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Holographic Noise in Interferometers

Craig J. Hogan

University of Chicago and Fermilab


Arguments based on general principles of quantum mechanics suggest that a minimum length or

time associated with Planck-scale unification may entail a new kind of observable uncertainty in

the transverse position of macroscopically separated bodies. Transverse positions vary randomly

about classical geodesics in space and time by about the geometric mean of the Planck scale and

separation, on a timescale corresponding to their separation. An effective theory based on a Planck

information flux limit, and normalized by the black hole entropy formula, is developed to predict

measurable correlations, such as the statistical properties of noise in interferometer signals. A con-

nection with holographic unification is illustrated by representing Matrix theory position operators

with a Schroedinger wave equation, interpreted as a paraxial wave equation with a Planck frequency

carrier. Solutions of this equation are used to derive formulas for the spectrum of beamsplitter

position fluctuations and equivalent strain noise in a Michelson interferometer, determined by the

Planck time, with no other parameters. The spectral amplitude of equivalent strain derived here is

a factor of √? smaller than previously published estimates. Signals in two nearly-collocated interferometers are predicted to be highly correlated, a feature that may provide convincing evidence for or against this interpretation of holography.

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