welcome: please sign in
Causal Dynamical Triangulations

Imagine a landscape composed of microscopic triangular structures that constantly rearrange themselves into new patterns. Seen from afar, the landscape looks perfectly smooth, but up close it is a churning cauldron of strange geometries. This deceptively simple model is at the heart of a new theory called causal dynamical triangulation (CDT), which has emerged as a promising approach to solving the most vexing problem in physics—unifying the laws of gravity with those of quantum mechanics.

For more than 20 years, the leading contender in the quest for unification has been string theory, which posits that the fundamental particles and forces are actually minuscule strings of energy. But some scientists say this theory is misguided because it sets the strings against a fixed background; a better model, they argue, would generate not only particles and forces but also the spacetime they inhabit. In the 1980s and 1990s these researchers developed loop quantum gravity, which describes space as a network of tiny volumes only 10-33 centimeters across. Although this approach has achieved some notable successes, such as predicting the properties of black holes, it has yet to pass an essential test: showing that the jumble of volumes always comes together to form the familiar four-dimensional spacetime of our everyday world.

CDT is less than 10 years old, but it has already cleared this hurdle. Conceived primarily by three European theorists—Renate Loll of Utrecht University in the Netherlands, Jan Ambjørn of Copenhagen University and Jerzy Jurkiewicz of Jagiellonian University in Poland—CDT constructs spacetime geometries from simple triangular structures, in much the same way that Buckminster Fuller used triangular surfaces to create geodesic domes. The basic building block is the 4-simplex, the equivalent of a tetrahedron but in four dimensions. (Just as a tetrahedron has four triangular faces, a 4-simplex is bounded by five tetrahedrons.) Although each simplex is geometrically flat, they can be glued together in a variety of patterns to produce curved spacetimes. Because quantum theory stipulates that the structure of spacetime at very small scales must be constantly changing, the researchers determine the overall geometry by summing the probabilities of all the possible configurations of simplexes.

Previous attempts to triangulate the universe in this way ended in nonsensical results: crumpled spacetimes with an infinite number of dimensions or rolled-up geometries with just two. The key insight of CDT was to exclude the configurations that were not causal (that is, patterns that would allow an event to precede its cause). The elimination of these unrealistic tilings did the trick: in 2004 Loll, Ambjørn and Jurkiewicz used computer simulations to show that model universes constructed from hundreds of thousands of simplexes are four-dimensional. More recently, the researchers demonstrated that the large-scale shape of their universes is just like that predicted by the standard theory of cosmology.

The next big step for CDT is incorporating matter into the model to see if it can simulate the full equations of general relativity. According to Lee Smolin of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, the theory may eventually yield testable predictions, such as slight changes in the speed of high-energy photons caused by the model's nonclassical geometries at small scales. One of the pioneers of loop quantum gravity, Smolin says CDT has so far not received the attention it deserves from theoretical physicists, possibly because the approach relies so much on computer simulation. "It's not easy stuff to get into," he says. "It's hard to get at by pencil and paper."

Causal_Dynamical_Triangulations (last edited 2011-09-21 18:23:27 by Chris)