equation (1). To evaluate any path integral you have to integrate over the realm of all possible paths the particle could take, so you need a measure on pathspace. In our case, to evaluate a GRAVITATIONAL path integral you need a measure on the realm of all possible spacetimes (all possible paths from initial to final geometry.) Incidentally, to make things simple they take the initial and final spatial geometries to be trivial---essentially just one-point spaces. To make it possible to do the integral, what the researchers do is restrict the realm of all possible spacetime geometries down to a REPRESENTATIVE SAMPLE. It's often called "regularizing". They restrict down to ALL THOSE SPACETIMES YOU CAN BUILD WITH LEGOBLOCKS. And then they let the Path Integral happen inside a computer (Monte Carlo style). ==================== It is quite a clever approach. A small number of researchers do it: Renate Loll, Jan Ambjorn, a few others. They call their approach CAUSAL DYNAMICAL TRIANGULATIONS From time to time they bring out surprising results. Now just this week Renate Loll posted an overview paper, written for non-specialists, which she gave as invited speaker at a big international conference at Sydney in July. It explains the whole thing very clearly, and it also tells us to expect a new paper to appear by Ambjorn Goerlich Jurkiewicz and Loll. This thread is to discuss the new CDT paper, if anyone wants to. I will get some quotes and paraphrase some stuff from the paper. A big point that both Jan Ambjorn made in his invited talk at Loops '07 in June and Renate Loll makes here is that if they generate a whole lot of spacetimes in the computer and average them up they get the four-sphere S4. That which is to deSitter space as euclidean is to lorentzian. They've also started including matter, so it is not just pure geometry, and there is some discussion of that.