The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

It has been suggested, on the one hand, that quantum states are just states of knowledge; and, on the other, that quantum theory is merely a theory of correlations. These suggestions are confronted with problems about the nature of psycho-physical parallelism and about how we could define probabilities for our individual future observations given our individual present and previous observations. The complexity of the problems is underlined by arguments that unpredictability in ordinary everyday neural functioning, ultimately stemming from small-scale uncertainties (...) in molecular motions, may overwhelm, by many orders of magnitude, many conventionally recognized sources of observed ``quantum'' uncertainty. Some possible ways of avoiding the problems are considered but found wanting. It is proposed that a complete understanding of the relationship between subjective experience and its physical correlates requires the introduction of mathematical definitions and indeed of new physical laws. (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 interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best (...) available interpretation defended. The main objections to the interpretation, including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all. (shrink)

This work is a critique of the program of "environment-induced decoherence" as advocated by Zurek, Zeh and Joos, among others. In particular, the alleged relevance of decoherence for a solution of the "measurement problem" is subjected to a detailed philosophical analysis. In the first chapter, an attempt is made to unravel what exactly this "measurement problem" amounts to for the decoherence theorists. The second chapter reviews the standard decoherence literature. The third chapter starts with a brief discussion of the philosophical (...) implications of the decoherence program, followed by a non-standard reconstruction of the decoherence argument that aims to uncover some (mostly hidden) assumptions underlying the approach. It is argued that different subsets of these assumptions result in different versions of the decoherence argument. Next, these assumptions are investigated in more detail, and a number of open problems for the decoherence approach is formulated, in addition to the well-known "problem of outcomes". These problems concern the interpretational relevance of the preferred basis, the role and status of the ignorance interpretation of mixed states, imperfect decoherence and the role of the environment and the definition of subsystems. The fourth chapter addresses the question to what extent the embedding of decoherence in an Everett-like interpretational framework, such as Zurek's "existentional interpretation" and Wallace's structural-realistic version of the many-worlds interpretation, helps to resolve these problems. The main conclusions are formulated in the fifth chapter. Namely: 1) decoherence cannot address the "preferred-basis problem" without adding new interpretational axioms to the standard formalism, 2) the the locality principle (that says that the environment is the "irrelevant" part and should therefore be ignored) is not only problematic but also interpretationally superfluous, 3) the decoherence approach, when formulated in terms of the standard interpretation of quantum mechanics, is predicated on a solution of the "problem of outcomes" and thus cannot claim to account (even partially) for the latter, and 4) that the results of the decoherence program do not increase the plausibility of a realist interpretation of the quantum state. (shrink)

The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit, for the reader's consideration, a tentative resolution to it. In particular, I argue, in this dissertation, that the physical explanation for quantum speedup is precisely the fact that the phenomenon of quantum entanglement enables a quantum computer to fully exploit the representational capacity of Hilbert space. This is impossible for classical systems, joint states of which must always be representable as product (...) states. I begin the dissertation by considering, in Chapter 2, the most popular of the candidate physical explanations for quantum speedup: the many worlds explanation of quantum computation. I argue that, although it is inspired by the neo-Everettian interpretation of quantum mechanics, unlike the latter it does not have the conceptual resources required to overcome objections such as the so-called `preferred basis objection'. I further argue that the many worlds explanation, at best, can serve as a good description of the physical process which takes place in so-called network-based computation, but that it is incompatible with other models of computation such as cluster state quantum computing. I next consider, in Chapter 3, a common component of most other candidate explanations of quantum speedup: quantum entanglement. I investigate whether entanglement can be said to be a necessary component of any explanation for quantum speedup, and I consider two major purported counter-examples to this claim. I argue that neither of these, in fact, show that entanglement is unnecessary for speedup, and that, on the contrary, we should conclude that it is. In Chapters 4 and 5 I then ask whether entanglement can be said to be sufficient as well. In Chapter 4 I argue that despite a result that seems to indicate the contrary, entanglement, considered as a resource, can be seen as sufficient to enable quantum speedup. Finally, in Chapter 5 I argue that entanglement is sufficient to explain quantum speedup as well. (shrink)

I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.

The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

A short review of some recent developments in the philosophy of physics is presented. I focus on themes which illustrate relations and points of common interest between philosophy of physics and three of its `neighboring' elds: Physics, metaphysics and general philosophy of science. The main examples discussed in these three `border areas' are decoherence and the interpretation of quantum mechanics; time in physics and metaphysics; and methodological issues surrounding the multiverse idea in modern cosmology.

The decision-theoretic account of probability in the Everett or many-worlds interpretation, advanced by David Deutsch and David Wallace, is shown to be circular. Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic.

The decision-theoretic account of probability in the Everett or many-worlds interpretation, advanced by David Deutsch and David Wallace, is shown to be circular. Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic.

The aim of this paper is to give a systematic account of the so-called “measurement problem” in the frame of the standard interpretation of quantum mechanics. It is argued that there is not one but five distinct formulations of this problem. Each of them depends on what is assumed to be a “satisfactory” description of the measurement process in the frame of the standard interpretation. Moreover, the paper points out that each of these formulations refers not to a unique problem, (...) but to a set of sub-problems. (shrink)

I discuss three connections between Dummett's writings about time and philosophical aspects of physics. The first connection arises from remarks of Dummett's about the different relations of observation to time and to space. The main point is uncontroversial and applies equally to classical and quantum physics. It concerns the fact that perceptual processing is so rapid, compared with the typical time-scale on which macroscopic objects change their observable properties, that it engenders the idea of a `common now', spread across space. (...) The other two connections are specific to quantum theory, as interpreted along the lines of Everett. So for these two connections, the physics side is controversial, just as the philosophical side is. In Section 3, I connect the subjective uncertainty before an Everettian `splitting' of the multiverse to Dummett's suggestion, inspired by McTaggart, that a complete, i.e. indexical-free description of a temporal reality is impossible. And in Section 4, I connect Barbour's denial that time is real---a denial along the lines of Everett, rather than McTaggart---to Dummett's suggestion that statements about the past are not determinately true or false, because they are not effectively decidable. (shrink)

Time, along with concepts as space and matter, is bound to be a central concept of any physical theory. The chapter first discusses how time is treated similarly in quantum and classical theories. It then provides a few references on time‐reversal. The chapter discusses three chosen authors' (Paul Busch, Jan Hilgevoord and Jos Uffink) clarifications of uncertainty principles in general. Next, the chapter follows Busch in distinguishing three roles for time in quantum physics. They are external time, intrinsic time and (...) observable time. It also provides a brief discussion on time operators, in particular Pauli's influential proof. Finally, the chapter talks about time‐energy uncertainty principles with intrinsic times. (shrink)

The degree-of-presence concept, accompanying that of the wavefunction-reality postulate, is introduced and studied in two ways. To begin with, an incomplete exposition of the present author's views is given. Subsequently, a short historical and philosophical review of answers to the question about the meaning of indeterminate individual-system probabilities is presented from the literature. It is done in the form of a carefully selected collage of quotations mostly with polemic comments by the present author and with further elaboration of his point (...) of view. The advocated notion of ‘degree of presence’ generalizes the intuitively most easily acceptable idea of ‘delocalization’ in wavelike behavior of a quantum system. (shrink)

This paper gives a philosophical assessment of the Montevideo interpretation of quantum theory, advocated by Gambini, Pullin and co-authors. This interpretation has the merit of linking its proposal about how to solve the measurement problem to the search for quantum gravity: namely by suggesting that quantum gravity makes for fundamental limitations on the accuracy of clocks, which imply a type of decoherence that “collapses the wave-packet”. I begin by sketching the topics of decoherence, and quantum clocks, on which the interpretation (...) depends. Then I expound the interpretation, from a philosopher's perspective. Finally, in Section 6, I argue that the interpretation, at least as developed so far, is best seen as a form of the Everett interpretation: namely with an effective or approximate branching, that is induced by environmental decoherence of the familiar kind, and by the Montevideans’ “temporal decoherence”. (shrink)