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arXiv:0803.3447 · Classical and Quantum Gravity

Intrinsic and fundamental decoherence: issues and problems

Charis Anastopoulos, B. L. Hu

Published Jul 22, 2008• 37 citations
arXivHTMLPDF

Abstract

We investigate the meaning of gravity-induced decoherence in quantum theory, known as ‘intrinsic’ or ‘fundamental’ decoherence in the literature. We explore a range of issues relevant to this problem, including the meaning of modified uncertainty relations, the interpretations of the Planck scale, the distinction between quantum and stochastic fluctuations and the role of the time variable in quantum mechanics. We examine the specific physical assumptions that enter into different approaches to the subject. In particular, we critique two representative approaches that identify time fluctuations as the origin of intrinsic or fundamental decoherence: one that models the fluctuations by stochastic process and one that purports to derive decoherence from the quantum fluctuations of real clocks.

DOI
10.1088/0264-9381/25/15/154003

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We investigate the meaning of gravity-induced decoherence in quantum theory, known as ‘intrinsic’ or ‘fundamental’ decoherence in the literature. We explore a range of issues relevant to this problem, including the meaning of modified uncertainty relations, the interpretations of the Planck scale, the distinction between quantum and stochastic fluctuations and the role of the time variable in quantum mechanics. We examine the specific physical assumptions that enter into different approaches to the subject. In particular, we critique two representative approaches that identify time fluctuations as the origin of intrinsic or fundamental decoherence: one that models the fluctuations by stochastic process and one that purports to derive decoherence from the quantum fluctuations of real clocks.
We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences, following a broadly Kantian tradition and distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Within this framework, theories are conceptual constructs applying to models generated in the phenomenal world within limited contexts.The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases of quantum mechanical states (entanglement). The quantum correlations are shared globally in the process of environment-induced decoherence whereby locally generated correlations are removed, the removal being especially manifest in the case of systems that appear as classical ones, in which case the process is almost instantaneous, being, in all likelihood, driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining its finest details, since Planck scale physics remains an obscure terrain. In other words, the present day quantum theory holds within a limited context set by the Planck scale.
Gravitational decoherence (GD) refers to the effects of gravity in actuating the classical appearance of a quantum system. Because the underlying processes involve issues in general relativity (GR), quantum field theory (QFT), and quantum information, GD has fundamental theoretical significance. There is a great variety of GD models, many of them involving physics that diverge from GR and/or QFT. This overview has two specific goals along with one central theme: (i) present theories of GD based on GR and QFT and explore their experimental predictions; (ii) place other theories of GD under the scrutiny of GR and QFT, and point out their theoretical differences. We also describe how GD experiments in space in the coming decades can provide evidence at two levels: (a) discriminate alternative quantum theories and non-GR theories; (b) discern whether gravity is a fundamental or an effective theory.
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
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schr\\"{o}dinger dynamics based on discrete time intervals with an intrinsic uncertainty. The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, in a way consistent with other modifications suggested by quantum gravity and string theory .
It has already been suggested that quantum theory needs to be reformulated or modified in order to explain the measurement process and the successive collapse of the wave- function. However, there are also models of another type which keep quantum theory intact and instead modify the classical gravity by introducing stochasticity to it. These models suggest that there is a fluctuation in the background gravitational field which eventually results in the decoherence of the wavefunction. These fluctuations limit the precision with which one can measure the properties of a spacetime geometry with a quantum probe. Two similar models along this line have been suggested by Karolyhazy (K-model) and Diósi(D-model). They are based upon apparently different spacetime bounds. The results obtained for the coherence length are also somewhat different. In this article, we show that, given certain conditions apply, the minimal spacetime bounds in these two models are equivalent. We also derive the two-point correlation for the fluctuation potential in K-model which turns out to be non-white, unlike in D-model, where the corresponding correlation is white noise in time. In our opinion, this is the origin of discrepancy in the predictions of the two models. We argue that the noise correlation cannot be determined uniquely from a given spacetime bound.
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.