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arXiv:quant-ph/9508021 · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences

Quantum spacetime fluctuations and primary state diffusion

Ian Colin Percival

Published Nov 8, 1995• 82 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1098/rspa.1995.0139

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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.
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.
Abstract Primary quantum state diffusion (PSD) theory is an alternative quantum theory from which classical dynamics, quantum dynamics and localization dynamics are derived. It is based on four principles, that a system is represented by an operator, its state by a normalized state vector, the state vector satisfies a Langevin-Itô state diffusion equation, and the resultant density operator for an ensemble must satisfy an equation of elementary Lindblad form. There are three conditions. The ז0 first determines the operator, to within an undetermined universal time constant ז0. The second and third conditions put opposing bounds on ז0. Dissipation of coherence is distinguished from destruction of coherence. The state diffusion destroys coherence and produces the localization or reduction that makes classical dynamics possible. PSD theory is a development of the environmental quantum state diffusion theory of Gisin and Percival and particularly resembles earlier proposals by Gisin and by Milburn. It is also related to the spontaneous localization theories of Ghirardi, Rimini and Weber, of Diósi and of Pearle. The non-relativistic PSD theory is of value only for systems which occupy small regions of space. Special relativity is needed for more extended systems even when they contain only slowly moving massive particles. Experiments on coherence lifetimes and matter interferometry are proposed which either measure ז0 or put bounds on it, and which might distinguish between PSD and ordinary quantum mechanics.
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.
We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also spacetime points are raised to the status of matrices [equivalently operators]. These matrices obey a deterministic Lagrangian dynamics at the Planck scale. By coarse-graining this matrix dynamics over time intervals much larger than Planck time, one derives quantum theory as a low energy emergent approximation. If a sufficiently large number of degrees of freedom get entangled, spontaneous localisation takes place, leading to the emergence of classical spacetime geometry and a classical universe. In our theory, dark energy is shown to be a large-scale quantum gravitational phenomenon. Quantum indeterminism is not fundamental, but results from our not probing physics at the Planck scale.
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.