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arXiv:0801.3411

Gravitational waves, diffusion and decoherence

Serge Reynaud, Brahim Lamine, Marc-Thierry Jaekel

Published Jan 22, 2008• 0 citations
arXivHTMLPDF

Abstract

The quite different behaviors exhibited by microscopic and macroscopic systems with respect to quantum interferences suggest that there may exist a naturally frontier between quantum and classical worlds. The value of the Planck mass (22$μ$g) may lead to the idea of a connection between this borderline and intrinsic fluctuations of spacetime. We show that it is possible to obtain quantitative answers to these questions by studying the diffusion and decoherence mechanisms induced on quantum systems by gravitational waves generated at the galactic or cosmic scales. We prove that this universal fluctuating environment strongly affects quantum interferences on macroscopic systems, while leaving essentially untouched those on microscopic systems. We obtain the relevant parameters which, besides the ratio of the system's mass to Planck mass, characterize the diffusion constant and decoherence time. We discuss the feasibility of experiments aiming at observing these effects in the context of ongoing progress towards more and more sensitive matter-wave interferometry.

DOI
10.48550/arxiv.0801.3411

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The quite different behaviors exhibited by microscopic and macroscopic systems with respect to quantum interferences suggest that there may exist a naturally frontier between quantum and classical worlds. The value of the Planck mass (22μμμg) may lead to the idea of a connection between this borderline and intrinsic fluctuations of spacetime. We show that it is possible to obtain quantitative answers to these questions by studying the diffusion and decoherence mechanisms induced on quantum systems by gravitational waves generated at the galactic or cosmic scales. We prove that this universal fluctuating environment strongly affects quantum interferences on macroscopic systems, while leaving essentially untouched those on microscopic systems. We obtain the relevant parameters which, besides the ratio of the system's mass to Planck mass, characterize the diffusion constant and decoherence time. We discuss the feasibility of experiments aiming at observing these effects in the context of ongoing progress towards more and more sensitive matter-wave interferometry.
The quite different behaviors exhibited by microscopic and macroscopic systems with respect to quantum interferences suggest the existence of a borderline beyond which quantum systems loose their coherences and can be described classically. Gravitational waves, generated within our galaxy or during the cosmic expansion, constitute a universal environment susceptible to lead to such a quantum decoherence mechanism. We assess this idea by studying the quantum decoherence due to gravitational waves on typical microscopic and macoscopic systems, namely an atom interferometer (HYPER) and the Earth-Moon system. We show that quantum interferences remain unaffected in the former case and that they disappear extremely rapidly in the latter case. We obtain the relevant parameters which, besides the ratio of the system's mass to Planck mass, characterize the loss of quantum coherences.
The quite different behaviors exhibited by microscopic and macroscopic systems with respect to quantum interferences suggest the existence of a borderline beyond which quantum systems loose their coherences and can be described classically. Gravitational waves, generated within our galaxy or during the cosmic expansion, constitute a universal environment susceptible to lead to such a quantum decoherence mechanism. We assess this idea by studying the quantum decoherence due to gravitational waves on typical microscopic and macoscopic systems, namely an atom interferometer (HYPER) and the Earth-Moon system. We show that quantum interferences remain unaffected in the former case and that they disappear extremely rapidly in the latter case. We obtain the relevant parameters which, besides the ratio of the system's mass to Planck mass, characterize the loss of quantum coherences.
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that any such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
Stochastic backgrounds of gravitational waves are intrinsic fluctuations of spacetime which lead to an unavoidable decoherence mechanism. This mechanism manifests itself as a degradation of the contrast of quantum interferences. It defines an ultimate decoherence border for matter-wave interferometry using larger and larger molecules. We give a quantitative characterization of this border in terms of figures involving the gravitational environment as well as the sensitivity of the interferometer to gravitational waves. The known level of gravitational noise determines the maximal size of the molecular probe for which interferences may remain observable. We discuss the relevance of this result in the context of ongoing progresses towards more and more sensitive matter-wave interferometry.
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.