The Everett (many-worlds) interpretation of quantum mechanics faces a prima facie problem concerning quantum probabilities. Research in this area has been fast-paced over the last few years, following a controversial suggestion by David Deutsch that decision theory can solve the problem. This article provides a non-technical introduction to the decision-theoretic program, and a sketch of the current state of the debate.

The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the second of two reviews of the Everett interpretation, and focuses on probability. Branching processes are identified as chance processes, and the squares of branch amplitudes are chances. Since branching is emergent, physical probability is emergent (...) as well. (shrink)

The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the first of two reviews of the Everett interpretation, and focuses on structure, with particular attention to the role of decoherence theory. Written in terms of the quantum histories formalism, decoherence theory just is the theory (...) of branching structure, in Everett's sense. (shrink)

The Everett interpretation of quantum mechanics - better known as the Many-Worlds Theory - has had a rather uneven reception. Mainstream philosophers have scarcely heard of it, save as science fiction. In philosophy of physics it is well known but has historically been fairly widely rejected. Among physicists, it is taken very seriously indeed, arguably tied for first place in popularity with more traditional operationalist views of quantum mechanics. In this article, I provide a fairly short and self-contained (...) introduction to the Everett interpretation as it is currently understood. I use little technical machinery, although I do assume the reader has encountered the measurement problem already. (shrink)

I propose an account of probability in the Everett interpretation of quantum mechanics. According to the account, probabilities are objective chances of centered propositions. As I show, the account solves a number of problems concerning the role of probability in the Everett interpretation. It also challenges an implicit assumption, concerning the aim and scope of fundamental physical theories, that is made throughout the philosophy of physics literature.

According to the Everett interpretation, branching structure and ratios of norms of branch amplitudes are the objective correlates of chance events and chances; that is, 'chance' and 'chancing', like 'red' and 'colour', pick out objective features of reality, albeit not what they seemed. Once properly identified, questions about how and in what sense chances can be observed can be treated as straightforward dynamical questions. On that basis, given the unitary dynamics of quantum theory, it follows that relative and (...) never absolute chances can be observed; that only on repetition of a large numbers of similar trials can relative probabilities be measured; and so on. The epistemology of objective chances can in this way be worked out from the dynamics. its curious features are thus explained. But one aspect of chance set-ups seems to resist this subsuming of chancing to branching: how is it that chance involves uncertainty? And if that is not possible, on Everettian lines, then the whole project is doomed. I argue that in fact there is no difficulty in making sense of uncertainty in the face of branching. Contrary to initial impressions, the unitary formalism is consistent with a well-defined notion of self-locating uncertainty. It is also consistent without: the mathematics under-determines the metaphysics in these respects. (shrink)

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)

David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation (...) in which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest. (shrink)

This is a review of Barrett and Byrne's commented edition of Everett's collected works, originally published in HOPOS 3, 348-352, but here including footnotes and references.

An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this context, it essentially succeeds. Some comments are made about the criticism of Deutsch's proof by Barnum, Caves, Finkelstein, Fuchs, and Schack; it is argued that the flaw which they point out in the proof does not apply if the Everett (...) interpretation is assumed. (shrink)

I consider exactly what is involved in a solution to the probability problem of the Everett interpretation, in the light of recent work on applying considerations from decision theory to that problem. I suggest an overall framework for understanding probability in a physical theory, and conclude that this framework, when applied to the Everett interpretation, yields the result that that interpretation satisfactorily solves the measurement problem. Introduction What is probability? 2.1 Objective probability and the Principal (...) Principle 2.2 Three ways of satisfying the functional definition 2.3 Cautious functionalism 2.4 Is the functional definition complete? The Everett interpretation and subjective uncertainty 3.1 Interpreting quantum mechanics 3.2 The need for subjective uncertainty 3.3 Saunders' argument for subjective uncertainty 3.4 Objections to Saunders' argument 3.5 Subjective uncertainty again: arguments from interpretative charity 3.6 Quantum weights and the functional definition of probability Rejecting subjective uncertainty 4.1 The fission program 4.2 Against the fission program Justifying the axioms of decision theory 5.1 The primitive status of the decision-theoretic axioms 5.2 Holistic scepticism 5.3 The role of an explanation of decision theory Conclusion. (shrink)

Three aspects of the Everett interpretation of quantum mechanics are considered. It is first shown that the proof of the metatheorem is not complete—thus it is an open question as to whether or not it is true. Next, some difficulties for the Everett interpretation and the metatheorem, which arise from consideration of the physics developed by observers in maverick universes, are discussed. Finally, it is shown that the universal state description of an ever-branching universe with each (...) branch corresponding to a possible perceived universe fails completely in the limit of an infinite number of successive branchings. (shrink)

In this article, I briefly explain the quantum measurement problem and the Everett interpretation, in a way that is faithful to modern physics and yet accessible to readers without any physics training. I then consider the metaphysical lessons for ontology from quantum mechanics under the Everett interpretation. My conclusions are largely negative: I argue that very little can be said in full generality about the ontology of quantum mechanics, because quantum mechanics, like abstract classical mechanics, is (...) a framework within which we can consider different physical theories which have very little in common at the level of ontology. Along the way I discuss, and criticise, several positive ontological proposals that have been made in the context of the Everett interpretation: ontologies based on the so-called "eigenstate-eigenvalue link", ontologies based on taking the "many-worlds" language seriously at the fundamental level, and ontologies that treat the wavefunction as a complex field on a high-dimensional space. (shrink)

Sometimes we learn what the world is like, and sometimes we learn where in the world we are. Are there any interesting differences between the two kinds of cases? The main aim of this article is to argue that learning where we are in the world brings into view the same kind of observation selection effects that operate when sampling from a population. I will first explain what observation selection effects are ( Section 1 ) and how they are relevant (...) to learning where we are in the world ( Section 2 ). I will show how measurements in the Many Worlds Interpretation of quantum mechanics can be understood as learning where you are in the world via some observation selection effect ( Section 3 ). I will apply a similar argument to the Sleeping Beauty Problem ( Section 4 ) and explain what I take the significance of the analogy to be ( Section 5 ). Finally, I will defend the Restricted Principle of Indifference on which some of my arguments depend ( Section 6 ). (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)

The Everett interpretation of quantum theory requires either the existence of an infinite number of conscious minds associated with each brain or the existence of one universal consciousness. Reasons are given, and the two ideas are compared.

The existence of probability in the sense of the frequency interpretation, i.e., probability as “long term relative frequency,” is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encountered in applying to the Everett interpretation previous results regarding relative frequency and probability in quantum mechanics. The ontology of the Everett interpretation in the Heisenberg picture is also discussed.

This is the first of two papers reviewing and analysing the approach to locality and to mind-body dualism proposed in Everett interpreta- tions of quantum mechanics. The planned companion paper will focus on the contemporary decoherence-based approaches to Everett. This paper instead treats the explicitly mentalistic Many Minds Interpreta- tion proposed by David Albert and Barry Loewer (Albert and Loewer 1988). In particular, we investigate what kind of supervenience of the mind on the body is implied by Albert (...) and Loewer’s Many Minds In- terpretation, and how the interpretation of the related ‘mindless hulks’ problem affects the issue of locality within this interpretation. (shrink)

Spinoza’s metaphysics has returned in the work of Hugh Everett as physics— as a complete and consistent interpretation of Quantum Mechanics that resolves the traditional puzzles of the standard interpretation of Quantum Mechanics.

We have, then, a theory which is objectively causal and continuous, while at the same time subjectively probabilistic and discontinuous. It can lay claim to a certain completeness, since it applies to all systems, of whatever size, and is still capable of explaining the appearance of the macroscopic world. The price, however, is the abandonment of the concept of the uniqueness of the observer, with its somewhat disconcerting philosophical implications.

Everett’s relative states interpretation of quantum mechanics has met with problems related to probability, the preferred basis, and multiplicity. The third theme, I argue, is the most important one. It has led to developments of the original approach into many-worlds, many-minds, and decoherence-based approaches. The latter especially have been advocated in recent years, in an effort to understand multiplicity without resorting to what is often perceived as extravagant constructions. Drawing from and adding to arguments of others, I show (...) that proponents of decoherence-based approaches have not yet succeeded in making their ontology clear. (shrink)

I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. In short, probability is degree of truth. These ideas appear to be new, but they are natural and intuitive, and relate to traditional naive ideas (...) of time and chance. Indeed, I argue that Everettian quantum mechanics is the only form of scientific theory that truly incorporates the perception that the future is open. (shrink)

What would it mean to apply quantum theory, without restriction and without involving any notion of measurement and state reduction, to the whole universe? What would realism about the quantum state then imply? This book brings together an illustrious team of philosophers and physicists to debate these questions. The contributors broadly agree on the need, or aspiration, for a realist theory that unites micro- and macro-worlds. But they disagree on what this implies. Some argue that if unitary quantum evolution has (...) unrestricted application, and if the quantum state is taken to be something physically real, then this universe emerges from the quantum state as one of countless others, constantly branching in time, all of which are real. The result, they argue, is many worlds quantum theory, also known as the Everett interpretation of quantum mechanics. No other realist interpretation of unitary quantum theory has ever been found. Others argue in reply that this picture of many worlds is in no sense inherent to quantum theory, or fails to make physical sense, or is scientifically inadequate. The stuff of these worlds, what they are made of, is never adequately explained, nor are the worlds precisely defined; ordinary ideas about time and identity over time are compromised; no satisfactory role or substitute for probability can be found in many worlds theories; they can't explain experimental data; anyway, there are attractive realist alternatives to many worlds. Twenty original essays, accompanied by commentaries and discussions, examine these claims and counterclaims in depth. They consider questions of ontology - the existence of worlds; probability - whether and how probability can be related to the branching structure of the quantum state; alternatives to many worlds - whether there are one-world realist interpretations of quantum theory that leave quantum dynamics unchanged; and open questions even given many worlds, including the multiverse concept as it has arisen elsewhere in modern cosmology. A comprehensive introduction lays out the main arguments of the book, which provides a state-of-the-art guide to many worlds quantum theory and its problems. (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)

Much of the evidence for quantum mechanics is statistical in nature. The Everett interpretation, if it is to be a candidate for serious consideration, must be capable of doing justice to reasoning on which statistical evidence in which observed relative frequencies that closely match calculated probabilities counts as evidence in favour of a theory from which the probabilities are calculated. Since, on the Everett interpretation, all outcomes with nonzero amplitude are actualized on different branches, it is (...) not obvious that sense can be made of ascribing probabilities to outcomes of experiments, and this poses a prima facie problem for statistical inference. It is incumbent on the Everettian either to make sense of ascribing probabilities to outcomes of experiments in the Everett interpretation, or to find a substitute on which the usual statistical analysis of experimental results continues to count as evidence for quantum mechanics, and, since it is the very evidence for quantum mechanics that is at stake, this must be done in a way that does not presuppose the correctness of Everettian quantum mechanics. This requires an account of theory confirmation that applies to branching-universe theories but does not presuppose the correctness of any such theory. In this paper, we supply and defend such an account. The account has the consequence that statistical evidence can confirm a branching-universe theory such as Everettian quantum mechanics in the same way in which it can confirm a probabilistic theory. (shrink)

Interpretations that follow Everett's idea that the universal wave function contains a multiplicity of coexisting realities, usually claim to give a completely local account of quantum mechanics. That is, they claim to give an account that avoids both a non-local collapse of the wave function, and the action at a distance needed in hidden variable theories in order to reproduce the quantum mechanical violation of the Bell inequalities. In this paper, I sketch how these claims can be substantiated in (...) two renderings of Everett's ideas, namely the many-minds interpretation of Albert and Loewer, and versions of many-worlds interpretations that rely on the concepts of the theory of decoherence. (shrink)

Pour résoudre les paradoxes bien connus de la mécanique quantique, on propose une interprétation par ramification (ou univers parallèles) analogue à celle d?Everett, mais avec des différences: (i) on propose une infinité continue de branches, dont les poids (o[ugrave] probabilités) se calculent par intégrale; (ii) les branches sont séparées par des ramifieurs qui se propagent à la vitesse de la lumière. Lorsqu?est négligeable la composante d?énergie négative de la fonction d?onde, le poids de chaque branche en un point donné (...) u est égal au flux du quadrivecteur (courant-densité de présence), soit à travers l'élément d?écran antérieur à u sur lequel l'impact est perçu, soit à travers le cône passé de u si aucun impact n?est perçu. In order to solve well-known paradoxes in quantum mechanics, we propose a reworking of Everett's interpretation with ramified branches (or many worlds), yet somewhat different: (i) branches form an infinity continuum and each weight (probability) is defined by an integral; (ii) branches are separated by ramifiers which propagate themselves with the velocity of light. Assuming we can neglect the negative-energy component in the wave function, then the weight of each branch at a given point u is equal to the flux of the quadrivector (current-presence density), either through the screen element where the impact occurs, or through the past light-cone of u if no impact occurs. (shrink)

How does it come about then, that great scientists such as Einstein, Schrödinger and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. [...] The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden (...) a concept, unjustified by experience, which we must eliminate to open up the road. (Born [ 1954 ], pp. 8, 11) It is truly surprising how little difference all this makes. Most physicists use quantum mechanics every day in their working lives without needing to worry about the fundamental problem of its interpretation. (Weinberg [ 1992 ], p. 66) I endorse the view that it may be of no relevance to the acceptability of the Everett interpretation of quantum mechanics as a physical theory whether or not an informed observer can be uncertain about the outcome of a quantum measurement prior to its having occurred. However, I suggest that the very possibility of post-measurement, pre-observation uncertainty has an essential role to play in both confirmation theory and decision theory in a branching universe. This is supported by arguments which do not appeal to van Fraassen’s Reflection Principle. (shrink)

It is often objected that the Everett interpretation of QM cannot make sense of quantum probabilities, in one or both of two ways: either it can’t make sense of probability at all, or it can’t explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections. He argues not only that rational decision under uncertainty makes sense in the Everett interpretation, but also that under reasonable assumptions, the credences of (...) a rational agent in an Everett world should be constrained by the Born rule. David Wallace has developed and defended Deutsch’s proposal, and greatly clarified its conceptual basis. In particular, he has stressed its reliance on the distinguishing symmetry of the Everett view, viz., that all possible outcomes of a quantum measurement are treated as equally real. The argument thus tries to make a virtue of what has usually been seen as the main obstacle to making sense of probability in the Everett world. In this note I outline some objections to the Deutsch-Wallace argument, and to related proposals by Hilary Greaves about the epistemology of Everettian QM. (In the latter case, my arguments include an appeal to an Everettian analogue of the Sleeping Beauty problem.) The common thread to these objections is that the symmetry in question remains a very significant obstacle to making sense of probability in the Everett interpretation. (shrink)

Q0 Why this FAQ? Q1 Who believes in many-worlds? Q2 What is many-worlds? Q3 What are the alternatives to many-worlds? Q4 What is a "world"? Q5 What is a measurement? Q6 Why do worlds split? What is decoherence? Q7 When do worlds split? Q8 When does Schrodinger's cat split? Q9 What is sum-over-histories? Q10 What is many-histories? What is the environment basis? Q11 How many worlds are there? Q12 Is many-worlds a local theory? Q13 Is many-worlds a deterministic theory? Q14 (...) Is many-worlds a relativistic theory? What about quantum field theory? What about quantum gravity? Q15 Where are the other worlds? Q16 Is many-worlds (just) an interpretation? Q17 Why don't worlds fuse, as well as split? Do splitting worlds imply irreversible physics? Q18 What retrodictions does many-worlds make? Q19 Do worlds differentiate or split? Q20 What is many-minds? Q21 Does many-worlds violate Ockham's Razor? Q22 Does many-worlds violate conservation of energy? Q23 How do probabilities emerge within many-worlds? Q24 Does many-worlds allow free-will? Q25 Why am I in this world and not another? Why does the universe appear random? Q26 Can wavefunctions collapse? Q27 Is physics linear? Could we ever communicate with the other worlds? Why do I only ever experience one world? Why am I not aware of the world (and myself) splitting? Q28 Can we determine what other worlds there are? Is the form of the Universal Wavefunction knowable? Q29 Who was Everett? Q30 What are the problems with quantum theory? Q31 What is the Copenhagen interpretation? Q32 Does the EPR experiment prohibit locality? What about Bell's Inequality? Q33 Is Everett's relative state formulation the same as many-worlds? Q34 What is a relative state? Q35 Was Everett a "splitter"? Q36 What unique predictions does many-worlds make? Q37 Could we detect other Everett-worlds? Q38 Why quantum gravity? Q39 Is linearity exact? (shrink)

This paper attempts an interpretation of Everett's relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like ‘worlds’ or ‘minds’. Starting from Everett's quantum mechanical model of an observer, it is argued that an observer's belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such (...) beliefs are constructed. From an analysis of these subjective states and their dynamics it is argued that Everett's pure wave mechanics is subjectively consistent with von Neumann's classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed. (shrink)