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arXiv:gr-qc/0606120

A possible experimental test of quantized gravity

P. J. Salzman, Steven J. Carlip

Published Jun 28, 2006• 24 citations
arXivHTMLPDF

Abstract

While it is widely believed that gravity should ultimately be treated as a quantum theory, there remains a possibility that general relativity should not be quantized. If this is the case, the coupling of classical gravity to the expectation value of the quantum stress-energy tensor will naturally lead to nonlinearities in the Schrodinger equation. By numerically investigating time evolution in the nonrelativistic "Schrodinger-Newton" approximation, we show that such nonlinearities may be observable in the next generation of molecular interferometry experiments.

DOI
10.48550/arxiv.gr-qc/0606120

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While it is widely believed that gravity should ultimately be treated as a quantum theory, there remains a possibility that general relativity should not be quantized. If this is the case, the coupling of classical gravity to the expectation value of the quantum stress-energy tensor will naturally lead to nonlinearities in the Schrodinger equation. By numerically investigating time evolution in the nonrelativistic "Schrodinger-Newton" approximation, we show that such nonlinearities may be observable in the next generation of molecular interferometry experiments.
No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling between classical gravity and quantum matter according to the semi-classical Einstein equations, yields a nonlinear modification of the Schrödinger equation. Here, effects of this so-called Schrödinger-Newton equation are discussed, which allow for technologically feasible experimental tests.
Abstract In quantum mechanics, the time evolution of particles is given by the Schrödinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not required. This has been verified in countless experiments when the interaction is of electromagnetic origin, but also corrections due to the quantised field are readily observed. When the interaction is due to gravity, then one cannot expect to see effects of the quantised field in current-technology Earth-bound experiments. However, this does not yet guarantee that in the accessible regime, the time evolution is accurately given by the Schrödinger equation. Here we propose to measure the effects of an asymmetric mass configuration on a quantum particle in an interferometer. For this setup we show that with parameters within experimental reach, one can be sensitive to possible deviations from the Schrödinger equation, beyond the already verified lowest-order regime. Performing this experiment will hence directly test the nonclassical behaviour of a quantum particle in the gravitational field.
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.
The Schr\"odinger-Newton equation has frequently been studied as a nonlinear modification of the Schr\"odinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on the interference of massive particles is studied by numerically solving the Schr\"odinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment-induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics.
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.
Abstract We quote a definitive simple proof that neither classical stochastic dynamics nor quantum dynamics can be nonlinear if we stick to their standard statistical interpretations. A recently proposed optomechanical test of gravity’s classicality versus quantumness is based on the nonlinear Schrödinger—Newton equation (SNE) which is the nonrelativistic limit of standard semiclassical gravity. While in typical cosmological applications of semiclassical gravity the predicted violation of causality is ignored, it cannot be disregarded in applications of the SNE in high sensitive laboratory tests hoped for the coming years. We reveal that, in a recently designed experiment, quantum optical monitoring of massive probes predicts fake action-at-a-distance (acausality) on a single probe already. The proposed experiment might first include the direct test of this acausality.