  An effective theory based on wave optics is used to describe indeterminacy of
position in holographic spacetime with a UV cutoff at the Planck scale.
Wavefunctions describing spacetime positions are modeled as complex
disturbances of quasi-monochromatic radiation. It is shown that the product of
standard deviations of two position wavefunctions in the plane of a holographic
light sheet is equal to the product of their normal separation and the Planck
length. For macroscopically separated positions the transverse uncertainty is
much larger than the Planck length, and is predicted to be observable as a
"holographic noise" in relative position with a distinctive shear spatial
character, and an absolutely normalized frequency spectrum with no parameters
once the fundamental wavelength is fixed from the theory of gravitational
thermodynamics. The spectrum of holographic noise is estimated for the GEO600
interferometric gravitational-wave detector, and is shown to approximately
account for currently unexplained noise between about 300 and 1400Hz. In a
holographic world, this result directly and precisely measures the fundamental
minimum interval of time.
