  In Einstein's gedankenexperiment for measuring space and time, an ensemble of
clocks moving through curved spacetime measures geometry by sending signals
back and forth, as in the global positioning system (GPS). Combining well-known
quantum limits to measurement with the requirement that the energy density of
clocks and signals be be no greater than the black hole density leads to the
quantum geometric limit: the total number of ticks of clocks and clicks of
detectors that can be contained in a four volume of spacetime of radius r and
temporal extent t is less than or equal to rt/\pi l_P t_P, where l_P, t_P are
the Planck length and time. The quantum geometric limit suggests that each
event or `op' that takes place in a four-volume of spacetime is associated with
a Planck-scale area. This paper shows that the quantum geometric limit can be
used to derive general relativity: if each quantum event is associated with a
Planck-scale area removed from two-dimensional surfaces in the volume in which
the event takes place, then Einstein's equations must hold.
