Causal dynamical triangulation

Causal dynamical triangulation

Causal dynamical triangulation is another approach to a theory of quantum gravity. The approach at quantization of spacetime, is by use of something called a simplex. A simplex is the analogue of a triangle to other dimensions. A 3-simplex is a tetrahedron. However, the building blocks of spacetime at the Planck scale in Causal dynamical triangulation are the 4-simplex, or the pentachoron. 

Causal dynamical triangulation

An approach to quantum gravity, that is background independent. (like loop quantum gravity). This means it is possible not to have to refer to a certain coordinate system in the theory’s defining equations. There is no assumed, pre-existing arena.

Causal dynamical triangulation attempts to show how the very fabric of spacetime evolves in time. It involves a discrete causal structure that assumes a specific relationship between geometry and the lattice of spacetime itself. 

Causal dynamical triangulation, especially in 2005, showed to be a pivotal insight for quantum gravity theorists as a semiclassical description.

In causal dynamical triangulation, spacetime, at the Planck scale, is 2-dimensional.

There are slices of constant time, with a fractal structure.

However, the 4-dimensional spacetime that we are familiar with is recreated macroscopically. 

Causal dynamical triangulation can derive the observed properties of the nature of spacetime using only a small set of assumptions and non-adjustable elements or factors. 

Space can be modeled, both at the Planck scale, and, at the large scale structure of the cosmos. This is attractive to physicists and suggests that it could provide insight into the nature of reality. 

We can simulate the observable implications of the Causal dynamical triangulation with computer programs.

Spacetime, near the Planck scale, where it’s very structure is believed to be revealed, should be constantly changing. This change is the result of quantum, as well as topological fluctuations. 

Causal dynamical triangulation is going to follow a process of triangularization, which I will describe to make spacetime discrete. This process will vary dynamically throughout the system. However, it will follow some deterministic rules, thus, this space will resemble our world.

It has also been shown that this is an excellent way to map out the evolution of the early universe. 

The idea is that we have a structure, known as a simplex. We can use these simplexes to divine the very fabric of space to be triangulated. Space is divided into these tiny tiny triangular sections. A simplex, we should note, is a triangle, or a tetrahedron, generalized to some higher dimension. In other words: a simplex is the analogue of a triangle to higher dimensions. For example: a tetrahedron is a 3-simplex and a pentachoron is a 4-simplex. The pentachoron is the basic building block of spacetime in Causal dynamical triangulation. 

Now, the simplexs are flat, at least geometrically speaking, however, can be attached or glued together to produce or to simulate spacetime curvature. Space is locally flat at these simplexes, however, is curved globally.

• This is an improvement from earlier theories of triangulated quantum spaces. These earlier theories either had too many or too few dimensions.

• The way that Causal dynamical triangulation avoids this issue is only allowing configurations of simplexes where all of the edges are joined in ways that really agree. 

• The key element is that causality is preserved in the evolution of these networks of simplices. We can calculate (non-perturbatively) a path integral for these networks, if you know quantum mechanics, that means that we can calculate the sum of all possible allowed configurations of spatial geometries. 

• The interval, or the distance, between two points in some arbitrary triangulation can be calculated as an eigenstate in a distance operator.