Little, Brown, 1992 Review by Glenn Branch on Jul 5th 1999 Volume: 3, Number: 27.

There has been a lot of interest over the last fifteen years or so in no-collapse interpretations of quantum mechanics. The Bohm interpretation of quantum mechanics has received several thorough accounts, perhaps most notably by Bohm himself.

Jeffrey Barrett presents the most comprehensive study yet of a problem that has puzzled physicists and philosophers since the 1930s.

Presents a guide to the basics of quantum mechanics and measurement.

In a revolutionary new book, a theoretical physicist attacks the foundations of modern scientific theory, including the notion of time, as he shares evidence of ...

The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. _Philosophical Theories of Probability_ is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

Challenging, with several powerful arguments, some of our deepest beliefs about rationality, morality, and personal identity, Parfit claims that we have a false view about our own nature. It is often rational to act against our own best interersts, he argues, and most of us have moral views that are self-defeating. We often act wrongly, although we know there will be no one with serious grounds for complaint, and when we consider future generations it is very hard to avoid conclusions (...) that most of us will find very disturbing. (shrink)

A key to modern studies of 18th century Western philosophy, the Treatise considers numerous classic philosophical issues, including causation, existence, freedom and necessity and morality. This abridged edition has an introduction which explain's Hume's thought and places it in the context of its times.

This is a discussion of how we can understand the world-view given to us by the Everett interpretation of quantum mechanics, and in particular the role played by the concept of 'world'. The view presented is that we are entitled to use 'many-worlds' terminology even if the theory does not specify the worlds in the formalism; this is defended by means of an extensive analogy with the concept of an 'instant' or moment of time in relativity, with the lack of (...) a preferred foliation of spacetime being compared with the lack of a preferred basis in quantum theory. Implications for identity of worlds over time, and for relativistic quantum mechanics, are discussed. (shrink)

I address the problem of indefiniteness in quantum mechanics: the problem that the theory, without changes to its formalism, seems to predict that macroscopic quantities have no definite values. The Everett interpretation is often criticised along these lines, and I shall argue that much of this criticism rests on a false dichotomy: that the macroworld must either be written directly into the formalism or be regarded as somehow illusory. By means of analogy with other areas of physics, I develop the (...) view that the macroworld is instead to be understood in terms of certain structures and patterns which emerge from quantum theory (given appropriate dynamics, in particular decoherence). I extend this view to the observer, and in doing so make contact with functionalist theories of mind. (shrink)

State-reduction and the notion of actuality are compared to passage through time and the notion of the present; already in classical relativity the latter give rise to difficulties. The solution proposed here is to treat both tense and value-definiteness as relational properties or facts as relations; likewise the notions of change and probability. In both cases essential characteristics are absent: temporal relations are tenselessly true; probabilistic relations are deterministically true. The basic ideas go back to Everett, although the technical development (...) makes use of the decoherent histories theory of Griffiths, Omnès, and Gell-Mann and Hartle. Alternative interpretations of the decoherent histories framework are also considered. (shrink)

A variety of ideas arising in decoherence theory, and in the ongoing debate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert Space (...) norm. The familiar objection that Everett's approach yields probabilities different from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical, minimal criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of the chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content. (shrink)

A physical and mathematical framework for the analysis of probabilities in quantum theory is proposed and developed. One purpose is to surmount the problem, crucial to any reconciliation between quantum theory and space-time physics, of requiring instantaneous “wave-packet collapse” across the entire universe. The physical starting point is the idea of an observer as an entity, localized in space-time, for whom any physical system can be described at any moment, by a set of (not necessarily pure) quantum states compatible with (...) his observations of the system at that moment. The mathematical starting point is the theory of local algebras from axiomatic relativistic quantum field theory. A function defining thea priori probability of mistaking one local state for another is analysed. This function is shown to possess a broad range of appropriate properties and to be uniquely defined by a selection of them. Through a general model for observations, it is argued that the probabilities defined here are as compatible with experiment as the probabilities of conventional interpretations of quantum mechanics but are more likely to be compatible, not only with modern developments in mathematical physics, but also with a complete and consistent theory of measurement. (shrink)

It is proposed that the physical structure of an observer in quantum mechanics is constituted by a pattern of elementary localized switching events. A key preliminary step in giving mathematical expression to this proposal is the introduction of an equivalence relation on sequences of spacetime sets which relates a sequence to any other sequence to which it can be deformed without change of causal arrangement. This allows an individual observer to be associated with a finite structure. The identification of suitable (...) switching events in the human brain is discussed. A definition is given for the sets of sequences of quantum states which such an observer could occupy. Finally, by providing an a priori probability for such sets, the definitions are incorporated into a complete mathematical framework for a many-worlds interpretation. At a less ambitious level, the paper can be read as an exploration of some of the technical and conceptual difficulties involved in constructing such a framework. (shrink)

The book is an extended study of the problem of consciousness. After setting up the problem, I argue that reductive explanation of consciousness is impossible , and that if one takes consciousness seriously, one has to go beyond a strict materialist framework. In the second half of the book, I move toward a positive theory of consciousness with fundamental laws linking the physical and the experiential in a systematic way. Finally, I use the ideas and arguments developed earlier to defend (...) a form of strong artificial intelligence and to analyze some problems in the foundations of quantum mechanics. (shrink)

In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field theory. In this paper, which could also serve as an introduction to the earlier papers, three issues are discussed. First, a significant, but fairly straightforward, revision in some of the technical details is proposed. This is used as an opportunity to introduce the formalism. Then (...) the probabilistic structure of the theory is revised, and it is proposed that the experience of an individual observer can be modelled as the experience of observing a particular, identified, discrete stochastic process. Finally, it is argued that the formalism can be modified to give a physics in which no constants are required. Instead, “constants” have to be determined by observation, and are fixed only to the extent to which they have been observed. (shrink)

I explore whether it is possible to make sense of the quantum mechanical description of physical reality by taking the proper subject of physics to be correlation and only correlation, and by separating the problem of understanding the nature of quantum mechanics from the hard problem of understanding the nature of objective probability in individual systems, and the even harder problem of understanding the nature of conscious awareness. The resulting perspective on quantum mechanics is supported by some elementary but insufficiently (...) emphasized theorems. Whether or not it is adequate as a new Weltanschauung, this point of view toward quantum mechanics provides a different perspective from which to teach the subject or explain its peculiar character to people in other fields. (shrink)

Abstract: This paper assesses the Everettian approach to the measurement problem, especially the version of that approach advocated by Simon Saunders and David Wallace. I emphasise conceptual, indeed metaphysical, aspects rather than technical ones; but I include an introductory exposition of decoherence. In particular, I discuss whether---as these authors maintain---it is acceptable to have no precise definition of 'branch' (in the Everettian kind of sense). (A version of this paper will appear in a CTNS/Vatican Observatory volume on Quantum Theory and (...) Divine Action, ed. Robert Russell et al.). (shrink)

This paper is a response to some recent discussions of many-minds interpretations in the philosophical literature. After an introduction to the many-minds idea, the complexity of quantum states for macroscopic objects is stressed. Then it is proposed that a characterization of the physical structure of observers is a proper goal for physical theory. It is argued that an observer cannot be defined merely by the instantaneous structure of a brain, but that the history of the brain's functioning must also be (...) taken into account. Next the nature of probability in many-minds interpretations is discussed and it is suggested that only discrete probability models are needed. The paper concludes with brief comments on issues of actuality and identity over time. (shrink)

Technical results about the time dependence of eigenvectors of reduced density operators are considered, and the relevance of these results is discussed for modal interpretations of quantum mechanics which take the corresponding eigenprojections to represent definite properties. Continuous eigenvectors can be found if degeneracies are avoided. We show that, in finite dimensions, the space of degenerate operators has co-dimension 3 in the space of all reduced operators, suggesting that continuous eigenvectors almost surely exist. In any dimension, even when degeneracies are (...) hit, we find conditions under which a theorem due to Rellich can provide continuous eigenvectors. We use this result to formulate an extended version of the modal interpretation. We also discuss eigenvector instability which we argue poses a serious problem for the modal interpretation, even in our extended version. Many examples are given to illustrate the mathematics. (shrink)

A human brain operates as a pattern of switching. An abstract definition of a quantum mechanical switch is given which allows for the continual random fluctuations in the warm wet environment of the brain. Among several switch-like entities in the brain, we choose to focus on the sodium channel proteins. After explaining what these are, we analyse the ways in which our definition of a quantum switch can be satisfied by portions of such proteins. We calculate the perturbing effects of (...) normal variations in temperature and electric field on the quantum state of such a portion. These are shown to be acceptable within the fluctuations allowed for by our definition. Information processing and unpredictability in the brain are discussed. The ultimate goal underlying the paper is an analysis of quantum measurement theory based on an abstract definition of the physical manifestations of consciousness. The paper is written for physicists with no prior knowledge of neurophysiology, but enough introductory material has also been included to allow neurophysiologists with no prior knowledge of quantum mechanics to follow the central arguments. (shrink)