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arXiv:0807.3376

Decoherence and the (non)emergence of classicality

Steven J. Weinstein

Published Jul 22, 2008• 1 citation
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Abstract

We consider the claim that decoherence explains the emergence of classicality in quantum systems, and conclude that it does not. We show that, given a randomly chosen universe composed of a variety of subsystems, some of which are macroscopic and subject to decoherence-inducing interactions, and some of which are microscopic, the macroscopic subsystems will not display any distinctively classical behavior. Therefore, a universe in which macroscopic and microscopic do display distinct behavior must be in a very special, highly nongeneric quantum state.

DOI
10.48550/arxiv.0807.3376

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We consider the claim that decoherence explains the emergence of classicality in quantum systems, and conclude that it does not. We show that, given a randomly chosen universe composed of a variety of subsystems, some of which are macroscopic and subject to decoherence-inducing interactions, and some of which are microscopic, the macroscopic subsystems will not display any distinctively classical behavior. Therefore, a universe in which macroscopic and microscopic do display distinct behavior must be in a very special, highly nongeneric quantum state.
We consider the claim that decoherence explains the emergence of classicality in quantum systems, and conclude that it cannot. We show that, given a universe composed of a variety of subsystems, some of which are macroscopic and subject to decoherence-inducing interactions, and some of which are microscopic, the macroscopic subsystems do not display any distinctively classical behavior. Therefore, a universe in which macroscopic and microscopic do display distinct behavior must be in a very special, highly nongeneric quantum state.
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In this paper we will present the \\QTR{it}{self-induced approach} to decoherence, which does not require the interaction between the system and the environment: decoherence in closed quantum systems is possible. This fact has relevant consequences in cosmology, where the aim is to explain the emergence of classicality in the universe conceived as a closed (non-interacting) quantum system. In particular, we will show that the self-induced approach may be used for describing the evolution of a closed quantum universe, whose classical behavior arises as a result of decoherence.
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear explanation was given for why everyday objects, which are merely collections of atoms, are observed to obey Newton's laws. It would seem that, if quantum mechanics explains all the properties of atoms accurately, they, too, should obey quantum mechanics. This reasoning led some scientists to believe in a distinct macroscopic, or ``big and complicated,'' world in which quantum mechanics fails and classical mechanics takes over, although there has never been experimental evidence for such a failure. Even those who insisted that Newtonian mechanics would somehow emerge from the underlying quantum mechanics as the system became increasingly macroscopic were hindered by the lack of adequate experimental and theoretical tools. In the last decade, however, this quantum-to-classical transition has become accessible to experimental study and quantitative description, and the resulting insights are the subject of this article.
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to refer to the uncontrollable environment of a system (decoherence) nor to change the quantum laws itself (collapse models), but puts the stress on the limits of observability of quantum phenomena due to the imprecision of our measurement apparatuses. For a certain class of time evolutions it is this mere restriction to coarse-grained measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum formalism. But there also exist "non-classical" Hamiltonians for which a classical spatiotemporal description of the system's time evolution remains impossible even under fuzzy measurements or decoherence. It is argued that such Hamiltonians are unlikely to be spontaneously realized in nature because of their high complexity. The last part addresses the question of the origin of quantum randomness and proposes a link with mathematical undecidability.