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A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review (...) 

I show that centered propositions—also called de se propositions, and usually modeled as sets of centered worlds—pose a serious problem for various versions of Lewis's Principal Principle. The problem, put roughly, is that in scenarios like Elga's `Sleeping Beauty' case, those principles imply that rational agents ought to have obviously irrational credences. To solve the problem, I propose a centered version of the Principal Principle. My version allows centered propositions to be objectively chancy. 

Everettian quantum mechanics faces the challenge of how to make sense of probability and probabilistic reasoning in a setting where there is typically no unique outcome of measurements. Wallace has built on a proof by Deutsch to argue that a notion of probability can be recovered in the many worlds setting. In particular, Wallace argues that a rational agent has to assign probabilities in accordance with the Born rule. This argument relies on a rationality constraint that Wallace calls state supervenience. (...) 

The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1/3 to be in a headsawakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1/2. The problem is that she is in a headsawakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is the problem (...) 

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 (...) 

What exists at the fundamental level of reality? On the standard picture, the fundamental reality contains (among other things) fundamental matter, such as particles, fields, or even the quantum state. Nonfundamental facts are explained by facts about fundamental matter, at least in part. In this paper, I introduce a nonstandard picture called the "cosmic void” in which the universe is devoid of any fundamental material ontology. Facts about tables and chairs are recovered from a special kind of laws that satisfy (...) 

In this paper, I explore the link between consciousness and quantum mechanics. Often explanations that invoke consciousness to help explain some of the most perplexing aspects of quantum mechanics are not given serious attention. However, casual dismissal is perhaps unwarranted, given the persistence of the measurement problem, as well as the mysterious nature of consciousness. Using data accumulated from experiments in parapsychology, I examine what anomalous data with respect to consciousness might tell us about various explanations of quantum mechanics. I (...) 

The apparent nonlocality of quantum theory has been a persistent concern. Einstein et al. and Bell emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everettinspired many worlds interpretation try to circumvent it. In this paper, we review Bell's "nogo" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the (...) 

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the timeasymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with (...) 

Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett’s seminal idea is that all possible definite futures on the pointer basis exist as components of a macroscopic linear superposition. I demonstrate that these two conceptions of what is involved in quantum processes are linked via two alternative interpretations of the mindbody relation. This leads to a fission, rather than divergence, interpretation of Everettian theory and (...) 

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. / The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the (...) 

This paper raises a simple continuous spectrum issue in manyworlds interpretation of quantum mechanics, or Everettian interpretation. I will assume that Everettian interpretation refers to manyworlds understanding based on quantum decoherence. The fact that some operators in quantum mechanics have continuous spectrum is used to propose a simple thought experiment based on probability theory. Then the paper concludes it is untenable to think of each possibility that wavefunction $\Psi \rangle$ gives probability as actual universe. While the argument that continuous spectrum (...) 

We provide a derivation of the Born Rule in the context of the Everett (ManyWorlds) approach to quantum mechanics. Our argument is based on the idea of selflocating 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 (...) 

GRW theory offers precise laws for the collapse of the wave function. These collapses are characterized by two new constants, \ and \ . Recent work has put experimental upper bounds on the collapse rate, \ . Lower bounds on \ have been more controversial since GRW begins to take on a manyworlds character for small values of \ . Here I examine GRW in this odd region of parameter space where collapse events act as natural disasters that destroy branches (...) 

ABSTRACTA popular strategy for understanding the probabilities that arise in physics is to interpret them via reductionist accounts of chance—indeed, it is sometimes claimed that such accounts are uniquely wellsuited to make sense of the probabilities in classical statistical mechanics. Here it is argued that reductionist accounts of chance carry a steep but unappreciated cost: when applied to physical theories of the relevant type, they inevitably distort the relations of probability that they take as input. 

We defend the manyworlds 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 selflocation probabilities. We formulate a probability postulate for the MWI: the probability of selflocation 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 (...) 

After a brief introduction to issues that plague the realization of a theory of quantum gravity, I suggest that the main one concerns defining superpositions of causal structures. This leads me to a distinction between time and space, to a further degree than that present in the canonical approach to general relativity. With this distinction, one can make sense of superpositions as interference between alternative paths in the relational configuration space of the entire Universe. But the full use of relationalism (...) 

It is argued that the manyworlds 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 selflocating uncertainty. 

The inherent difficulty in talking about quantum decoherence in the context of quantum cosmology is that decoherence requires subsystems, and cosmology is the study of the whole Universe. Consistent histories gave a possible answer to this conundrum, by phrasing decoherence as loss of interference between alternative histories of closed systems. When one can apply Boolean logic to a set of histories, it is deemed ‘consistent’. However, the vast majority of the sets of histories that are merely consistent are blatantly nonclassical (...) 

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 nonprobabilistic 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 (...) 

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 (...) 

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 blockuniverse picture, which rules out Everettstyle (...) 