  A new kind of quantum indeterminacy of transverse position is shown to arise
from quantum degrees of freedom of spacetime, based on the assumption that
classical trajectories can be defined no better than the diffraction limit of
Planck scale waves. Indeterminacy of the angular orientation of particle
trajectories due to wave/particle duality at the Planck scale leads to
indeterminacy of a nearly-flat spacetime metric, described as a small
nonvanishing quantum commutation relation between transverse position operators
at different events along a null trajectory. An independent derivation of the
same effect is presented based on the requirement of unitarity in black hole
evaporation. The indeterminacy is interpreted as a universal holographic
quantum spacetime noise, with a frequency-independent spectrum of metric
perturbation amplitude, h_H^2^{1/2} \simeq \sqrt{l_P}=2.3 \times 10^{-22}
/\sqrt{Hz}, where l_P denotes the Planck length. The effect is estimated to be
directly measurable using current interferometer technology similar to LIGO and
LISA.
