Indeterminacy of Holographic Quantum Geometry

Abstract

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.

4 pages, LaTeX. Considerably shortened from earlier version. Conclusions are unchanged. Submitted to PRD

References in corpus (18)

• The World as a Hologram
• M Theory As A Matrix Model: A Conjecture
• Thermodynamics of Spacetime: The Einstein Equation of State
• The holographic principle
• Detector Description and Performance for the First Coincidence Observations between LIGO and GEO
• An interferometric gravitational wave detector as a quantum-gravity apparatus
• Entropy of Null Surfaces and Dynamics of Spacetime
• The Search for Quantum Gravity Signals
• Gravity-wave interferometers as probes of a low-energy effective quantum gravity
• Gravity: A New Holographic Perspective
• A phenomenological description of quantum-gravity-induced space-time noise
• Measurement of Quantum Fluctuations in Geometry
• Quantum-gravity-motivated Lorentz-symmetry tests with laser interferometers
• Generic predictions of quantum theories of gravity
• Quantum Gravitational Uncertainty of Transverse Position
• Spacetime Indeterminacy and Holographic Noise
• Holographic Indeterminacy, Uncertainty and Noise
• Quantum Indeterminacy of Emergent Spacetime

Cited by in corpus (14)

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• Interferometric Constraints on Quantum Geometrical Shear Noise Correlations
• Holographic Geometry and Noise in Matrix Theory
• Statistical Measures of Planck Scale Signal Correlations in Interferometers
• Statistical Model of Exotic Rotational Correlations in Emergent Space-Time
• Pattern of perturbations from a coherent quantum inflationary horizon
• Revisiting holographic dark energy from the perspective of multi-messenger gravitational wave astronomy: future joint observations with short gamma-ray bursts
• Models of Exotic Interferometer Cross-Correlations in Emergent Space-Time
• Relativistic Generalized Uncertainty Principle and Its Implications
• Level of holographic noise in interferometry