String Theory and Causal Dynamical Triangulations
Causal dynamical triangulations’ biggest flaw in comparison to string theory is that it doesn’t tell us anything about where matter comes from, whereas matter arises naturally in string theory from the interactions of fundamental strings.
The causal dynamical triangulations (CDT) approach consists of taking tiny building blocks of space, called 4-simplices (sort of like multidimensional triangles), and using them to construct the space-time geometry.
The result is a sequence of geometric patterns that are causally related in a sequence where one construction follows another (in other words, one pattern causes the next pattern). This system was developed by Renate Loll of Utrecht University in the Netherlands, and also by colleagues Jan Ambjørn and Jerzy Jurkiewicz.
One of the most important aspects of CDT is that time becomes an essential component of space-time, because Loll includes the causal link as a crucial part of the theory. Relativity tells us that time is distinctly different from space (the time dimension has a negative in front of it in relativity), but Stephen Hawking and others have suggested that the difference between time and space could perhaps be ignored.
Loll then takes her causally linked configurations of 4-simplices and sums over all possible configurations of the shapes. (Feynman used a similar approach in quantum mechanics, summing over all possible paths to obtain quantum physics results.) The result is classical space-time geometry!
If true, CDT shows that it’s impossible to ignore the difference between space and time. The causal link of changes in space-time geometry — in other words, the “time” part of space-time — is absolutely necessary to get classical space-time geometry that is governed by general relativity and matches what science knows of standard cosmological models.
At the tiniest scales, though, CDT shows that space-time is only 2-dimensional. The model turns into a fractal pattern, where the structures repeat themselves at smaller and smaller scales, and there’s no proof that real space-time behaves that way.