Abstract In the classical framework, not only can systems be identified by their space-time location, but they also possess mutually independent existences: they are individuals in the philosophical meaning of the concept. In the quantum domain, by contrast, matters are no so easy. Quantum systems cannot be labelled. Nor can they be assigned precise trajectories. Moreover, after interacting, quantum systems become interrelated in a way that does not diminish with either time or space: quantum correlations challenge the independent existence of the subsystems of a composite quantum system. Therefore, in the quantum framework the identification of open systems is a subtle issue. In this chapter I will emphasise the relative nature of open quantum systems in standard quantum mechanics by pointing out how this relativity is manifested under different forms: the relativity of entanglement, the identification of systems in decoherence, and the many ways in which a quantum system can be decomposed. Therefore, any view that considers open quantum systems as fundamental must take this relativity into account. The general purpose is to argue that the closed systems view and the open-system view are complementary approaches that need not be considered rival.
Abstract In the classical framework, not only can systems be identified by their space-time location, but they also possess mutually independent existences: they are individuals in the philosophical meaning of the concept. In the quantum domain, by contrast, matters are no so easy. Quantum systems cannot be labelled. Nor can they be assigned precise trajectories. Moreover, after interacting, quantum systems become interrelated in a way that does not diminish with either time or space: quantum correlations challenge the independent existence of the subsystems of a composite quantum system. Therefore, in the quantum framework the identification of open systems is a subtle issue. In this chapter I will emphasise the relative nature of open quantum systems in standard quantum mechanics by pointing out how this relativity is manifested under different forms: the relativity of entanglement, the identification of systems in decoherence, and the many ways in which a quantum system can be decomposed. Therefore, any view that considers open quantum systems as fundamental must take this relativity into account. The general purpose is to argue that the closed systems view and the open-system view are complementary approaches that need not be considered rival.
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their relations, are considered. Emphasis is placed on mutually global and irreducible structures. Is there a privileged structure of the closed system? Is there a preferred (bipartite) structure of an open system? Are there any practical advantages of certain alternative structures of the system? Is there a simple dynamical relation for a pair of structures? The [necessarily partial] answers are rather intriguing. Relativity of quantum correlations (that include entanglement as well as the "one-way" and "two-way" discord) is carefully presented. Emphasis is placed on the "parallel occurrence of decoherence" in the quantum Brownian motion. The environment-selected preferred structure of an open composite system is presented for a pair of harmonic oscillators (or the field modes). A limitation of the Nakajima-Zwanzig projection method appears as a consequence of quantum correlations relativity. Hence, describing dynamics of an alternate open-system is a delicate task. Certain interpretational issues, which include "quantum reference frames" issue, are discussed. Some recent experiments are also discussed. To this end, the option that "there are no particles" on the most fundamental physical level naturally follows. Certain open questions and prospects for further research are highlighted.
Abstract There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is evolving under the influence of its environment, this is always described in terms of a coupling between it and a separate system which taken together are isolated. In this chapter, we introduce the theoretical framework that we call standard quantum theory (ST), formulated in accordance with the closed systems view, and we consider approaches to interpreting the formalism of ST that take it to be complete in some sense. Broadly speaking, these can be grouped into two families. The first includes (neo-)Bohrian and related approaches, the second (neo-)Everettian. We argue, from the point of view of each, that although ST is formulated in accordance with the closed systems view, it is nevertheless ontologically committed to open systems in a way that other, for instance, classical, theoretical frameworks are not. We close with the suggestion that philosophical and foundational progress may be made through the adoption of an alternative theoretical framework, which might in principle involve a change in corresponding view, within which one can make sense of open systems dynamics in fundamental terms.
At present there is a consensus about the fact that the emergence of the classical world from the underlying quantum reality involves the physical phenomenon of decoherence, which is usually studied in the version proposed by Zurek and his collaborators. According to this version, decoherence is a process resulting from the interaction between a quantum system and its environment (environment-induced decoherence, EID); this process singles out the observables that receive definite classical values. The aim of this paper is to propose a top-down approach to decoherence, which takes the perspective of the whole closed system, and considers whether each set of degrees of freedom decoheres or not. This approach is more general than the orthodox open-system perspective and dissolves some of its conceptual problems. Although decoherence becomes relative to the way in which the closed system is decomposed, the quantum-to-classical transition defines unequivocally the realm of classicality by identifying the observables with classical-like behavior.
A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system. Not every set of alternative coarse-grained histories that can be described may be consistently assigned probabilities because of quantum mechanical interference between individual histories of the set. In “Copenhagen” quantum mechanics, probabilities can be assigned to histories of a subsystem that have been “measured”. In the quantum mechanics of closed systems, containing both observer and observed, probabilities are assigned to those sets of alternative histories for which there is negligible interference between individual histories as a consequence of the system's initial condition and dynamics. Such sets of histories are said to decohere. We define decoherence for closed systems in the simplified case when quantum gravity can be neglected and the initial state is pure. Typical mechanisms of decoherence that are widespread in our universe are illustrated. Copenhagen quantum mechanics is an approximation to the more general quantum framework of closed subsystems. It is appropriate when there is an approximately isolated subsystem that is a participant in a measurement situation in which (among other things) the decoherence of alternative registrations of the apparatus can be idealized as exact. Since the quantum mechanics of closed systems does not posit the existence of the quasiclassical domain of everyday experience, the domain of the approximate aplicability of classical physics must be explained.
A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system. Not every set of alternative coarse-grained histories that can be described may be consistently assigned probabilities because of quantum mechanical interference between individual histories of the set. In “Copenhagen ” quantum mechanics, probabilities can be assigned to histories of a subsystem that have been “measured”. In the quantum mechanics of closed systems, containing both observer and observed, probabilities are assigned to those sets of alternative histories for which there is negligible interference between individual histories as a consequence of the system’s initial condition and dynamics. Such sets of histories are said to decohere. We define decoherence for closed systems in the simplified case when quantum gravity can be neglected and the initial state is pure. Typical mechanisms of decoherence that are widespread in our universe are illustrated. Copenhagen quantum mechanics is an approximation to the more general quantum framework of closed subsystems. It is appropriate when there is an approximately isolated subsystem that is a participant in a measurement situation in which (among other things) the decoherence of alternative registrations of the apparatus can be idealized as exact. Since the quantum mechanics of closed systems does not posit the existence of the quasiclassical domain of everyday experience, the domain of the approximate aplicability of classical physics must be explained. We describe how a quasiclassical domain described by averages of densities of approximately conserved quantities could be an emergent feature of an initial condition of the universe that implies the approximate classical behavior of spacetime on accessible scales.
… in apprehension, how like a god! The beauty of the world … Shakespeare , Hamlet, Act 2 Scene 2 Open theories When it comes to the issues of reductionism, scientific methodology, and theory change, the views of Werner Heisenberg and Paul Dirac diverge in fundamental and interesting ways. They revisited their disagreements over these philosophical issues many times throughout their careers, and their disagreements can be most succinctly described as a debate over whether physical theories are “open” or “closed.” As we saw in the last chapter, Heisenberg's belief that classical and quantum mechanics are closed leads him to view these theories as perfectly accurate within their domains, inalterable, and correct for all time. Although Dirac never uses the term, his own views on classical and quantum mechanics can be fruitfully understood as a rival account of “open theories.” Dirac argues that even the most well-established parts of quantum theory are open to future revision; indeed he takes no part of physics to be a permanent achievement, correct for all time. Instead of viewing classical mechanics as a theory that had been replaced, he sees it as a theory that should continue to be developed, modified, and extended. Unlike Heisenberg, who views physics as a set of consistent axiomatic systems, Dirac sees physics as a discipline much closer to engineering.