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AIP conference proceedings

State reduction and cosmic anisotropy

C. H. Woo

Published Jan 1, 1991• 0 citations
Publisher

Abstract

Between the quantum domain and the classical world of facts there is an intermediate domain for which a ‘‘classical’’ probabilistic description is appropriate. As a result of decoherence, such a description obeys the classical additivity of probabilities. In contrast to the usual interpretation in classical probability theory, however, the ‘‘classical’’ probability which emerges from an underlying quantum theory is meant to be applicable to a single system, such as the universe.It is argued that small inhomogeneities and anisotropies in the very early universe should be described probabilistically. If, furthermore, the transition between this probabilistic description and a later deterministic description happens as late as after the decoupling of photons, then the smoothness of the microwave background receives a different interpretation: it is not because the fluctuations at decoupling were extremely small, but because the contributions from different fluctuations add to smooth things out.

DOI
10.1063/1.40442

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Between the quantum domain and the classical world of facts there is an intermediate domain for which a ‘‘classical’’ probabilistic description is appropriate. As a result of decoherence, such a description obeys the classical additivity of probabilities. In contrast to the usual interpretation in classical probability theory, however, the ‘‘classical’’ probability which emerges from an underlying quantum theory is meant to be applicable to a single system, such as the universe.It is argued that small inhomogeneities and anisotropies in the very early universe should be described probabilistically. If, furthermore, the transition between this probabilistic description and a later deterministic description happens as late as after the decoupling of photons, then the smoothness of the microwave background receives a different interpretation: it is not because the fluctuations at decoupling were extremely small, but because the contributions from different fluctuations add to smooth things out.
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We sketch a quantum-mechanical framework for the universe as a whole. \nWithin that framework we propose a program for describing the ultimate \norigin in quantum cosmology of the "quasiclassical domain" of familiar experience and for characterizing the process of measurement. Predictions \nin quantum mechanics are made from probabilities for sets of alternative \nhistories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. \nDecoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative \nhistories of the universe. A quasiclassical domain consists of a branching set \nof alternative decohering histories, described by a coarse graining that is, in \nan appropriate sense, maximally refined consistent with decoherence, with \nindividual branches that exhibit a high level of classical correlation in time. \nWe pose the problem of making these notions precise and quantitative. A \nquasiclassical domain is emergent in the universe as a consequence of the \ninitial condition and the action function of the elementary particles. It is \nan important question whether all the quasiclassical domains are roughly \nequivalent or whether there are various essentially inequivalent ones. A \nmeasurement is a correlation with variables in a quasiclassical domain. An "observer" (or information gathering and utilizing system) is a complex \nadaptive system that has evolved to exploit the relative predictability of a \nquasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that \nresolution of many of the problems of interpretation presented by quantum \nmechanics is to be accomplished, not by further scrutiny of the subject as it \napplies to reproducible laboratory situations, but rather by an examination \nof alternative histories of the universe, stemming from its initial condition, \nand a study of the problem of quasiclassical domains.
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a description has a statistical character. Deterministic laws link it to statistical descriptions of the cosmic medium at later times, and because these laws do not privilege any position or direction in space, the same must be true of these descriptions. If the universe is infinite, we can identify the probability that the energy density at a particular instant and a particular point in space (relative to a system of spacetime coordinates in which the postulated spatial symmetries are manifest) lies in a given range with the fractional volume occupied by points where the energy density lies in this range; and similarly with all other probabilities that figure in the statistical description. The probabilities that figure in a complete description of the cosmic medium at any given moment thus have an exact and objective physical interpretation. The statistical entropy and the information associated with each cosmological probability distribution are likewise objective properties of the universe, defined in terms of relative frequencies or spatial averages.
On the line of a recent paper, the problem of interpretation of Quantum Theory (QT) is reconsidered in a cosmological perspective and of Bohr’s idea that the classical language is the language of our experience and QT acquires a meaning only with a reference to it. A classical or macroscopic level is distinguished and a quantum or microscopic one that is perceived only through the modifications that it induces in the first. The macroscopic state is specified by a classical energy-momentum tensor and conserved currents, which are supposed to have always well-defined values. The microscopic dynamics are expressed by the usual QT formalism. Fundamental idea: the usual probability rule of QT, based on an observables self-ajoint operators correspondence, is replaced with a distribution of probability directly for the macroscopic variables, defined in terms of the corresponding quantum operators and a quantum density operator. For the universe, a variance of the standard model with Ω=1 is assumed, one inflaton, a Goldstone type potential, initial time at t =−∞, expectation values of all fundamental fields vanishing for t → −∞. The scalar fluctuations in the cosmic microwave background can be correctly explained giving appropriate values to the potential parameters, but the absence of the tensor fluctuations remains not understood. This seems to suggest that gravity is a pure classical phenomenon, what could be consistently accommodated in our framework but it is inconsistent with the usual formalism.
There is a persistent state of confusion regarding the account of the quantum origin of the seeds of cosmological structure during inflation. The issue is the transition from the quantum uncertainties in the homogeneous and isotropic initial state, into the late-time "classical" anisotropies and inhomogeneities. There seems to be a widespread belief that decoherence addresses the issue in a satisfactory way. This view is taken, often implicitly, by most researchers working in the field. This can be seen most clearly in those accounts intended on facing the issue directly. For instance, a recent article [C. Kiefer and D. Polarski, arXiv: 0810.0087] argues just that, and presents a detailed explanation of the justifications. The explicit nature of that account will allow us to discuss the issue in detail. There are, of course, various other works that often indirectly address the issue with similar approaches (see Refs. 2–13). This type of arguments do not only implicitly assume that decoherence offers a satisfactory solution to the measurement problem in quantum mechanics, but also that, in particular, such approach is applicable to these quantum aspects of cosmology. We will review here, why do we, together with various other researchers in the field, consider that this assumption is not correct in general. Moreover as previously discussed in Refs. 22–26, we will argue that the cosmological situation is one where the measurement problem of quantum mechanics appears in a particular exacerbated form, and that, it is this, even sharper conundrum, that should be addressed when dealing with the inflationary account of the origin of the seeds of cosmic structure in the early Universe. We briefly discuss the ideas behind what we feel might be a promising approach to deal with this problem.