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Holographic Quantum Geometry

Technology Type:  Influences on other Scientific Disciplines

Interferometers as Probes of Planckian Quantum Geometry

** Originator:  Craig J. Hogan
** Contact:  Sam Waldman  sam.waldman(at)ligo.org
** Institutions:  University of Chicago and Fermilab
** Supporting Agency:  U.S. Department of Energy
** Technology Source:  Advanced LIGO

Theoretical studies of black hole thermodynamics have long suggested an underlying two-dimensional nature to our three-dimensional world. Recent studies in string theory suggest that gravity may exist in 11-space time dimensions, most of which exist at the Planck scale but some of which may be observable at macroscopic length scales. Moreover recent cosmological evidence points to a cosmological constant 120 orders of magnitude times smaller than predicted by a naive counting of the quantum mechanical vacuum. From this mix of puzzling observations, Hogan et al. (PRD 2008) conjectured that our three-dimensional world could be an emergent property of a Planck-scale space-time.

According to this conjecture, information about spatial coordinates is transmitted through time by a Planck wavelength carrier. The carrier encodes two coordinates of a test mass and as the test mass propagates through time and space, diffraction of the carrier's finite wavelength creates uncertainty in the coordinates. This effect is physically observable if two coordinates of the same test mass are measured at two different times by a photon. In the presence of the "holographic noise", the mass will appear to "jitter" in the plane of the two coordinates. The jitter is understood to appear as a random shift of the coordinates in the plane transverse to the carrier by a Planck length in a Planck time.

Gravitational wave interferometer technology could provide a means to confirm this conjecture. Considered in this framework, the beamsplitter of a Michelson interferometer is a test mass measured by photons at two times separated by the round trip time of the arms. The Michelson geometry measures the X and Y coordinates simultaneously. In the language of gravitational wave interferometry, the effective strain of holographic noise is given by the square root of the Planck time: h ≈ 10^-22Hz^-1/2 

Since 2009, several members of the LIGO Laboratory have participated in the Fermilab Holometer, a purpose-built experiment designed to measure the holographic noise directly. Based on an original design by LIGO's Prof. Rainer Weiss, the experiment correlates the output of two overlapping interferometers. If the holographic noise exists, the two interferometers' beamsplitters will appear to move in a correlated fashion as a result of the space-time uncertainty. Because the noise occurs at the Planck frequency, the noise signal will be broad band, extending up to the 4 MHz bandwidth of the interferometers. Crucially, the experiment includes a null configuration, in which the two interferometers remain co-located but are rotated 90 degrees with respect to each other, removing the holographic correlation.

The work of the gravitational wave community has enabled the Fermilab Holometer and its design is based directly on GEO 600 topology and the Caltech 40 m prototype interferometer construction. The Holometer project uses LIGO electronic circuit designs and has even borrowed initial LIGO optics including a pre-mode cleaner. In short, the Fermilab Holometer has substantially benefited from the direct contributions of gravitational wave community ideas, designs and experience.

References

1.  Interferometers as Probes of Planckian Quantum Geometry  FERMILAB-PUB-10-036-A-T
2.  Indeterminacy of Holographic Quantum Geometry  C.J. Hogan, Phys. Rev. D 78, 087501 (2008)