  A model is proposed to demonstrate that classical general relativity can
emerge from loop quantum gravity, in a relational description of gravitational
field in terms of the coordinates given by matter. Local Dirac observables and
coherent states are defined to explore physical content of the model.
Expectation values of commutators between the observables for the coherent
states recover the four-dimensional diffeomorphism algebra and the large-scale
dynamics of the gravitational field relative to the matter coordinates. Both
results conform with general relativity up to calculable corrections near
singularities.
