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arXiv:quant-ph/9607011 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Detection of spacetime fluctuation by a model interferometer

Ian Colin Percival, Walter T. Strunz

Published Feb 8, 1997• 77 citations
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Abstract

In papers on primary state diffusion (Percival 1994, 1995), numerical estimates suggested that fluctuations in the spacetime metric on the scale of the Planck time (ca.10–44s) could be detected using atom interferometers. In this paper we first specify a stochastic metric obtained from fluctuations that propagate with the velocity of light, and then develop the non–Markovian quantum state diffusion theory required to estimate the resulting decoherence effects on a model matter interferometer. Both commuting and non–commuting fluctuations are considered. The effects of the latter are so large that if they applied to some real atom interferometry experiments they would have suppressed the observed interference. The model is too crude to conclude that such fluctuations do not exist, but it does demonstrate that the small numerical value of the Planck time does not alone prevent experimental access to Planck–scale phenomena in the laboratory.

DOI
10.1098/rspa.1997.0025

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In papers on primary state diffusion (Percival 1994, 1995), numerical estimates suggested that fluctuations in the spacetime metric on the scale of the Planck time (ca.10–44s) could be detected using atom interferometers. In this paper we first specify a stochastic metric obtained from fluctuations that propagate with the velocity of light, and then develop the non–Markovian quantum state diffusion theory required to estimate the resulting decoherence effects on a model matter interferometer. Both commuting and non–commuting fluctuations are considered. The effects of the latter are so large that if they applied to some real atom interferometry experiments they would have suppressed the observed interference. The model is too crude to conclude that such fluctuations do not exist, but it does demonstrate that the small numerical value of the Planck time does not alone prevent experimental access to Planck–scale phenomena in the laboratory.
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.
Abstract Non-differentiable fluctuations in spacetime on a Planck scale introduce stochastic terms into the equations for quantum states, resulting in a proposed new foundation for an existing alternative quantum theory: primary state diffusion (PSD). Planck-scale stochastic spacetime structure results in quantum fluctuations, whilst larger-scale curvature is responsible for gravitational forces. The gravitational field and the quantum fluctuation field are the same, differing only in scale. The quantum mechanics of small systems, classical mechanics of large systems and the physics of quantum experiments are all derived dynamically, without any prior division into classical and quantum domains, and without any measurement hypothesis. Unlike the earlier derivation of PSD, the new derivation, based on a stochastic spacetime differential geometry, has essentially no free parameters. However, many features of this structure remain to be determined. The theory is falsifiable in the laboratory, and critical matter interferometry experiments, to distinguish it from ordinary quantum mechanics, might be feasible within the next decade.
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.
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.
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at the Planck scale. If directions in emergent quantum geometry do not commute, new quantum-geometrical degrees of freedom can produce detectable macroscopic deviations from classicality: spatially coherent, transverse position indeterminacy between any pair of world lines, with a displacement amplitude much larger than the Planck length. Positions of separate bodies are entangled with each other, and undergo quantum-geometrical fluctuations that are not describable as metric fluctuations or gravitational waves. These fluctuations can either be cleanly identified or ruled out using interferometers. A Planck-precision test of the classical coherence of space-time on a laboratory scale is now underway at Fermilab.