**Authors**: Craig J. Hogan

**Date**: 29 May 2009

**Abstract**: General arguments based on black hole physics suggest the possibility of a new kind of indeterminacy in the relative position of bodies in spacetime, corresponding to the diffraction limit of Planck wavelength radiation. Suitably designed instruments should display a new phenomenon, a randomly varying shear in relative position, with a flat power spectral density at low frequencies given approximately by the Planck time, and with no other parameters. An effective theory is presented to connect fundamental theory with macroscopic phenomena, such as the statistical properties of noise in signals of interferometers. A theory of spacetime wavefunctions based on the paraxial wave equation with a carrier wave at the Planck frequency, or equivalently a Schrodinger wave equation, is motivated by a particular interpretation of Matrix theory in the macroscopic limit. A model based on gaussian-beam solutions of this equation is used to derive formulas in the time and frequency domain for autocorrelation of beamsplitter position. The cross-correlation between two non-coincident interferometers as a function of separation is estimated. The cross-correlation signature may be exploited in the design of experiments to provide convincing evidence for or against the holographic hypothesis.

0905.4803
(/preprints)

2009-06-01, 20:06
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*