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.
Taking the Average
Spacetime can take on a huge number of possible shapes. According to quantum theory, the shape we are most likely to observe is a superposition, or weighted average, of all these possibilities. When constructing shapes from triangles, theorists weight each shape depending on how exactly they glue together triangles to form it. The authors have discovered that the triangles must follow certain rules for the average to match what we observe. In particular, the triangles must have a built-in arrow of time.
Two Possible Gluing Rules
Anything Goes: When physicists consider all possible ways of arranging triangles—a total free-for-all—the outcome is a tightly wadded ball with an infinite number of dimensions. (below)
Restricted by Principle of Causality: When physicists add the rule that adjacent triangles must have a consistent notion of time—so that cause and effect are unambiguously distinguished—the outcome is a four-dimensional spacetime that looks tantalizingly like our universe. (below)