The quantum geometric limit

This talk presents fundamental quantum limits to measuring space-time geometry. By applying the fundamental physical bounds to measurement accuracy to ensembles of clocks and signals moving in curved spacetime -- e.g., the global positioning system -- I derive 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 $rt/\pi \ell_P t_P$, where $\ell_P$, $t_P$ are the Planck length and time.