Surprising and promising results have not come too frequently in quantum gravity research, but the Causal Dynamical Triangulations program led by Renate Loll, Jan Ambørn and Jerzy Jurkiewicz had an exciting moment in 2004. A computer simulation showed that a space-time model with the right dimensionality arose from a path integral superposition of fairly generic microscopic geometric building blocks. The team has kept up a steady stream of research investigating and seeking to extend this result, and now they have published a popular article in the latest Scientific American.
I recommend the article, if one has access to it. I also discussed (as best I could) the basics of the CDT approach in this earlier post, so I won’t repeat all that here. Also, I coincidentally had just read a recent paper by the team which showed how they have generated not just the right dimensionality, but also specifically find a de Sitter universe in a simulation.
The thing I find most interesting about CDT is that it may give some evidence that selecting asymmetric time and causality as fundamental features is important in quantum gravity (a caveat is that their simulation uses globally synchronized time, and I wonder if they can relax this assumption).
One reason to be cautious is that CDT at this point only deals with space-time, not matter. Like in Loop Quantum Gravity, there is an expectation that matter fields can be coupled to the theory later on. This is in contrast to research by Fotini Markopoulou and Olaf Dreyer (see posts here and here), who think that it is the matter fields which are to emerge from a micro-quantum substrate, and that space-time geometry is to be inferred from the matter. If this works, it seems conceptually more appealing, since you’ve dealt with both space-time and matter at once. (See also this recent FQXi article on Markopoulou and Dreyer).
One last interesting aspect which I hadn’t thought much about before was discussed in the recent paper. This is the fact that CDT (and I assume other “emergence-style” programs) need to be investigated by computer simulation, rather than by deriving a specific analytical result through mathematical formalism. This essentially means giving up on the traditional idea of a “theory of everything” which can be written down in a set of equations. The CDT team doesn’t see this as a weakness, and cites condensed matter theory (see also this post) for example as a field where emergent behaviors are profitably studied without the possibility of precise description at the micro-level. They also invoke the idea of “self-organizing” complex systems. Here’s a quote:
“Think of quantum gravity as a strongly coupled system of a very large number of microscopic constituents, which by its nature is largely inaccessible to analytic pen-and-paper methods. This is no reason for despair, but a common situation in many complex systems of theoretical interest in physics, biology and elsewhere, and merely calls for a dedicated set of technical tools and conceptual notions.”