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.

We defend the many-worlds interpretation of quantum mechanics against the objection that it cannot explain why measurement outcomes are predicted by the Born probability rule. We understand quantum probabilities in terms of an observer's self-location probabilities. We formulate a probability postulate for the MWI: the probability of self-location in a world with a given set of outcomes is the absolute square of that world's amplitude. We provide a proof of this postulate, which assumes the quantum formalism and two principles concerning (...) symmetry and locality. We also show how a structurally similar proof of the Born rule is available for collapse theories. We conclude by comparing our account to the recent account offered by Sebens and Carroll. (shrink)

Since the publication of Elga's seminal paper in 2000, the Sleeping Beauty paradox has been the source of much discussion, particularly in this journal. Over the past few decades the Everettian interpretation of quantum mechanics 1 has also been much debated. There is an interesting connection between the way these two topics raise issues about subjective probability assignments.This connection is often alluded to, but as far as we know Peter J. Lewis's ‘Quantum Sleeping Beauty’ is the first attempt to examine (...) it explicitly. Lewis claims that the two debates are not independent: to be specific, he argues that accepting the Everettian interpretation of quantum mechanics requires you to be a ‘halfer’ about Sleeping Beauty, in opposition to the more widely accepted ‘thirder’ solution.This paper will argue that Lewis is wrong. Everettians do not have to be halfers. It is perfectly cogent to be both an Everettian and a thirder. (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 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.

It is argued that the many-worlds interpretation is by far the best interpretation of quantum mechanics. The key points of this view are viewing the wave functions of worlds in three dimensions and understanding probability through self-locating uncertainty.

We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via decoherence and an observer registering the outcome of the measurement, that observer can know the state of the universe precisely without knowing which branch they are on. We show that there is a uniquely rational way to apportion credence in such cases, which (...) leads directly to the Born Rule. Our analysis generalizes straightforwardly to cases of combined classical and quantum self-locating uncertainty, as in the cosmological multiverse. (shrink)

Historically, appearance of the quantum theory led to a prevailing view that Nature is indeterministic. The arguments for the indeterminism and proposals for indeterministic and deterministic approaches are reviewed. These include collapse theories, Bohmian Mechanics and the many-worlds interpretation. It is argued that ontic interpretations of the quantum wave function provide simpler and clearer physical explanation and that the many-worlds interpretation is the most attractive since it provides a deterministic and local theory for our physical Universe explaining the illusion of (...) randomness and nonlocality in the world we experience. (shrink)

In this paper I review three different positions on the wave function, namely: nomological realism, dispositionalism, and configuration space realism by regarding as essential their capacity to account for the world of our experience. I conclude that the first two positions are committed to regard the wave function as an abstract entity. The third position will be shown to be a merely speculative attempt to derive a primitive ontology from a reified mathematical space. Without entering any discussion about nominalism, I (...) conclude that an elimination of abstract entities from one’s ontology commits one to instrumentalism about the wave function, a position that therefore is not as unmotivated as it has seemed to be to many philosophers. (shrink)

Next SectionAn attempt to resolve the controversy regarding the solution of the Sleeping Beauty Problem in the framework of the Many-Worlds Interpretation led to a new controversy regarding the Quantum Sleeping Beauty Problem. We apply the concept of a measure of existence of a world and reach the solution known as ‘thirder’ solution which differs from Peter Lewis’s ‘halfer’ assertion. We argue that this method provides a simple and powerful tool for analysing rational decision theory problems.

In the last few decades, the relevance of quantum mechanics to the free-will debate has been discussed at length, especially in relation to the prospects of libertarianism. Basing his interpretation on Anscombe’s seminal work, Putnam argued in 1979 that, given that quantum mechanical indeterminacy is holistic at the macrolevel—i.e., it is not traceable to atomistic events such as quantum jumps of single atoms—it can provide libertarians with the kind of freedom they seek. As shown in this article, however, Putnam ultimately (...) reached the conclusion—together with the other author of this article—that his argument was wrong due to problems with the way it appealed to the Uncertainty Principle.**. (shrink)

In this paper, we investigate similarities and differences between the main neo-Copenhagen (or “epistemic–pragmatist”) interpretations of quantum mechanics, here identified as those defined by the rejection of an ontological nature of the quantum states and the simultaneous avoidance of hidden variables, while maintaining the quantum formalism unchanged. We argue that there is a single general interpretive framework in which the core claims that the various interpretations in the class are committed to, and which they emphasize to varying degrees, can be (...) represented. We also identify, however, remaining differences of a more substantial nature, and we offer a first analysis of them. We also argue that these remaining differences cannot be resolved within the formalism of quantum mechanics itself and identify the more general philosophical considerations that can be used in order to break this interpretation underdetermination. (shrink)

The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.

This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a Ψ-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement problem and simultaneously allow us to think sensibly about probability and evolution in quantum cosmology. Our analysis draws upon recent work on the problem of time in quantum gravity and causally symmet- ric local hidden variable theories. Our conclusion weighs the strengths and weaknesses of the approach (...) and points towards paths for future development. (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 Copenhagen interpretation of quantum entanglement experiments is at best incomplete, since the intermediate state induced by collapse of the wave function apparently depends upon the inertial rest frame in which the experiment is observed. While Everett’s Many Worlds Interpretation avoids the issue of wave function collapse, it, too, is a casualty of the special theory of relativity. This requires all events in the universe, past, present and future, to be unique, as in the block-universe picture, which rules out Everett-style (...) branching. The benefits of MWI may be retained, however, by postulating a multiverse of discrete, parallel, block universes which are identical to each other up to certain points in the MWI “trunk” before they diverge according to the MWI branching. The quantum probability of an event then emerges from the number of parallel universes in which the event happens divided by the total number of universes. This means that the total number of such universes is finite. Such a picture is more easily envisaged by thinking of it as a purely mathematical structure, as in Tegmark’s Mathematical Universe Hypothesis. However, while Tegmark wished to avoid contamination from Gödelian self-referential knots, not only does such contamination appear to be inevitable, it brings an unexpected benefit. The mathematical hierarchy required by Gödel’s enigmatic footnote 48a leads to an explanation for a unitary evolution of deterministic quantum rules across the multiverse while accounting for quantum uncertainty within an individual universe. Other aspects of this structure, called here the Plexus, are discussed, including awareness of existence and other questions raised by the hypothesis. (shrink)