We discuss some difficulties that arise in attempting to interpret the Page–Wootters and Internal Quantum Reference Frames formalisms, then use a ‘final measurement’ approach to demonstrate that there is a workable single-world realist interpretation for these formalisms. We note that it is necessary to adopt some interpretation before we can determine if the ‘reference frames’ invoked in these approaches are operationally meaningful, and we argue that without a clear operational interpretation, such reference frames might not be suitable to define an (...) equivalence principle. We argue that the notion of superposition should take into account the way in which an instantaneous state is embedded in ongoing dynamical evolution, and this leads to a more nuanced way of thinking about the relativity of superposition in these approaches. We conclude that typically the operational content of these approaches appears only in the limit as the size of at least one reference system becomes large, and therefore these formalisms have an important role to play in showing how our macroscopic reference frames can emerge out of wholly relational facts. (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)

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.

I argue that the Carroll-Chen cosmogonic model does not provide a plausible scientific explanation of the past hypothesis (the thesis that our universe began in an extremely low-entropy state). I suggest that this counts as a welcomed result for those who adopt a Mill-Ramsey-Lewis best systems account of laws and maintain that the past hypothesis is a brute fact that is a non-dynamical law.

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)

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss (...) the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory. (shrink)

To solve the probability problem of the Many Worlds Interpretation of Quantum Mechanics, D. Wallace has presented a formal proof of the Born rule via decision theory, as proposed by D. Deutsch. The idea is to get subjective probabilities from rational decisions related to quantum measurements, showing the non-probabilistic parts of the quantum formalism, plus some rational constraints, ensure the squared modulus of quantum amplitudes play the role of such probabilities. We provide a new presentation of Wallace’s proof, reorganized to (...) simplify some arguments, and analyze it from a formal perspective. Similarities with classical decision theory are made explicit, to clarify its structure and main ideas. A simpler notation is used, and details are filled in, making it easier to follow and verify. Some problems have been identified, and we suggest possible corrections. (shrink)

Having analyzed the formal aspects of Wallace’s proof of the Born rule, we now discuss the concepts and axioms upon which it is built. Justification for most axioms is shown to be problematic, and at times contradictory. Some of the problems are caused by ambiguities in the concepts used. We conclude the axioms are not reasonable enough to be taken as mandates of rationality in Everettian Quantum Mechanics. This invalidates the interpretation of Wallace’s result as meaning it would be rational (...) for Everettian agents to decide using the Born rule. (shrink)

Abstract: This paper develops and advocates a rule for assigning self-locating credences in quantum branching scenarios, called Indexed Branch-Counting. It is argued that Indexed Branch-Counting can be justified on both accuracy-theoretic grounds and on the grounds that it satisfies a requirement of exchangeability for probability assignments. Since Indexed Branch-Counting diverges from the Born Rule, this poses trouble for Everettian approaches to probability. The paper also addresses a common argument against branch-counting, namely that the rule is incoherent in light of putative (...) vagueness in the number of branches. Finally, the paper addresses a recent proposal from Simon Saunders that aims to reconcile branch-counting with the Born Rule, arguing that the proposal faces challenges. (shrink)

I propose a new class of interpretations, real world interpretations, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one factor. They give a mathematical characterisation of the different possible worlds arising in an evolving closed quantum system, in which each possible world corresponds to a (generally mixed) evolving quantum state. In a realistic model, the states corresponding to different worlds should be expected to tend towards orthogonality as (...) different possible quasiclassical structures emerge or as measurement-like interactions produce different classical outcomes. However, as the worlds have a precise mathematical definition, real world interpretations need no definition of quasiclassicality, measurement, or other concepts whose imprecision is problematic in other interpretational approaches. It is natural to postulate that precisely one world is chosen randomly, using the natural probability distribution, as the world realised in Nature, and that this world’s mathematical characterisation is a complete description of reality. (shrink)

Following a proposal of Vaidman The Stanford encyclopaedia of philosophy, 2014) The probable and the improbable: understanding probability in physics, essays in memory of Itamar Pitowsky, 2011), Sebens and Carroll , have argued that in Everettian quantum theory, observers are uncertain, before they complete their observation, about which Everettian branch they are on. They argue further that this solves the problem of making sense of probabilities within Everettian quantum theory, even though the theory itself is deterministic. We note some problems (...) with these arguments. (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)

Hugh Everett III proposed his relative-state formulation of pure wave mechanics as a solution to the quantum measurement problem. He sought to address the theory’s determinate record and probability problems by showing that, while counterintuitive, pure wave mechanics was nevertheless empirically faithful and hence empirical acceptable. We will consider what Everett meant by empirical faithfulness. The suggestion will be that empirical faithfulness is well understood as a weak variety of empirical adequacy. The thought is that the very idea of empirical (...) adequacy might be renegotiated in the context of a new physical theory given the theory’s other virtues. Everett’s argument for pure wave mechanics provides a concrete example of such a renegotiation. (shrink)

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)

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.

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)