Dr. Michael Reisenberger
Theiss Research
Project Title
Classical and Quantum Gravity Without Constraints
Project Summary
Gravity bends light. The proposal is to reformulate Einstein's theory of gravity, describing the gravitational field (almost) entirely in terms of its effect on light rays, and to begin to develop a corresponding quantum theory. Einstein's theory describes gravity when quantum phenomena can be neglected. To explore quantum gravity experiments are needed, and here plausible theories are invaluable. Generically quantum gravitational phenomena are far too small to be measured, but in a given theory there usually are some effects that, by a conspiracy of factors particular to that theory, are much larger than would be expected on general grounds, providing testable predictions.
After 80 years of searching we have only pieces of plausible theories, but in 1993 a radical new guiding principle was proposed: that the three dimensional world of our experience is a sort of holographic projection of an underlying two dimensional world. This principle was argued to be a consequence of quantum mechanics and the gravitational bending of light (and apparently it is realized in quantum models of certain universes different from ours). The proposed description of gravity is the ideal setting to evaluate these arguments, and to incorporate this holographic principle in a quantum theory of gravity.
Technical Abstract
It is proposed to develop a canonical framework for classical and quantum gravity using free initial data on null hypersurfaces, specifically on "double null sheets". These are swept out by the two congruences of null geodesics emerging normally toward the future from a space-like disk, and are truncated before the geodesics cross.
Advantages are: There are no constraints; Gauge is essentially fixed, facilitating the definition of observables and evolution; The framework is ideal for attempting a proof, for vacuum gravity, of Bousso's conjectured entropy bound, and to look for a quantization compatible with the holographic principle; The framework is "quasi-local": Data on a double null sheet defines the geometry of its domain of dependence, without assumptions about global spacetime structure. No "state of the universe" is needed. Larger regions are described by consistent data on a network of double null sheets.
The two main goals of the present project are to find the consistency conditions on data on different double null sheets, and to quantize the data on a single double null sheet, using the Poisson bracket recently obtained by the author (leaving for the future the quantum implementation of the consistency conditions, the last step in a complete quantization).
Hide Technical Abstract
It is proposed to develop a canonical framework for classical and quantum gravity using free initial data on null hypersurfaces, specifically on "double null sheets". These are swept out by the two congruences of null geodesics emerging normally toward the future from a space-like disk, and are truncated before the geodesics cross.
Advantages are: There are no constraints; Gauge is essentially fixed, facilitating the definition of observables and evolution; The framework is ideal for attempting a proof, for vacuum gravity, of Bousso's conjectured entropy bound, and to look for a quantization compatible with the holographic principle; The framework is "quasi-local": Data on a double null sheet defines the geometry of its domain of dependence, without assumptions about global spacetime structure. No "state of the universe" is needed. Larger regions are described by consistent data on a network of double null sheets.
The two main goals of the present project are to find the consistency conditions on data on different double null sheets, and to quantize the data on a single double null sheet, using the Poisson bracket recently obtained by the author (leaving for the future the quantum implementation of the consistency conditions, the last step in a complete quantization).
Hide Technical Abstract
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