  This letter analyzes the limits that quantum mechanics imposes on the
accuracy to which spacetime geometry can be measured. By applying the physics
of computation to ensembles of clocks, as in GPS, we present a covariant
version of the quantum geometric limit, which states that 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
x_P t_P, where x_P, t_P are the Planck length and time. The quantum geometric
bound limits the number of events or `ops' that can take place in a four-volume
of spacetime and is consistent with and complementary to the holographic bound
which limits the number of bits that can exist within a three-volume of
spacetime.
