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The classical limit of quantum mechanics: Self-induced decoherence and macroscopicity

Mario Castagnino, Olímpia Lombardi

Jan 1, 20063 citations

The role of self-induced decoherence in the problem of the classical limit of quantum mechanics

Mario Castagnino, Manuel Gadella

Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity: when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system becomes equivalent to the description of an ensemble of classical trajectories on phase space weighted by their corresponding probabilities.Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity: when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system becomes equivalent to the description of an ensemble of classical trajectories on phase space weighted by their corresponding probabilities.

arXiv:quant-ph/0306014Jun 2, 20034 citations

Self-Induced Decoherence and the Classical Limit of Quantum Mechanics

Mario Castagnino, Olímpia Lombardi

In this paper we argue that the emergence of the classical world from the underlying quantum reality involves two elements: self-induced decoherence and macroscopicity. Self-induced decoherence does not require the openness of the system and its interaction with the environment: a single closed system can decohere when its Hamiltonian has continuous spectrum. We show that, if the system is macroscopic enough, after self-induced decoherence it can be described as an ensemble of classical distributions weighted by their corresponding probabilities. We also argue that classicality is an emergent property that arises when the behavior of the system is described from an observational perspective.In this paper we argue that the emergence of the classical world from the underlying quantum reality involves two elements: self-induced decoherence and macroscopicity. Self-induced decoherence does not require the openness of the system and its interaction with the environment: a single closed system can decohere when its Hamiltonian has continuous spectrum. We show that, if the system is macroscopic enough, after self-induced decoherence it can be described as an ensemble of classical distributions weighted by their corresponding probabilities. We also argue that classicality is an emergent property that arises when the behavior of the system is described from an observational perspective.

Philosophy of ScienceDec 1, 200555 citations

Decoherence and Classical Behaviour in Quantum Mechanics

Gianfausto Dell’Antonio, Rodolfo Figari, Alessandro Teta

Springer eBooksJan 1, 20030 citations

On the classical limit of quantum mechanics

Jorge Bernal, A. Martín-Ruiz, J. C. García-Melgarejo

Jan 6, 20110 citations

Decoherence and Intertheory Relations in Quantum Realism

Nahuel Sznajderhaus

The complex relation between quantum mechanics and classical mechanics is crucial in the philosophy of modern physics, and it cuts across current quantum physics. This paper is divided in two parts. In the first part I will offer a critical analysis of the role that decoherence plays in the account of the quantum-classical limit. In the second part I will mention three ways in which philosophers are engaging with the realist interpretation of quantum mechanics in light of the assessment that the problem of the quantum-classical limit is still open to debate. My main claim is that the problem of the quantum-classical limit is overrated and it receives too much attention for the realist who looks at quantum mechanics. The question that the realist wants to focus on is the crucial interpretation question: what is a quantum system?The complex relation between quantum mechanics and classical mechanics is crucial in the philosophy of modern physics, and it cuts across current quantum physics. This paper is divided in two parts. In the first part I will offer a critical analysis of the role that decoherence plays in the account of the quantum-classical limit. In the second part I will mention three ways in which philosophers are engaging with the realist interpretation of quantum mechanics in light of the assessment that the problem of the quantum-classical limit is still open to debate. My main claim is that the problem of the quantum-classical limit is overrated and it receives too much attention for the realist who looks at quantum mechanics. The question that the realist wants to focus on is the crucial interpretation question: what is a quantum system?

Metatheoria – Revista de Filosofía e Historia de la CienciaApr 1, 20190 citations

The Problem of the Classical Limit of Quantum Mechanics and the Role of Self-Induced Decoherence

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