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Causal dynamical triangulation (CDT), theorized byRenate Loll,Jan Ambjørn and Jerzy Jurkiewicz, is an approach toquantum gravity that, likeloop quantum gravity, isbackground independent.
This means that it does not assume any pre-existing arena (dimensional space) but, rather, attempts to show how thespacetime fabric itself evolves.
There is evidence[1]that, at large scales, CDT approximates the familiar 4-dimensional spacetime but shows spacetime to be 2-dimensional near thePlanck scale, and reveals afractal structure on slices of constant time. These interesting results agree with the findings of Lauscher and Reuter, who use an approach calledQuantum Einstein Gravity, and with other recent theoretical work.
Near thePlanck scale, the structure ofspacetime itself is supposed to be constantly changing due toquantum fluctuations and topological fluctuations. CDT theory uses atriangulation process which variesdynamically and followsdeterministic rules, to map out how this can evolve into dimensional spaces similar to that of our universe.
The results of researchers suggest that this is a good way to model theearly universe[citation needed], and describe its evolution. Using a structure called asimplex, it divides spacetime into tiny triangular sections. A simplex is the multidimensional analogue of atriangle [2-simplex]; a 3-simplex is usually called atetrahedron, while the 4-simplex, which is the basic building block in this theory, is also known as thepentachoron. Each simplex is geometrically flat, but simplices can be "glued" together in a variety of ways to create curved spacetimes. Whereas 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 in which the timelines of all joined edges of simplices agree.
CDT is a modification of quantumRegge calculus where spacetime is discretized by approximating it with a piecewise linearmanifold in a process calledtriangulation. In this process, ad-dimensional spacetime is considered as formed by space slices that are labeled by a discrete time variablet. Each space slice is approximated by asimplicial manifold composed by regular (d − 1)-dimensional simplices and the connection between these slices is made by a piecewise linear manifold ofd-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 ageodesic 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 timet with one at timet + 1. The crucial development is that the network of simplices is constrained to evolve in a way that preservescausality. This allows apath integral to be calculatednon-perturbatively, 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?] fashion, and eventually creates the observed framework of dimensions. CDT builds upon the earlier work ofBarrett,Crane, andBaez, but by introducing the causality constraint as a fundamental rule (influencing the process from the very start), Loll, Ambjørn, and Jurkiewicz created something different.
CDT has some similarities withloop quantum gravity, especially with itsspin foam formulations. For example, the LorentzianBarrett–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. Moreover, in spin foams the discreteness is thought to be fundamental, while in CDT it is viewed as a regularization of the path integral, to be removed by thecontinuum limit.
Another approach to quantum gravity that is closely related to causal dynamical triangulation is calledcausal 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 relatively general, whereas CDT assumes a more 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 there is more freedom in how one might write down an action for causal-set theory.
In the continuum limit, CDT is probably related to some version ofHořava–Lifshitz gravity. In fact, both theories rely on a foliation of spacetime, and thus they can be expected to lie in the same universality class. In 1+1 dimensions they have actually been shown to be the same theory,[2] while in higher dimensions there are only some hints, as understanding the continuum limit of CDT remains a difficult task.
Early papers on the subject:
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