Causal dynamical triangulation

From Wikipedia, the free encyclopedia

It has been suggested that this article or section be merged with Discrete Lorentzian quantum gravity. (Discuss)

Causal dynamical triangulation (abbreviated as "CDT") invented by Renate Loll, Jan Ambjørn 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, and reveals a fractal structure on slices of constant time. These interesting results agree with the findings of Lauscher and Reuter, who use an approach called Quantum Einstein Gravity, and with other recent theoretical work. A brief article appeared in the February 2007 issue of Scientific American, which gives an overview of the theory, explains why some physicists are excited about it, and puts it in historical perspective.

1 Explanation
2 Derivation
3 Disadvantages
4 See also
5 References
6 External links

[edit] 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. A simplex is the generalized form of a triangle, in various dimensions. A 3-simplex is also called a tetrahedron, and the basic building block in this theory is the 4-simplex, which is also called the pentatope, or pentachoron. 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.

[edit] 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 line segments which make up each triangle can represent either a space-like or time-like extent, depending on whether they lie on a given time slice, or connect a vertex at time t with one at time t+1. The crucial development, which makes this a relatively successful theory, is that the network of simplices is constrained to evolve in a way that preserves causality. This allows a path integral to be calculated non-perturbatively, by summation of all possible (allowed) configurations of the simplices, and correspondingly, of all possible spatial geometries.

[edit] 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. Also; it has been argued that discrete time-slicing may not accurately reproduce all possible modes of a dynamical system. However; research by Markopoulou and Smolin demonstrates that the cause for those concerns may be limited. Ergo; many physicists regard this line of reasoning as promising.