This story is a supplement to the feature "Using Causality to Solve the Puzzle of Quantum Spacetime" which was printed in the July 2008 issue of Scientific American.
String theory
The approach favored by most theoretical physicists, it is a theory not just of quantum gravity but of all matter and forces. It is based on the idea that particles (including the hypothetical ones that transmit gravity) are vibrating strings.
Loop Quantum Gravity
The main alternative to string theory, it invokes a new technique for applying quantum rules to Einstein’s general theory of relativity. Space is divided into discrete “atoms” of volume.
Euclidean Quantum Gravity
Made famous by physicist Stephen Hawking, this approach supposes that spacetime emerges from a grand quantum average of all possible shapes. It puts time on the same footing as space.
Causal Dynamical Triangulations
This approach, the subject of this article, is a modern version of the Euclidean approach. It approximates spacetime as a mosaic of triangles, which have a built-in distinction between space and time. On small scales, spacetime takes on a fractal shape.
