Everettian Quantum Mechanics Research Articles

Everettian quantum mechanics and the ghost of fission

Abstract Arguments from fission cases, most notably made by Parfit, have historically been utilized in discussions of Everettian quantum mechanics (EQM) in an attempt to illuminate details of familiar accounts in which an agent ‘splits’. Whilst such imagery is often seen as an innocuous depiction of Everett's theory, it is in fact a poisoned chalice. I argue firstly that the fission case analogy is responsible for the conceptual foundations of probability arguments in EQM and secondly, following a number of disanalogies between fission cases and Everettian branching, I argue that the analogy is unfounded. I conclude that much of the discussion of the probability problem over the past 20 years has been predicated on a problematic analogy and its effects are still apparent today.

Metaphysical indeterminacy in Everettian quantum mechanics

The question of whether Everettian quantum mechanics (EQM) justifies the existence of metaphysical indeterminacy has recently come to the fore. Metaphysical indeterminacy has been argued to emerge from three sources: coherent superpositions, the indefinite number of branches in the quantum multiverse and the nature of these branches. This paper reviews the evidence and concludes that those arguments don’t rely on EQM alone and rest on metaphysical auxiliary assumptions that transcend the physics of EQM. We show how EQM can be ontologically interpreted without positing metaphysical indeterminacy by adopting a deflationary attitude towards branches. Two ways of developing the deflationary view are then proposed: one where branches are eliminated, and another where they are reduced to the universal quantum state.

How Everett Solved the Probability Problem in Everettian Quantum Mechanics

A longstanding issue in the Everettian (Many-Worlds) interpretation is to justify and make sense of the Born rule that underlies the statistical predictions of standard quantum mechanics. The paper offers a reappraisal of Everett’s original account in light of the recent literature on the concept of typicality. It argues that Everett’s derivation of the Born rule is sound and, in a certain sense, even an optimal result, and defends it against the charge of circularity. The conclusion is that Everett’s typicality argument can successfully ground post-factum explanations of Born statistics, while questions remain about the predictive power of the Many-Worlds interpretation.

WHAT MAKES A QUANTUM PHYSICS BELIEF BELIEVABLE? MANY‐WORLDS AMONG SIX IMPOSSIBLE THINGS BEFORE BREAKFAST

AbstractAn extraordinary, if circumscribed, positive shift has occurred since the mid‐twentieth century in the perceived status of Hugh Everett III's 1956 theory of the universal wave function of quantum mechanics, now widely called the Many‐Worlds Interpretation (MWI). Everett's starkly new interpretation denied the existence of a separate classical realm, contending that the experimental data can be seen as presenting a state vector for the whole universe. Since there is no state vector collapse, reality as a whole is strictly deterministic. Explained jointly by the dynamical variables and the state vector, “this reality is not the reality we customarily think of, but is a reality composed of many worlds,” wrote Everett's colleague Bryce DeWitt. In this essay, I account briefly for the change of status in conventional scientific terms, yet chiefly in extended terms of three sets of ideas that I argue can be understood to affect believability in both scientific and religious contexts, illuminating helpfully the MWI phenomenon, and its engagement with theology: orthodoxy and heresy, language and reference, and faith and agnosticism. One's orientation relative to the variable content of these dynamic, socially oriented categories helps to make belief in ideas as metaphysically challenging as Everettian Quantum Mechanics, or particular ideas about God, either more or less believable. The categories will have the same function in a theology engaging Everett's theory, and in any theology at all written in a society deeply marked by what I further argue is a subtle, powerful, and pervasive mode of quasi‐scientific thinking we can call societal constructive agnosticism, of which anyone doing theology today must be aware.

THE MANY WORRIES OF MANY WORLDS

AbstractTheological engagement with quantum mechanics has been dominated by the Copenhagen interpretation, failing to reflect the fact that philosophers and physicists alike are increasingly moving away from the Copenhagen interpretation in favor of other approaches. One such approach, Hugh Everett's so‐called Many Worlds Interpretation (MWI), is being taken increasingly seriously. As the MWI's credibility grows, it is imperative that metaphysicians, theologians, and philosophers of religion engage with its ideas and their implications. This article does just that, setting out some implications of Everettian Quantum Mechanics that are particularly relevant to theism. It argues that taking seriously the radical consequences of the Everett interpretation means facing at least three major worries for theism pertaining to personal identity, the problem of evil, and salvation. The article concludes by calling on theologians and philosophers of religion to address these worries, in order that these matters of religious significance remain both coherent and credible if the MWI turns out to be correct.

Whence Deep Realism for Everettian Quantum Mechanics?

`Shallow' and `deep' versions of scientific realism may be distinguished as follows: the shallow realist is satisfied with belief in the existence of the posits of our best scientific theories; by contrast, deep realists claim that realism can be legitimate only if such entities are described in metaphysical terms. We argue that this methodological discussion can be fruitfully applied in Everettian quantum mechanics, specifically on the debate concerning the existence of worlds and the recent dispute between Everettian actualism and quantum modal realism. After presenting what is involved in such dispute, we point to a dilemma for realists: either we don't have the available metaphysical tools to answer the deep realist's demands, and realism is not justified in this case, or such demands of metaphysical dressing are not mandatory for scientific realism, and deep versions of realism are not really required.

Epistemic Separability and Everettian Branches: A Critique of Sebens and Carroll

Abstract We discuss the proposal by Sebens and Carroll to derive the Born rule in Everettian quantum mechanics from a principle they call ‘ESP-QM’. We argue that the proposal fails: ESP-QM is not, as Sebens and Carroll argue, a ‘less general version’ of an independently plausible principle, ESP, and can only be motivated by the empirical success of quantum mechanics, including use of the Born rule. Therefore, ESP-QM cannot have the status of a meta-theoretical principle of reasoning and provides no viable basis for deriving the Born rule.

Everettian Mechanics with Hyperfinitely Many Worlds

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.

Everettian Quantum Mechanics and the Metaphysics of Modality

Abstract This article sits at a point of intersection between the philosophy of physics and the metaphysics of modality. There are clear similarities between Everettian quantum mechanics and various modal metaphysical theories, but there have hitherto been few attempts at exploring how the two topics relate. In this article, I build on a series of recent papers by Wilson ([2011], [2012], [2013]), who argues that Everettian quantum mechanics’ connections with traditional modal metaphysics are vital in defending it against objections. I show that Wilson’s preferred version of Everettian quantum mechanics has two problems. First, it is unable to account for the contingency of various intuitively contingent modal claims. Second, it fails to yield intuitive truth values on modal claims about the number of branches in a given Everettian multiverse. Since modal claims about branch number are instrumental in decision-theoretic solutions to Everettian quantum mechanics’ problem(s) with probability, this second problem has wider dialectical implications. I suggest amendments to the underlying metaphysics that overcome these problems. The result is a more robust version of Everettian quantum mechanics.

Making New Tools From the Toolbox of Metaphysics

In this review, I specify the metametaphysical background against which Alastair Wilson’s “The Nature of Contingency” (Oxford University Press, 2020) should be properly understood. Metaphysics, as a philosophical discipline, is standing on thin ice. The caricature of the situation is polarized, and is often presented as follows: metaphysics is either entirely extracted from science or it is entirely independent of science. There is a recent trend that focuses on the middle ground between these extremes, searching the philosophical literature for metaphysical theories that can fill the gap, i.e., leaving metaphysics as a free discipline to produce spoils for the eventual needs of philosophers of science. We can appreciate it better with the following distinction between the tasks of ontology and metaphysics, as complementary disciplines. If, on the one hand, we understand ontology as dealing with what exists, we can somehow extract the entities that are existentially postulated by scientific theories. Metaphysics, on the other hand, would be located as an extra layer, in charge of investigating questions about the nature of the entities obtained in this “naturalized ontology”. As a tailor, Wilson adjusts a metaphysical theory in order to perfectly dress the physical and ontological nuances of Everettian quantum mechanics, thus creating a metaphysical theory that gives us intelligibility, with the concept of modality, in two areas: in quantum mechanics, and analytic metaphysics.

Quantum fractionalism: The Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces.Postulating the existence of a continuum infinity of identical quantum universes, all with the same quasi-classical worlds, we show that projection factors give relative amounts of worlds. These appear as relative frequencies of results in quantum experiments, and play the role of probabilities in decisions and inference. This solves the probability problem of Everett's theory, allowing its preferred basis problem to be solved as well, and may help settle questions about the nature of probability.

Projection Factors and Generalized Real and Complex Pythagorean Theorems

Projection factors describe the contraction of Lebesgue measures in orthogonal projections between subspaces of a real or complex inner product space. They are connected to Grassmann's exterior algebra and the Grassmann angle between subspaces, and lead to generalized Pythagorean theorems, relating measures of subsets of real or complex subspaces and their orthogonal projections on certain families of subspaces. The complex Pythagorean theorems differ from the real ones in that the measures are not squared, and this may have important implications for quantum theory. Projection factors of the complex line of a quantum state with the eigenspaces of an observable give the corresponding quantum probabilities. The complex Pythagorean theorem for lines corresponds to the condition of unit total probability, and may provide a way to solve the probability problem of Everettian quantum mechanics.

Analysis of Wallace’s Proof of the Born Rule in Everettian Quantum Mechanics II: Concepts and Axioms

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.

Analysis of Wallace’s Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects

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.

In defence of Everettian decision theory

I consider the interrelations between two decision-theoretic approaches to probability which have been developed in the context of Everettian quantum mechanics: that due to Deutsch and Wallace on the one hand, and that due to Greaves and Myrvold on the other. Having made precise these interrelations, I defend Everettian decision theory against recent objections raised by Dawid and Thébault. Finally, I discuss the import of these results from decision theory for the rationality of an Everettian agent's betting in accordance with the Born rule.

Asymmetric Personal Identity

AbstractPersonal identity is not always symmetric: even if I will not be a later person, the later person may have been me. What makes this possible is that the relations that are criterial of personal identity—such as memory and anticipation—are asymmetric and ‘count in favor of personal identity from one side only’. Asymmetric personal identity can be accommodated by temporal counterpart theory but not by Lewisian overlapping aggregates of person stages. The question of uncertainty in cases of personal fission (and in Everettian quantum mechanics) is also discussed.

Everettian actualism

There is an interpretation of Everettian Quantum Mechanics [EQM] known as the Relative Facts Interpretation [RFI] which is a single-world interpretation of EQM and takes generally all facts about objects to be relational. In this paper I argue that from the perspective of the RFI the best theory of modality for EQM is actualism rather than some version of modal realism, as has been suggested by Alastair Wilson. To argue this I draw a parallel between actualism as it was developed by Alvin Plantinga and actualism as it can be developed from the context of the RFI of EQM. The contention is not that Plantinga-style actualism is the only way one can be an actualist with respect to EQM, but rather that showing how one can be an actualist in at least one way, demonstrates that there are options for a modal metaphysics from the context of EQM.

Everettian quantum mechanics and physical probability: Against the principle of “State Supervenience”

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. I argue that state supervenience is not defensible as a rationality constraint for Everettian agents unless we already invoke probabilistic notions.

The Quantum Doomsday Argument

If the most familiar overlapping interpretation of Everettian quantum mechanics (EQM) is correct, then we are constantly splitting into multiple people. This consequence gives rise to the quantum doomsday argument, which threatens to draw crippling epistemic consequences from EQM. However, a diverging (ʻparallel universeʼ) interpretation of EQM undermines the quantum doomsday argument completely. This appears to tell in favour of the diverging interpretation. But it is surprising that a metaphysical question that is apparently underdetermined by the physics should be settled by purely epistemological considerations; and I argue that the argument for divergence based on the quantum doomsday effect is ultimately unsuccessful. I discuss how some influential treatments of Everettian confirmation handle the quantum doomsday puzzle, and suggest that it can most satisfyingly be resolved via a naturalistic approach to the metaphysics of modality.

Against the empirical viability of the Deutsch–Wallace–Everett approach to quantum mechanics

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.