Classical geometry from a physical state in canonical quantum gravity

We construct a weave state which approximates a degenerate three-metric of rank 2 at large scales. It turns out that a nondegenerate metric region can be evolved from this degenerate metric by the classical Ashtekar equations; hence, the degeneracy of the three-metrics is not preserved by the evolution of Ashtekar’s equations. As the s-knot state corresponding to this weave is shown to solve all the quantum constraints in loop quantum gravity, a physical state in canonical quantum gravity is related to the familiar classical geometry.