Causal dynamical triangulation

From Wikipedia, the free encyclopedia

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.

Contents

[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 dynamically-varying and follows deterministic rules, or is 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 usually called a tetrahedron, and the 4-simplex, which is the basic building block in this theory, is also known as 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 dimensions, or minimal universes with too few, 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. 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. Therefore, many physicists regard this line of reasoning as promising.

[edit] Related theories

CDT has some similarities with loop quantum gravity, especially with its spin foam formulations. For example, Lorentzian Barrett-Crane model is essentially a non-perturbative prescription for computing path integrals, just like CDT. There are important differences, however. Spin foam formulations of quantum gravity use different degrees of freedom and different Lagrangians. For example, in CDT, the distance, or "the interval", between any two points in a given triangulation can be calculated exactly (triangulations are eigenstates of the distance operator). This is not true for spin foams or loop quantum gravity in general.

Another approach to quantum gravity that is closely related to Causal dynamic triangulation is called Causal Sets. Both CDT and Causal Sets attempt to model the spacetime with a discrete causal structure. The main difference between the two is that the causal set approach is very general, whereas CDT assumes a specific relationship between the lattice of spacetime events and geometry. Consequently, the Lagrangian of CDT is constrained by the initial assumptions to the extent that it can be written down explicitly and analyzed (see, for example, hep-th/0505154, page 5), whereas Causal Set theory is not nearly as completely developed at this point.

[edit] See also

[edit] References

  • Alpert, Mark "The Triangular Universe" Scientific American page 24, February 2007

Early papers on the subject:

[edit] External links

v • d • e
Theories of gravitation