Renate Loll's approach, primarily through Causal Dynamical Triangulations (CDT), posits that spacetime emerges from a quantum superposition of geometries. CDT uses discrete building blocks to model spacetime, ensuring causality and allowing for a well-defined path integral over geometries, which aims to recover classical spacetime at large scales.
CDT differs from other quantum gravity theories by maintaining a clear distinction between time and space, preserving causality at a fundamental level. Unlike approaches such as Loop Quantum Gravity or String Theory, CDT constructs spacetime from simplexes (triangular building blocks) and focuses on a sum-over-histories approach that respects Lorentzian structure, aiming to produce a classical spacetime continuum in the large-scale limit.
In CDT, simplices (higher-dimensional generalizations of triangles) serve as the fundamental building blocks of spacetime. These simplices are pieced together in a way that respects causality and allows for a discrete approximation of spacetime. By summing over possible configurations of these simplices, CDT attempts to model the quantum behavior of spacetime and derive its emergent large-scale structure.
Evidence supporting CDT includes its ability to reproduce key features of classical spacetime, such as dimensionality and geometric properties, at large scales. Numerical simulations of CDT have shown that it can lead to a universe with four-dimensional spacetime, similar to our observed universe. These results suggest that CDT can successfully bridge the gap between quantum and classical descriptions of spacetime.
CDT faces several challenges, including computational complexity in simulating large systems, understanding the continuum limit, and addressing potential anomalies at small scales. Additionally, integrating matter fields and other fundamental forces within the CDT framework remains an ongoing area of research. Despite these challenges, CDT continues to be a promising approach in the quest for a quantum theory of gravity.