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.

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)

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)

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)

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)

`Quantum theory' is not a single physical theory but a framework in which many different concrete theories fit. As such, a solution to the quantum measurement problem ought to provide a recipe to interpret each such concrete theory, in a mutually consistent way. But with the exception of the Everett interpretation, the mainextant solutions either try to make sense of the abstract framework as if it were concrete, or else interpret one particular quantum theory under the fiction that it (...) is fundamental and exact. In either case, these approaches are unable to help themselves to the very theory-laden, level-relative ways in which quantum theory makes contact with experiment in mainstream physics, and so are committed to major revisionary projects which have not been carried out even in outline. As such, only the Everett interpretation is currently suited to make sense of quantum physics as we find it. (shrink)

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)

It seems to be widely assumed that the only effect of the Ghirardi-Rimini-Weber dynamical collapse mechanism on the `tails' of the wavefunction is to reduce their weight. In consequence it seems to be generally accepted that the tails behave exactly as do the various branches in the Everett interpretation except for their much lower weight. These assumptions are demonstrably inaccurate: the collapse mechanism has substantial and detectable effects within the tails. The relevance of this misconception for the dynamical-collapse theories (...) is debatable, though. (shrink)

I make the case that the Universe according to unitary quantum theory has a branching structure, and so can literally be regarded as a "many-worlds" theory. These worlds are not part of the _fundamental_ ontology of quantum theory - instead, they are to be understood as structures, or patterns, emergent from the underlying theory, through the dynamical process of decoherence. That they are structures in this sense does not mean that they are in any way unreal: indeed, pretty much all (...) higher-level ontology in science, from tables to phonons to tigers, is likewise emergent. Unitary quantum theory is therefore a "many-worlds" theory without any modification of the mathematical structure of the theory: the Everett interpretation does not consist in adding worlds to the formalism, but in realising that they are there already. Our grounds for accepting the reality of those worlds is no more, but no less, than our grounds for accepting any other not-directly observable consequence of an empirically very successful theory. (shrink)

I criticize the widely-defended view that the quantum measurement problem is an example of underdetermination of theory by evidence: more specifically, the view that the unmodified, unitary quantum formalism (interpreted following Everett) is empirically indistinguishable from Bohmian Mechanics and from dynamical-collapse theories like the GRW or CSL theories. I argue that there as yet no empirically successful generalization of either theory to interacting quantum field theory and so the apparent underdetermination is broken by a very large class of quantum (...) experiments that require field theory somewhere in their description. The class of quantum experiments reproducible by either is much smaller than is commonly recognized and excludes many of the most iconic successes of quantum mechanics, including the quantitative account of Rayleigh scattering that explains the color of the sky. I respond to various arguments to the contrary in the recent literature. (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 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.

An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Contact is made with Lewis's Principal Principle linking subjective credence with objective chance: an Everettian Principal Principle (...) is formulated, and shown to be at least as defensible as the usual Principle. Some consequences of (Everettian) quantum mechanics for decision theory itself are also discussed. -/- [NB: this this long (70 pages) and occasionally rambling online-only paper has been almost entirely superseded by material in subsequent; if something is not included in them it usually means that I have had second thoughts. I include it for completeness only. (shrink)

The subjective Everettian approach to quantum mechanics presented by Deutsch and Wallace fails to constitute an empirically viable theory of quantum phenomena. The decision theoretic implementation of the Born rule realized in this approach provides no basis for rejecting Everettian quantum mechanics in the face of empirical data that contradicts the Born rule. The approach of Greaves and Myrvold, which provides a subjective implementation of the Born rule as well but derives it from empirical data rather than decision theoretic (...) arguments, avoids the problem faced by Deutsch and Wallace and is empirically viable. However, there is good reason to cast doubts on its scientific value. (shrink)

NGC 1300 (shown in figure 1) is a spiral galaxy 65 million light years from Earth.1 We have never been there, and (although I would love to be wrong about this) we will never go there; all we will ever know about NGC 1300 is what we can see of it from sixty-five million light years away, and what we can infer from our best physics. Fortunately, “what we can infer from our best physics” is actually quite a lot. To (...) take a particular example: our best theory of galaxies tells us that that hazy glow is actually made up of the light of hundreds of billions of stars; our best theories of planetary formation tell us that a sizable fraction of those stars.. (shrink)

Quantum theory plays an increasingly significant role in contemporary early-universe cosmology, most notably in the inflationary origins of the fluctuation spectrum of the microwave background radiation. I consider the two main strategies for interpreting standard quantum mechanics in the light of cosmology. I argue that the conceptual difficulties of the approaches based around an irreducible role for measurement - already very severe - become intolerable in a cosmological context, whereas the approach based around Everett's original idea of treating quantum (...) systems as closed systems handles cosmological quantum theory satisfactorily. Contemporary cosmology, which indeed applies standard quantum theory without supplementation or modification, is thus committed - tacitly or explictly - to the Everett interpretation. (shrink)

I make the case that the Universe according to unitary quantum theory has a branching structure, and so can literally be regarded as a "many-worlds" theory. These worlds are not part of the _fundamental_ ontology of quantum theory - instead, they are to be understood as structures, or patterns, emergent from the underlying theory, through the dynamical process of decoherence. That they are structures in this sense does not mean that they are in any way unreal: indeed, pretty much all (...) higher-level ontology in science, from tables to phonons to tigers, is likewise emergent. Unitary quantum theory is therefore a "many-worlds" theory without any modification of the mathematical structure of the theory: the Everett interpretation does not consist in adding worlds to the formalism, but in realising that they are there already. Our grounds for accepting the reality of those worlds is no more, but no less, than our grounds for accepting any other not-directly observable consequence of an empirically very successful theory. (shrink)

The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.

Following Lewis, it is widely held that branching worlds differ in important ways from diverging worlds. There is, however, a simple and natural semantics under which ordinary sentences uttered in branching worlds have much the same truth values as they conventionally have in diverging worlds. Under this semantics, whether branching or diverging, speakers cannot say in advance which branch or world is theirs. They are uncertain as to the outcome. This same semantics ensures the truth of utterances typically made about (...) quantum mechanical contingencies, including statements of uncertainty, if the Everett interpretation of quantum mechanics is true. The ‘incoherence problem’ of the Everett interpretation, that it can give no meaning to the notion of uncertainty, is thereby solved. IntroductionMetaphysicsPersonal fissionBranching worldsPhysicsObjections. (shrink)

I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then prove it formally, and lastly consider a number of proposed ``counter-examples'' to show exactly which premises of the argument they violate. (This is a preliminary version of a chapter to appear --- under the title ``How to prove the Born Rule'' --- in Saunders, Barrett, Kent and (...) class='Hi'>Wallace, "Many worlds? Everett, quantum theory and reality", forthcoming from Oxford University Press.). (shrink)

Simon Saunders and David Wallace attempt to use a modified form of David Lewis's analysis of personal fission to ground the claim that prior to undergoing Everett branching an informed subject can be uncertain about which outcome s/he will observe. I argue that a central assumption of this seductive idea is questionable despite appearing innocuous and that at the very least further argument is needed in support of it. CiteULike Connotea Del.icio.us What's this?

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)

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 State Interpretation has gained increasing interest due to the progress of understanding the role of decoherence. In order to fulfill its promise as a realistic description of the physical world, two postulates are formulated. In short they are for a system with continuous coordinates \, discrete variable j, and state \\), the density \=|\psi _j|^2\) gives the distribution of the location of the system with the respect to the variables \ and j; an equation of motion for (...) the state \. The first postulate connects the mathematical description to the physical reality, which has been missing in previous versions. The contents of the standard postulates are derived, including the appearance of Hilbert space and the Born rule. The approach to probabilities earlier proposed by Greaves replaces the classical probability concept in the Born rule. The new quantum probability concept, earlier advocated by Deutsch and Wallace, is void of the requirement of uncertainty. (shrink)

Hugh Everett III died of a heart attack in July 1982 at the age of 51. Almost 26 years later, a New York Times obituary for his PhD advisor, John Wheeler, mentioned him and Richard Feynman as Wheeler’s most prominent students. Everett’s PhD thesis on the relative state formulation of quantum mechanics, later known as the “Many Worlds Interpretation”, was published (in its edited form) in 1957, and later (in its original, unedited form) in 1973, and since then (...) has given rise to one of the most radical schools of thought in the foundations of quantum theory. Several years ago two conferences held in Oxford and in the Perimeter Institute celebrated the occasion of 50 years to the first publication of Everett’s thesis. The book Many worlds? grew out from contributions to these conferences, but, as its editors emphasize, it is more than mere conference proceedings. Instead, an attempt was made to assemble an impressive collection of papers which together illustrate the promise of the many worlds interpretation and the obstacles it faces. 23 papers divided into six sections follow an introduction by Simon Saunders, one of Oxford’s fiercest Everettians. The first four sections cover two thorny issues that have been flagged by contemporary opponents to the many worlds interpretation, namely, the problem of ontology and the problem of probability, while the fifth discusses alternatives to Everett such as Bohmian mechanics and information–theoretic approaches to quantum theory. The sixth section seems to be a wild card, hosting several papers unrelated to each other, including one of the most interesting contributions to this volume on the history of Everett’s thesis and his (some may say all too) short academic career. Each section concludes with transcripts of the discussion session that took place after the talks, thus giving an additional emphasis to the points of contention. Apart from general comments on the volume, in what follows I would like to concentrate on few papers I found especially illuminating. Start with ontology.. (shrink)

We review and discuss the recent monograph by David Wallace on Everettian Quantum Mechanics. This book is a high point of two decades of work on Everett in both physics and philosophy. It is also a beautiful and welcome exemplar of a modern way of doing metaphysics. We discuss certain aspects more critically, and take the opportunity to sketch an alternative pragmatist approach to probability in Everett, to be fully developed elsewhere.

This is a Critical Notice for the general philosophical journal, Philosophy, of the anthology 'Many Worlds? Everett, Quantum Theory and Reality', edited by Simon Saunders, Jonathan Barrett, Adrian Kent and David Wallace.

I continue to maintain that David Lewis’s concept of overlapping persons cannot yield pre-measurement uncertainty in the Everett interpretation of quantum mechanics in the way that Simon Saunders and David Wallace originally seemed to suggest. However, I argue that in their reply to me they make it clear that they do not wish to invoke overlap of persons after all. That makes it mysterious why they defended their interpretation of personal overlap in the first place and questionable what (...) role overlap has to play in their proposal. If Everettian branching can be understood to involve the divergence of distinct, non-overlapping worlds a concept of pre-measurement uncertainty is available. That idea was first proposed by David Deutsch but required an ad hoc postulate. Saunders has recently suggested that a similar scheme arises naturally out of the physics. If correct, that is important as it offers escape from some bizarre consequences of current alternative ways of understanding probability in the Everett interpretation. (shrink)

We claim that, as it stands, the Deutsch–Wallace–Everett approach to quantum theory is conceptually incoherent. This charge is based upon the approach’s reliance upon decoherence arguments that conflict with its own fundamental precepts regarding probabilistic reasoning in two respects. This conceptual conflict obtains even if the decoherence arguments deployed are aimed merely towards the establishment of certain ‘emergent’ or ‘robust’ structures within the wave function: To be relevant to physical science notions such as robustness must be empirically grounded, (...) and, on our analysis, this grounding can only plausibly be done in precisely the probabilistic terms that lead to conceptual conflict. Thus, the incoherence problems presented necessitate either the provision of a new, non-probabilistic empirical grounding for the notions of robustness and emergence in the context of decoherence, or the abandonment of the Deutsch–Wallace–Everett programme for quantum theory. (shrink)

David Wallace has given a decision-theoretic argument for the Born Rule in the context of Everettian quantum mechanics. This approach promises to resolve some long-standing problems with probability in EQM, but it has faced plenty of resistance. One kind of objection charges that the requisite notion of decision-theoretic uncertainty is unavailable in the Everettian picture, so that the argument cannot gain any traction; another kind of objection grants the proof’s applicability and targets the premises. In this article I propose (...) some novel principles connecting the physics of EQM with the metaphysics of modality, and argue that in the resulting framework the incoherence problem does not arise. These principles also help to justify one of the most controversial premises of Wallace’s argument, ‘branching indifference’. Absent any a priori reason to align the metaphysics with the physics in some other way, the proposed principles can be adopted on grounds of theoretical utility. The upshot is that Everettians can, after all, make clear sense of objective probability. 1 Introduction2 Setup3 Individualism versus Collectivism4 The Ingredients of Indexicalism5 Indexicalism and Incoherence5.1 The trivialization problem5.2 The uncertainty problem6 Indexicalism and Branching Indifference6.1 Introducing branching indifference6.2 The pragmatic defence of branching indifference6.3 The non-existence defence of branching indifference6.4 The indexicalist defence of branching indifference7 Conclusion. (shrink)

Confusion prevails in the anthropological literature concerning the nature of spirit possession belief and its effects. In large, this is due to the difficulty in differentiating between culture‐specific categories of altered states of consciousness and reconciling these to analytical categories. Theories of spirit possession tend either toward description of the culture context without reference to outside theories, thus lacking comparability, or toward application of externally derived categories to the possession behavior, which often lack on‐the‐ground relevance. Since comparison is the aim (...) of anthropology, we need categories which enable us to accomplish that and still reflect cultural belief. I propose focusing on "ritual states of consciousness" rather than just altered states, which may or may not be spirit possession according to different criteria. This will enable us to retain the culturally relevant categorization while achieving a useful comparability among cultures. I test this idea by analyzing the Spiritual Baptists of St. Vincent and other Caribbean religions. (shrink)

Responsibility and the Moral Sentiments offers an account of moral responsibility. It addresses the question: what are the forms of capacity or ability that render us morally accountable for the things we do? A traditional answer has it that the conditions of moral responsibility include freedom of the will, where this in turn involves the availability of robust alternative possibilities. I reject this answer, arguing that the conditions of moral responsibility do not include any condition of alternative possibilities. In the (...) terms that have become familiar, the book thus defends a compatibilist account of moral responsibility. (shrink)

[Abstract and PDF at the Pittsburgh PhilSci Archive] A slightly shorter version of this paper is to appear in a volume edited by Jonathan Barrett, Adrian Kent, David Wallace and Simon Saunders, containing papers presented at the Everett@50 conference in Oxford in July 2007, and the Many Worlds@50 meeting at the Perimeter Institute in September 2007. The paper is based on my talk at the latter meeting (audio, video and slides of which are accessible here).

[Abstract and PDF at the Pittsburgh PhilSci Archive] A slightly shorter version of this paper is to appear in a volume edited by Jonathan Barrett, Adrian Kent, David Wallace and Simon Saunders, containing papers presented at the Everett@50 conference in Oxford in July 2007, and the Many Worlds@50 meeting at the Perimeter Institute in September 2007. The paper is based on my talk at the latter meeting (audio, video and slides of which are accessible here).

Proposed derivations of the Born rule for Everettian theory are controversial. I argue that they are unnecessary but may provide justification for a simplified version of the Principal Principle. It’s also unnecessary to replace Everett’s idea that a subject splits in measurement contexts with the idea that subjects have linear histories which partition Many worlds? Everett, quantum theory, and reality, Oxford University Press, Oxford, pp 181–205, 2010; Wallace in The emergent multiverse, Oxford University Press, Oxford, 2012, Chapter (...) 7; Wilson in Br J Philos Sci 64:709–737, 2013; The nature of contingency: quantum physics as modal realism, Oxford University Press, Oxford, forthcoming). Linear histories were introduced to provide a concept of pre-measurement uncertainty and I explain why pre-measurement uncertainty for splitting subjects is after all coherent, though not necessary because Everett’s original fission interpretation of branching can arguably be rendered coherent without it, via reference to Vaidman, Tappenden, Sebens and Carroll and McQueen and Vaidman. A deterministic and probabilistic quantum mechanics can be made intelligible by replacing the standard collapse postulate with a no-collapse postulate which identifies objective probability with relative branch weight, supplemented by the simplified Principal Principle and some revisionary metaphysics. (shrink)