What classicality? Decoherence and Bohr's classical concepts

Niels Bohr famously insisted on the indispensability of what he termed "classical concepts." In the context of the decoherence program, on the other hand, it has become fashionable to talk about the "dynamical emergence of classicality" from the quantum formalism alone. Does this mean that decoherence challenges Bohr's dictum -- for example, that classical concepts do not need to be assumed but can be derived? In this paper, we'll try to shed some light down the murky waters where formalism and philosophy mingle. To begin, we'll clarify the notion of classicality in the decoherence description. We'll then discuss Bohr's and Heisenberg's takes on the quantum-classical problem and reflect on the different meanings of the terms "classicality" and "classical concepts" in the writings of Bohr and his followers. This analysis will allow us to put forward some tentative suggestions for how we may better understand the relation between decoherence-induced classicality and Bohr's classical concepts.Comment: 6 page

Decoherence, the measurement problem, and interpretations of quantum mechanics

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.Comment: 41 pages. Final published versio

Chaos, Thermodynamics and Quantum Mechanics: an Application to Celestial Dynamics

We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar system as a whole as a case study: this author shows that the classicality of the planetary motion is ensured by the environment-induced decoherence. We show that equivalent results are provided by the theories of spontaneous fluctuations and that these latter theories, in some cases, result in a still faster process of decoherence. We show that, as an additional benefit, the assumption of spontaneous fluctuation makes it possible to genuinely derive thermodynamics from mechanics, namely, without implicitly assuming thermodynamics.Comment: 9 pages, two tables included, RevTex. Concluding part of Sec. IV revised and shortene

Decoherence: Concepts and Examples

We give a pedagogical introduction to the process of decoherence - the irreversible emergence of classical properties through interaction with the environment. After discussing the general concepts, we present the following examples: Localisation of objects, quantum Zeno effect, classicality of fields and charges in QED, and decoherence in gravity theory. We finally emphasise the important interpretational features of decoherence.Comment: 24 pages, LATEX, 9 figures, needs macro lamuphys.sty, to appear in the Proceedings of the 10th Born Symposiu

A model-theoretic interpretation of environmentally-induced superselection

Environmentally-induced superselection or "einselection" has been proposed as an observer-independent mechanism by which apparently classical systems "emerge" from physical interactions between degrees of freedom described completely quantum-mechanically. It is shown that einselection can only generate classical systems if the "environment" is assumed \textit{a priori} to be classical; einselection therefore does not provide an observer-independent mechanism by which classicality can emerge from quantum dynamics. Einselection is then reformulated in terms of positive operator-valued measures (POVMs) acting on a global quantum state. It is shown that this re-formulation enables a natural interpretation of apparently-classical systems as virtual machines that requires no assumptions beyond those of classical computer science.Comment: 15 pages, 1 figure; minor correction

An quantum approach of measurement based on the Zurek's triple model

In a close form without referring the time-dependent Hamiltonian to the total system, a consistent approach for quantum measurement is proposed based on Zurek's triple model of quantum decoherence [W.Zurek, Phys. Rev. D 24, 1516 (1981)]. An exactly-solvable model based on the intracavity system is dealt with in details to demonstrate the central idea in our approach: by peeling off one collective variable of the measuring apparatus from its many degrees of freedom, as the pointer of the apparatus, the collective variable de-couples with the internal environment formed by the effective internal variables, but still interacts with the measured system to form a triple entanglement among the measured system, the pointer and the internal environment. As another mechanism to cause decoherence, the uncertainty of relative phase and its many-particle amplification can be summed up to an ideal entanglement or an Shmidt decomposition with respect to the preferred basis.Comment: 22pages,3figure

Decoherence, einselection, and the quantum origins of the classical

Decoherence is caused by the interaction with the environment. Environment monitors certain observables of the system, destroying interference between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly non-local "Schr\"odinger cat" states. Classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit: Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation.Comment: Final version of the review, with brutally compressed figures. Apart from the changes introduced in the editorial process the text is identical with that in the Rev. Mod. Phys. July issue. Also available from http://www.vjquantuminfo.or