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| '''Causal dynamical triangulation''' (abbreviated as "CDT") invented by ], ] and ] is an approach to ] that like ] is ]. This means that it does not assume any pre-existing arena, but rather attempts to show how the ] fabric itself evolves. The conference hosted by many loop quantum gravity theorists included several presentations which |
'''Causal dynamical triangulation''' (abbreviated as "CDT") invented by ], ] and ] is an approach to ] that like ] is ]. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the ] fabric itself evolves. The 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 ]. This interesting result agrees with the findings of Lauscher and Reuter, using an approach called Quantum Einstein Gravity. | ||
| 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 ] process which is also dynamically-varying, or dynamical, to map out how this can evolve into dimensional spaces similar to that of our universe. Where previous attempts at triangulation of quantum spaces have produced universes with too many, or too few dimensions, CDT avoids this problem by allowing only those configurations whose cause precedes the effect. | |||
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| ⚫ | CDT is a modification of ] where ] is discretized by approximating it by a piecewise linear ] 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 ] composed by regular ''(d-1)''-dimensional simplices and the connection between these slices is made by a piecewise linear manifold of ''d''-]. In other words; in place of a smooth manifold there is a network of triangulation nodes, where space is locally flat but globally curved. The crucial development, which makes this a relatively sucessful theory, is that the network of simplices evolves in a way that preserves the local topology, and thus causality. This allows a ] to be calculated non-pertubatively. | ||
| The disadvantageous aspect of this theory is that it relies heavily on computer simulations, to demonstrate its value. 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 theory as promising. | The disadvantageous aspect of this theory is that it relies heavily on computer simulations, to demonstrate its value. 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 theory as promising. | ||
Revision as of 03:43, 21 March 2007
 | It has been suggested that this article be merged with Discrete Lorentzian quantum gravity. (Discuss) Proposed since March 2007. |
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, using an approach called Quantum Einstein Gravity.
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. Where previous attempts at triangulation of quantum spaces have produced universes with too many, or too few dimensions, CDT avoids this problem by allowing only those configurations whose cause precedes the effect.
CDT is a modification of quantum Regge calculus where spacetime is discretized by approximating it by 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 other words; in place of a smooth manifold there is a network of triangulation nodes, where space is locally flat but globally curved. The crucial development, which makes this a relatively sucessful theory, is that the network of simplices evolves in a way that preserves the local topology, and thus causality. This allows a path integral to be calculated non-pertubatively.
The disadvantageous aspect of this theory is that it relies heavily on computer simulations, to demonstrate its value. 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 theory as promising.
External links
References
Alpert, Mark "The Triangular Universe" Scientific American page 24, February 2007
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