A particular form for the quantum indeterminacy of relative spacetime position of events is derived from the context of a holographic geometry with a minimum length at the Planck scale. The indeterminacy predicts fluctuations from a classically defined geometry in the form of “holographic noise” whose spatial character, absolute normalization, and spectrum are predicted with no parameters. The noise has a distinctive transverse spatial shear signature and a flat power spectral density given by the Planck time. An interferometer signal displays noise due to the uncertainty of relative positions of reflection events. The noise corresponds to an accumulation of phase offset with time that mimics a random walk of those optical elements that change the orientation of a wavefront. It only appears in measurements that compare transverse positions and does not appear at all in purely radial position measurements. A lower bound on holographic noise follows from a covariant upper bound on gravitational entropy. The predicted holographic noise spectrum is estimated to be comparable to measured noise in the currently operating interferometric gravitational-wave detector GEO600. Because of its transverse character, holographic noise is reduced relative to gravitational wave effects in other interferometer designs, such as the LIGO observatories, where beam power is much less in the beam splitter than in the arms.
Physical Review D
- Pub Date:
- May 2008
- Phenomenology of quantum gravity;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Phenomenology
- 7 pages, 2 figures, LaTeX. Extensive rewrite of original version, including more detailed analysis. Main result is the same but the estimate of noise in strain units for GEO600, showing 1/f behavior at low f and flat at high f, is improved. To appear in Phys. Rev. D