The year 2007 was the fiftieth anniversary of Everett's “‘Relative State’ Formulation of Quantum Mechanics” (Review of Modern Physics 29:454–62) and the birth of the many-worlds interpretation. To celebrate this event, two major conferences were held, one at Oxford and the other at the Perimeter Institute. But this was no mere birthday; it was a coming-of-age celebration for the many-worlds interpretation, a cincuentañera. For much of its life, many-worlds was the awkward one among interpretations of quantum mechanics, with a bizarre ontology and a host of unresolved problems. But in a flurry of work in the past decade or so, it has been transformed into an elegant (if still exotic) theory.

This volume is the product of the two conferences, but it rises well above the standard conference proceedings. What is most remarkable about it is its cohesion; the introduction and first four sections comprise a compelling philosophical narrative such as one does not usually find in a collection. The volume begins with Simon Saunders's excellent substantive introduction, which combines the usual reader's guide with a concise and powerful overview of the argument in favor of the many-worlds interpretation: the argument that not only is many-worlds coherent, it is also compulsory. This is the case that everyone opposed to the many-worlds program will have to answer. Taking the introduction together with the papers of the first and third sections, which fill out the details, one gets a formidable case indeed—a many-worlds manifesto, if you will. The papers in these sections, in particular, will be widely cited for years to come.

The two main problems that plague older versions of many-worlds are ontology (the status of the worlds) and probability (the status of the Born rule). The first four sections of the volume explore the fascinating work that has gone into addressing these problems, based on decoherence theory in the former case and decision theory in the latter. The first section is a defense of a decoherence-based ontology of worlds; David Wallace provides a lucid account of how the familiar world of experience—in fact, many of them—can dynamically emerge from the quantum state, and Jim Hartle and Jonathan Halliwell summarize the state of the art in applying decoherence to derive (almost) classical physics at the macroscopic level from quantum mechanics at the fundamental level. In the second section, Tim Maudlin and John Hawthorne problematize the emergence of the familiar world from the quantum state, and James Ladyman replies.

The third section addresses several related aspects of the probability problem. Saunders argues that genuine uncertainty about the future can still be located within a structure in which every outcome of a measurement actually occurs. David Papineau argues that, given the mysterious nature of the connection between chance and action in one-world decision contexts, the many-worlds interpretation is no worse off than orthodoxy, even if Saunders's project fails to find a place for uncertainty in many-worlds. Wallace defends a decision-theoretic argument for the Born rule; rationality requires that an agent treat the squared amplitude of an outcome as if it were a chance. And Hilary Greaves and Wayne Myrvold construct a generalized Bayesian framework in which many-worlds theories and one-world theories alike can be confirmed and disconfirmed by evidence. Taken together, these arguments propose to demonstrate that squared amplitude in a many-worlds theory can perform all the essential functions of probability: quantifying uncertainty, guiding decision, mediating confirmation. The fourth section consists of forceful criticisms of these arguments by Adrian Kent, David Albert, and Huw Price.

The fifth and sixth sections are less cohesive and lie outside the tight narrative structure of the first four. The fifth section considers some alternatives to the many-worlds interpretation, in particular one-world theories that share some structure with Everettian quantum mechanics. The sixth is a collection of papers about the broader context of the many-worlds theory, including a fascinating journalistic piece by Peter Byrne on the fierce academic politics behind Everett's original publication. These are all solid, interesting papers in their own right, though, and insisting on an overall narrative sweep for the whole of an edited volume is, of course, asking too much.

One has to admire the work and ingenuity that has gone into defending the many-worlds program; it has produced some fine philosophy (and physics too). But how convincing, in the end, are the Everettian arguments? One gets the feeling that the Everettians think that their work is done—that they have proved their case, and now it is just a matter of waiting until everyone else sees the light. Indeed, in his contribution David Deutsch argues that Everettians would be better off applying the theory than trying to defend it further. But what is striking is that despite the acknowledged breakthroughs documented here, the debate has reached something of an impasse. Perhaps the case has indeed been made as strongly as it can be—but a large segment of the interested population remains unconvinced, and for what strike me as good reasons.

I am thinking particularly of the probability issue. Overall, this issue takes center stage in the volume, and rightly so; much of the most innovative work in defending many-worlds concerns probability, and the most incisive criticisms strike here too. The heart of these criticisms—made explicit in Price's contribution but also implicit in those of Kent and Albert—is that probability is conceptually tied to existence; it is essential to probability that one outcome exists and the rest do not. This is perhaps especially salient for the decision-theoretic role of probability; the Everettian proposal that all measurement outcomes are actual expands the range of available decision strategies. For example, you can prefer outcomes in which your successors have a variety of experiences over those in which they all experience the same thing (Wallace attributes this example to Adam Elga; 257). No such preference is available in the one-world case; preferring to decide by coin toss is not at all analogous (despite Wallace's claims to the contrary; 258). But then the squared amplitudes of Everettian worlds cannot play the role of classical chances in decision contexts.

Here is the impasse at its sharpest. Wallace and Greaves and Myrvold prove that world weights play the role of chances (in decision and confirmation, respectively) on the basis of axioms. They take their arguments for the axioms as stronger than the force of the proposed counterexamples; the critics take the reverse position. The critics maintain, plausibly, that one cannot dissociate probability and existence without wreaking havoc in decision theory and confirmation theory. But the Everettians respond, plausibly, that one cannot associate quantum probabilities with existence without abandoning realism about the quantum state; if the quantum state describes reality, then all outcomes exist (Saunders, 12; Wallace, 65).

Can we break the stalemate? Perhaps we can by taking a closer look at the way the concept of actuality is to be applied in an Everettian context. It is striking how much progress Everettians such as Wallace have made by assuming a thoroughgoing functionalism. A tiger is whatever plays the tiger role, and a world is whatever plays the world role; this is how Wallace recovers ordinary ontology from dynamical patterns in the quantum state. There are those who reject this functionalist approach (such as Maudlin and Hawthorne)—but look at what it achieves.

Everettians are not, however, disposed to take a similarly pragmatic attitude toward actuality. Realism by itself does not entail that quantum theory describes the structure of actuality rather than a structure of possibilities. There is no place for a priorism here; the best we can do, in Saunders's memorable phrase, is to adopt a metaphysics that “makes sense of our best physical theory, rather than nonsense” (200). But there is a prima facie case to be made that only one world plays the actual role for us—so why not say that only one world exists, thereby recovering probability? There are tricky issues here concerning what the actuality role is (and who constitutes us), but there is at least a respectable tradition of denying existence to things that could make no empirical difference. Thanks to decoherence, other worlds make no difference to us. Perhaps this is why Deutsch (546) exhorts us to investigate ways that other worlds could make a difference; otherwise it seems perfectly open to us—perhaps required of us—to deny them. The result might be a Bohmian theory (Valentini, chap. 16) or it might be something closer to Everett (Zurek, chap. 13), but it would not be a many-worlds theory.

A typical “reviewer's worry” about this volume might be its intended audience. It is certainly not an introduction to the many-worlds interpretation for the uninitiated; far too much is presupposed by all the authors. Its chapters range widely from pure philosophy to pure physics (insofar as there are such things). But this is part of the appeal of the many-worlds project; it truly is an interdisciplinary endeavor. And although the physics may be tough going for philosophers (and perhaps vice versa), it is worth it; Many Worlds? is an important contribution to an important debate.