Causal dynamical triangulation: Difference between revisions

no edit summary
(removed "peacock language" and added a solid reference)
 
There is evidence <ref>
{{cite journal | last=Loll | first=Renate| year =2019| title = Quantum gravity from causal dynamical triangulations: a review | journal = Classical and Quantum Gravity | volume = 37 | issue = 1 | page = 013002 | doi = 10.1088/1361-6382/ab57c7| arxiv= 1905.08669 }}</ref>
that at large scales CDT approximates the familiar 4-dimensional spacetime, but shows spacetime to be 2-dimensional 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 [[Asymptotic safety in quantum gravity#Quantum Einstein Gravity (QEG)|Quantum Einstein Gravity]], and with other recent theoretical work.
 
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 is that the network of simplices is constrained to evolve in a way that preserves [[Causality (physics)|causality]]. This allows a [[Path integral formulation|path integral]] to be calculated [[non-perturbative]]ly, by summation of all possible (allowed) configurations of the simplices, and correspondingly, of all possible spatial geometries.
 
Simply put, each individual simplex is like a building block of spacetime, but the edges that have a time arrow must agree in direction, wherever the edges are joined. This rule preserves causality, a feature missing from previous "triangulation" theories. When simplexes are joined in this way, the complex evolves in an orderly{{how|date=March 2013}} fashion, and eventually creates the observed framework of dimensions. CDT builds upon the earlier work of [[John W. Barrett|Barrett]] and, [[Louis Crane|Crane]], and [[John C. Baez|Baez]] and Barret, but by introducing the causality constraint as a fundamental rule (influencing the process from the very start), Loll, Ambjørn, and Jurkiewicz created something different.
 
== Advantages and disadvantages ==