the line connecting the planet to the Sun sweeps out equal areas in equal time
The basic idea involves applying Haggard and Rovelli's result about the rate of evolution of a quantum mechanical system, according to which a system in equilibrium evolves in such a way as to pass through an equal number of states in equal time intervals. Quantum Gravity (of the Loop variety) tells us that the fundamental observable in a quantum theory of geometry is the area of a surface embedded within a given spacetime.
The area swept out by a planet during the course of its motion around the Sun is far greater than $ A \gg A_p $(the basic quantum of area, where $A_p = l_p^2$ is the Planck length). However, if classical geometry as described by (classical) general relativity arises from a more fundamental quantum theory, and consistency of any theory of quantum gravity would require this, then it is natural to assume that the macroscopic area $\delta A$ swept out of by a planet in a time $\delta t$ emerges from an ensemble of quanta of Planck areas. If one could argue that planetary motion corresponds to an "equilibrium" configuration of the gravitational field, then Haggard and Rovelli's result can be applied and we obtain Kepler's Second Law as a trivial consequence.
