We discuss the meaning of probabilities in the many worlds interpretation of quantum mechanics. We start by presenting very briefly the many worlds theory, how the problem of probability arises, and some unsuccessful attempts to solve it in the past. Then we criticize a recent attempt by Deutsch to derive the quantum mechanical probabilities from the nonprobabilistic parts of quantum mechanics and classical decision theory. We further argue that the Born probability does not make sense even as an additional probability (...) rule in the many worlds theory. Our conclusion is that the many worlds theory fails to account for the probabilistic statements of standard (collapse) quantum mechanics. (shrink)

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics.In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to (...) modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation of the problem. (shrink)

There are currently several versions of Everett's relative state interpretation of quantum mechanics, responding to a number of perceived problems for the original proposal. One of those problems is whether Everett's idea is in accord with the standard 'probabilistic' interpretation implicit in the Born rule. I argue in defence of what appears to be Everett's original view on this. The contribution I aim to make is a more complete discussion of the central issues of the identity of objects and observers (...) over time and how the concept of expectation can be applied when all 'possible' outcomes of a measurement process are regarded as actually occurring. (shrink)

We argue that certain types of many minds (and many worlds) interpretations of quantum mechanics, e.g. Lockwood ([1996a]), Deutsch ([1985]) do not provide a coherent interpretation of the quantum mechanical probabilistic algorithm. By contrast, in Albert and Loewer's ([1988]) version of the many minds interpretation, there is a coherent interpretation of the quantum mechanical probabilities. We consider Albert and Loewer's probability interpretation in the context of Bell-type and GHZ-type states and argue that it implies a certain (weak) form of nonlocality. (...) 1 Introduction 2 Albert and Loewer's interpretation 3 Probabilities in Lockwood's interpretation 4 Sets of minds and their correlations 5 Many minds and GHZ. (shrink)

Hugh Everett III describes a quantum measurement as resulting in the “branching” of the quantum state of observer and measured system, with all possible measurement outcomes represented by the ensuing branches of the total quantum state. But Everett does not specify a general rule for decomposing a quantum state into branches, and commentators have long puzzled over how, and even whether, to regard Everett׳s notion of branching states as physically meaningful. It is common today to appeal to decoherence considerations as (...) a way of giving physical content to the Everettian notion of branches, but these appeals to decoherence are often regarded as considerations foreign to Everett׳s own approach. This paper contends that this assessment is only half right: though he does not invoke environmental decoherence, Everett does appeal to decoherence considerations, broadly understood, in his treatment of measurement. Careful consideration of his idealized models of measurement, and of the significance he ascribes to the branching of states corresponding to definite measurement outcomes, reveals that his notion of branching refers to a special physical characteristic of elements of a particular decomposition, namely the absence of interference between these component states as a result of the particular dynamics governing the evolution of the system. Characterizations of branching that appeal to the results of modern decoherence theory should therefore be regarded as a natural development of Everett׳s own physically meaningful conception of branching. (shrink)

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.

I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.

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)

Recent work on probability in the Everett interpretation of quantum mechanics yields a decision-theoretic derivation of David Lewis’ Principal Principle, and hence a general metaphysical theory of probability; part 1 is a discussion of this remarkable result. I defend the claim that the ‘subjective uncertainty’ principle is required for the derivation to succeed, arguing that it amounts to a theoretical identification of chance. In part 2, I generalize this account, and suggest that the Everett interpretation, in combination with a plausible (...) view of natural laws, has the potential to provide a reductive theory of metaphysical modality. I defend the resulting naturalistic modal realism, and outline some of its implications for other parts of metaphysics. (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)

This is a philosophical paper in favor of the many-worlds interpretation of quantum theory. The necessity of introducing many worlds is explained by analyzing a neutron interference experiment. The concept of the “measure of existence of a world” is introduced and some difficulties with the issue of probability in the framework of the MWI are resolved.

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)

I survey some of the connections between the metaphysics of the relation between mind and matter, and quantum theory’s measurement problem. After discussing the metaphysics, especially the correct formulation of physicalism, I argue that two state-reduction approaches to quantum theory’s measurement problem hold some surprises for philosophers’ discussions of physicalism. Though both approaches are compatible with physicalism, they involve a very different conception of the physical, and of how the physical underpins the mental, from what most philosophers expect. And one (...) approach exemplifies a a problem in the definition of physicalism which the metaphysical literature has discussed only in the abstract. A version of the paper has appeared in Consciousness and Human Identity, ed. John Cornwell, OUP 1998. (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)