  By analyzing a gedanken experiment designed to measure the distance $l$
between two spatially separated points, we find that this distance cannot be
measured with uncertainty less than $(ll_P^2)^{1/3}$, considerably larger than
the Planck scale $l_P$ (or the string scale in string theories), the
conventional wisdom uncertainty in distance measurements. This limitation to
space-time measurements is interpreted as resulting from quantum fluctuations
of space-time itself. Thus, at very short distance scales, space-time is
"foamy." This intrinsic foaminess of space-time provides another source of
noise in the interferometers. The LIGO/VIRGO and LISA generations of
gravity-wave interferometers, through future refinements, are expected to reach
displacement noise levels low enough to test our proposed degree of foaminess
in the structure of space-time. We also point out a simple connection to the
holographic principle which asserts that the number of degrees of freedom of a
region of space is bounded by the area of the region in Planck units.
