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arXiv:quant-ph/9811059 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Decoherence of quantum wave packets due to interaction with conformal space–time fluctuations

W. L. Power, Ian Colin Percival

Published Apr 8, 2000• 49 citations
arXivHTMLPDF

Abstract

One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper, we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero–point fluctuations, interact with the wave packets of massive particles. The result of this interaction is to produce decoherence within the wave packets which could be accessible in experiments at the atomic scale.Using a simple nonlinear model for the coherence properties of the gravitational field, we derive an equation for the evolution of the density matrix of such a wave packet. Following the primary state diffusion programme, the most promising source of space–time fluctuations for experimental detection is these zero–point energy fluctuations. According to our model, the absence of intrinsic irremovable decoherence in matter interferometry experiments puts bounds on some of the parameters of quantum gravity theories. Current experiments give λ >18, where λtPlanck is an effective cut–off for the validity of low–energy quantum gravity theories.

DOI
10.1098/rspa.2000.0544

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Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Mar 8, 1999•6 citations
One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper, we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero–point fluctuations, interact with the wave packets of massive particles. The result of this interaction is to produce decoherence within the wave packets which could be accessible in experiments at the atomic scale.Using a simple nonlinear model for the coherence properties of the gravitational field, we derive an equation for the evolution of the density matrix of such a wave packet. Following the primary state diffusion programme, the most promising source of space–time fluctuations for experimental detection is these zero–point energy fluctuations. According to our model, the absence of intrinsic irremovable decoherence in matter interferometry experiments puts bounds on some of the parameters of quantum gravity theories. Current experiments give λ >18, where λtPlanck is an effective cut–off for the validity of low–energy quantum gravity theories.
One of the biggest unsolved problems in fundamental physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance makes the issue particularly evasive. Recent models of decoherence demonstrated that conformal fluctuations of spacetime can change the correlation function of matter-waves. Latest progress on conformal decomposition in canonical gravity makes it possible for these decoherence models to be developed without freezing any degrees of freedom for general relativity. The new approach allows the roles of the conformal field and (spin-2) gravitational waves to be identified in the Brownian motion principle based on which Planck scale physics could be accessed. A spacecraft mission called Hyper was proposed to conduct matter-wave experiments in space. Orders of magnitude improvement may be gained by going into orbit reducing the effects of environmental interactions. Such experiments could put constraints on the upper bounds of measurements of decoherence of a matter-wave interferometer due to quantum fluctuations of spacetime.
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show that the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future. Physics on the large scale is based on Einstein’s theory of general relativity (GR), which interprets gravity as the curvature of spacetime. Despite its tremendous success as an isolated
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by the recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations, and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future.
One of the biggest unsolved problems in fundamental physics is the unification of quantum mechanics and gravity. One of the consequences of unification could be the existence of "incoherent conformal waves" in gravitational fields due to quantum mechanical zero-point fluctuations. Recent theories have demonstrated that these fluctuations change the first order correlation function of matterwaves. A spacecraft mission called Hyper is being designed to conduct matterwave experiments in space. An order of magnitude improvement may be gained by going into orbit reducing the effects of environmental interactions. Such experiments could put constraints on the upper bands of measurements of decoherence of a matterwave interferometer due to quantum fluctuations.
Abstract We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be accessible by relatively inexpensive table-top experiments, way before the scales where true quantum gravity effects become important. Therefore, they can provide a first experimental view on gravity in the quantum regime. We will survey models of decoherence induced both by classical and quantum gravitational fluctuations; it will be manifest that a clear understanding of gravitational decoherence is still lacking. Next we will review models where quantum theory is modified, under the assumption that gravity causes the collapse of the wave functions, when systems are large enough. These models challenge the quantum-gravity interplay, and can be tested experimentally. In the last part we have a look at the state of the art of experimental research. We will review efforts aiming at more and more accurate measurements of gravity ( G and g ) and ideas for measuring conventional and unconventional gravity effects on nonrelativistic quantum systems.
It has been suggested by Percival and Strunz that fluctuations in spacetime on the Planck scale might be detected by atom interferometers. Thus far, the models used to predict the impact of these fluctuations have been limited to a description of the atoms in terms of two states corresponding to the two arms of an interferometer. In this paper we generalise this model to include the effects of spacetime fluctuations on atomic wavepackets. When the fluctuations are assumed to have simple non–commutative properties, the density matrix of a wave packet is shown to evolve according to an equation of the same general form as that hypothesised by Ghirardi, Rimini and Weber, as a way of dealing with the measurement problem in quantum mechanics.