I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and the (...) boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate. (shrink)

R.I.G Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful.

In this sequence of philosophical essays about natural science, the author argues that fundamental explanatory laws, the deepest and most admired successes of modern physics, do not in fact describe regularities that exist in nature. Cartwright draws from many real-life examples to propound a novel distinction: that theoretical entities, and the complex and localized laws that describe them, can be interpreted realistically, but the simple unifying laws of basic theory cannot.

We prove a uniqueness theorem showing that, subject to certain natural constraints, all 'no collapse' interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determine (definite, sharp). We show how certain versions of the modal interpretation, Bohm's 'causal' interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different proposals for selecting (...) the preferred determinate observable--either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a 'beable' in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space). (shrink)

Unexpected discoveries in nonequilibrium physics and nonlinear dynamics are changing our understanding of complex phenomena. Recent research has revealed fundamental new properties of matter in far-from-equilibrium conditions, and the prevalence of instability-where small changes in initial conditions may lead to amplified effects.

We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.

It is demonstrated that neither the arguments leading to inconsistencies in the description of quantum-mechanical measurement nor those “explaining” the process of measurement by means of thermodynamical statistics are valid. Instead, it is argued that the probability interpretation is compatible with an objective interpretation of the wave function.

Conceptual Foundations of Quantum Mechanics provides a detailed view of the conceptual foundations and problems of quantum physics, and a clear and comprehensive account of the fundamental physical implications of the quantum formalism. This book deals with nonseparability, hidden variable theories, measurement theories and several related problems. Mathematical arguments are presented with an emphasis on simple but adequately representative cases. The conclusion incorporates a description of a set of relationships and concepts that could compose a legitimate view of the world.

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...) The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

The integration of recent work on decoherence into a so-called modal interpretation offers a promising new approach to the measurement problem in quantum mechanics. In this paper I explain and develop this approach in the context of the interactive interpretation presented in Healey (1989). I begin by questioning a number of assumptions which are standardly made in setting up the measurement problem, and I conclude that no satisfactory solution can afford to ignore the influence of the environment. Further, I argue (...) that there are good reasons to believe that on a modal interpretation environmental interactions rapidly ensure that a quantummechanically describable apparatus indeed records a definite result following a measurement interaction. (shrink)

It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical (...) theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the “projection postulate.” But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory. (shrink)

According to the modal interpretation, the standard mathematical framework of quantum mechanics specifies the physical magnitudes of a system, which have definite values. Probabilities are assigned to the possible values that these magnitudes may adopt. The interpretation is thus concerned with physical properties rather than with measurement results: it is a realistic interpretation. One of the notable achievements of this interpretation is that it dissolves the notorious measurement problem. The papers collected here, together with the introduction and concluding critical appraisal, (...) explain the various forms of the modal interpretation, survey its achievements, and discuss those problems that have yet to be solved. Audience: Philosophers of science, theoretical physicists, and graduate students in these disciplines. (shrink)

Atomistic metaphysics motivated an explanatory strategy which science has pursued with great success since the scientific revolution. By decomposing matter into its atomic and subatomic parts physics gave us powerful explanations and accurate predictions as well as providing a unifying framework for the rest of science. The success of the decompositional strategy has encouraged a widespread conviction that the physical world forms a compositional hierarchy that physics and other sciences are progressively articulating. But this conviction does not stand up to (...) a closer examination of how physics has treated composition, as a variety of case studies will show. (shrink)

By questioning the validity of some of our basic concepts, such as space, object, and causality, quantum physics contributes quite decisively to the dramatic changes now taking place in our world picture. Veiled Reality provides a detailed view of the reasons why such a questioning arises, a survey of the corresponding conceptual and theoretical problems, and a comprehensive, up-to-date account, useful to scientists and epistemologists alike, of the various ways present-day physicists tackle these problems.The book deals with the E.P.R. reality (...) criterion, local causality, and quantum measurement including relativistic quantum collapse, decoherence theories, consistent histories approaches, and ontologically interpretable theories. Questions bearing on the connection between counterfactuality and realism, intersubjective agreement, and limits of the bearing of the verbs “to have” and “to be,” follow naturally from the analysis and are thoroughly examined. Finally, distinguishing between empirical reality and a veiled independent reality whose only knowable features are structural yields a clue to a plausible interpretation of current physics.Accessible to readers with only very elementary background in modern physics, Veiled Reality offers nonspecialists, including students in physics and philosophy, easy access to basic problems in the foundation of physics. (shrink)

This article argues that most of the approaches to the foundations of statistical mechanics have severed their link with the original foundational project, the project of demonstrating how real mechanical systems can behave thermodynamically.

The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by (...) applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties. (shrink)

We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statistical mechanics. Our claim is based on the observations that dynamical systems for which statistical mechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behaviour for the finite set of observables that matter, but the behaviour must ensure that (...) the approach to equilibrium for these observables is on the appropriate time-scale. (shrink)

Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that the Born (...) probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation. (shrink)

The aim of this paper is to consider in what sense the modal-Hamiltonian interpretation of quantum mechanics satisfies the physical constraints imposed by the Galilean group. In particular, we show that the only apparent conflict, which follows from boost-transformations, can be overcome when the definition of quantum systems and subsystems is taken into account. On this basis, we apply the interpretation to different well-known models, in order to obtain concrete examples of the previous conceptual conclusions. Finally, we consider the role (...) played by the Casimir operators of the Galilean group in the interpretation. (shrink)

Interference phenomena are a well-known and crucial feature of quantum mechanics, the two-slit experiment providing a standard example. There are situations, however, in which interference effects are (artificially or spontaneously) suppressed. We shall need to make precise what this means, but the theory of decoherence is the study of (spontaneous) interactions between a system and its environment that lead to such suppression of interference. This study includes detailed modelling of system-environment interactions, derivation of equations (‘master equations’) for the (reduced) state (...) of the system, discussion of time-scales etc. A discussion of the concept of suppression of interference and a simplified survey of the theory is given in Section 2, emphasising features that will be relevant to the following discussion (and restricted to standard non-relativistic particle quantum mechanics.[1] A partially overlapping field is that of decoherent histories, which proceeds from an abstract definition of loss of interference, but which we shall not be considering in any detail. (shrink)

In this paper we argue that the formalisms for decoherence originally devised to deal just with closed or open systems can be subsumed under a general conceptual framework, in such a way that they cooperate in the understanding of the same physical phenomenon. This new perspective dissolves certain conceptual difficulties of the einselection program but, at the same time, shows that the openness of the quantum system is not the essential ingredient for decoherence. †To contact the authors, please write to: (...) Mario Castagnino, CONICET-IAFE, Universidad Nacional de Buenos Aires, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires, Argentina; Roberto Laura, IFIR-Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario, Argentina; Olimpia Lombardi, CONICET-Universidad Nacional de Buenos Aires, C. Larralde 3440, 6°D, 1430, Buenos Aires; e-mail: [email protected]. (shrink)

El propósito del presente artículo es evaluar en qué sentido y bajo qué condiciones la ergodicidad es relevante para explicar el éxito de la mecánica estadística. Se objeta la positión de quienes sostienen que la ergodicidad es irrelevante para tal explicatión, y se señala que las propiedades ergódicas desempeñan diferentes papeles en la mecánica estadística del equilibrio y en la descriptión de la evolución hacia el equilibrio: es posible prescindir de la ergodicidad en el primer caso pero no en el (...) segundo. Sobre esta base, se reformularán las definiciones de ergodicidad y mezcla, relativizándolas a la macrovariable particular cuya evolución irreversible se desea describir. Finalmente, se enfatiza la importancia de tomar en cuenta la elaboratión de modelos para evaluar la utilizatión de los métodos de Gibbs. /// The aim of this paper is to consider in what sense and under what conditions ergodicity is relevant for explaining the success of Statistical Mechanics. We argue against those who claim that ergodicity is irrelevant to this explanation, by noting that ergodic properties play different roles in equilibrium Statistical Mechanics and in the description of the approach to equilibrium: it is possible to do without it in the first case but not in the second one. On this basis, we reformulate the definitions of ergodicity and mixing, relativizing them to the particular macrovariable whose irreversible evolution is to be described. Finally, we stress the relevance of taking into account model-construction for evaluating the use of Gibbs' methods. (shrink)

The program of a physical concept of information is outlined in the framework of quantum theory. A proposal is made for how to avoid the intuitive introduction of observables. The conventional and the Everett interpretations in principle may lead to different dynamical consequences. An ensemble description occurs without the introduction of an abstract concept of information.

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’, which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion (...) of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems. (shrink)