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Causal dynamical triangulation (abbreviated as "CDT") invented by Renate Loll, Jan Ambjorn and Jerzy Jurkiewicz is an approach to quantum gravity that like loop quantum gravity is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. The Loops '05 conference, hosted by many loop quantum gravity theorists, included several presentations which discussed CDT in much greater depth, and reveal it to be a pivotal insight for theorists. It has sparked considerable interest as it appears to have a good semi-classical description. At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale. This interesting result agrees with the findings of Lauscher and Reuter, who use an approach called Quantum Einstein Gravity.
Explanation
It is widely accepted that, at the very smallest scales space is not static, but is instead dynamically-varying. Near the Planck scale, the structure of spacetime itself is constantly changing, due to quantum fluctuations. This theory uses a triangulation process which is also dynamically-varying, or dynamical, to map out how this can evolve into dimensional spaces similar to that of our universe. The results of researchers suggests that this is a good way to model the early universe, and describe its evolution. Using a structure called a simplex, it divides spacetime into tiny triangular sections. Each simplex is geometrically flat, but simplices can be 'glued' together in a variety of ways to create curved spacetimes. Where previous attempts at triangulation of quantum spaces have produced jumbled universes with far too many, or minimal universes with too few dimensions, CDT avoids this problem by allowing only those configurations where cause precedes any event.
Derivation
CDT is a modification of quantum Regge calculus where spacetime is discretized by approximating it with a piecewise linear manifold in a process called triangulation. In this process, a d-dimensional spacetime is considered as formed by space slices that are labeled by a discrete time variable t. Each space slice is approximated by a simplicial manifold composed by regular (d-1)-dimensional simplices and the connection between these slices is made by a piecewise linear manifold of d-simplices. In place of a smooth manifold there is a network of triangulation nodes, where space is locally flat (within each simplex) but globally curved, as with the individual faces and the overall surface of a geodesic dome. The crucial development, which makes this a relatively sucessful theory, is that the network of simplices is constrained to evolve in a way that preserves the local topology, and thus causality. This allows a path integral to be calculated non-perturbatively, by summation of all possible (allowed) configurations of those simplices.
Disadvantages
The disadvantageous aspect of this theory is that it relies heavily on computer simulations, to generate results or evidence. Some feel that this makes it a less 'elegant' solution to the problem of creating a completely successful quantum gravity theory. Still; many physicists regard this line of reasoning as promising.
See also
References
Alpert, Mark "The Triangular Universe" Scientific American page 24, February 2007