Peter J. Lewis

In 1994, Maudlin proposed an objection to retrocausal approaches to quantum mechanics in general, and to the transactional interpretation in particular, involving an absorber that changes location depending on the trajectory of the particle. Maudlin considered this objection fatal. However, the TI did not die; rather, a number of responses were developed, some attempting to accommodate Maudlin's example within the existing TI, and others modifying the TI. I argue that none of these responses is fully adequate. The reason, I submit, is that there are two aspects to Maudlin's objection; the more readily soluble aspect has received all the attention, but the more problematic aspect has gone unnoticed. I consider the prospects for developing a successful retrocausal quantum theory in light of this second aspect of the objection.

It is widely acknowledged that the link between quantum language and ordinary language must be "fuzzier" than the traditional eigenstate-eigenvalue link. In the context of spontaneous-collapse theories, Albert and Loewer argue that the form of this fuzzy link is a matter of convention, and can be freely chosen to minimize anomalies for those theories. I defend the position that the form of the link is empirical, and could be such as to render collapse theories idle. This means that defenders of spontaneous-collapse theories must gamble that the actual form of the link renders such theories tenable

The GRW theory is a recent attempt to solve the measurement problem in quantum mechanics, and the tails problem is a well-known and potentially fatal criticism of the GRW theory. The first half of the paper is an exposition of the measurement problem, the GRW theory, and the tails problem. In the remainder of the paper, two methods of dealing with the tails problem are considered: first, altering the GRW theory so as to avoid the tails problem; and second, denying that the tails problem is more than a novel aspect of a universal vagueness in the way scientific theories relate to everyday language.

This paper investigates the tenability of wavefunction realism, according to which the quantum mechanical wavefunction is not just a convenient predictive tool, but is a real entity figuring in physical explanations of our measurement results. An apparent difficulty with this position is that the wavefunction exists in a many-dimensional configuration space, whereas the world appears to us to be three-dimensional. I consider the arguments that have been given for and against the tenability of wavefunction realism, and note that both the proponents and the opponents assume that quantum mechanical configuration space is many-dimensional in exactly the same sense in which classical space is three-dimensional. I argue that this assumption is mistaken, and that configuration space can be taken as three-dimensional in a relevant sense. I conclude that wavefunction realism is far less problematic than it has been taken to be. Introduction Non-separability The instantaneous solution The dynamical solution Invariance What is configuration space, anyway? Conclusion

The main difficulty facing no-collapse theories of quantum mechanics in the Everettian tradition concerns the role of probability within a theory in which every possible outcome of a measurement actually occurs. The problem is two-fold: First, what do probability claims mean within such a theory? Second, what ensures that the probabilities attached to measurement outcomes match those of standard quantum mechanics? Deutsch has recently proposed a decision-theoretic solution to the second problem, according to which agents are rationally required to weight the outcomes of measurements according to the standard quantum-mechanical probability measure. I show that this argument admits counterexamples, and hence fails to establish the standard probability weighting as a rational requirement.

I examine recent arguments based on functionalism that claim to show that Bohm's theory fails to solve the measurement problem, or if it does so, it is only because it reduces to a form of the many-worlds theory. While these arguments reveal some interesting features of Bohm's theory, I contend that they do not undermine the distinctive Bohmian solution to the measurement problem. ‡I would like to thank Harvey Brown, Martin Thomson-Jones, and David Wallace for helpful discussions. †To contact the author, please write to: Department of Philosophy, University of Miami, P.O. Box 248054, Coral Gables, FL 33124–4670; e-mail: [email protected].

Protective measurement might be taken to put the last nail in the coffin of ensemble interpretations of the quantum state. My goal here is to show that even though ensemble interpretations face formidable obstacles, protective measurements don't lead to any additional difficulties. Rather, they provide us with a nice illustration of a conclusion for which we had considerable indirect evidence already, namely that quantum mechanics leads to a blurring of the distinction between the intrinsic properties of a system and the statistical properties of the ensemble of which it is a member. This conclusion goes for all realist interpretations of the quantum state, both the mainstream ones that take the wave function to be a real field and the more conjectural ones that take the wave function to describe our knowledge of an ensemble.

The main problem with the many‐worlds theory is that it is not clear how the notion of probability should be understood in a theory in which every possible outcome of a measurement actually occurs. In this paper, I argue for the following theses concerning the many‐worlds theory: If probability can be applied at all to measurement outcomes, it must function as a measure of an agent’s self‐location uncertainty. Such probabilities typically violate reflection. Many‐worlds branching does not have sufficient structure to admit self‐location probabilities. Decision‐theoretic arguments do not solve this problem. †To contact the author, please write to: Department of Philosophy, University of Miami, P.O. Box 248054, Coral Gables, FL 33124‐4670; e‐mail: [email protected]

Spontaneous collapse theories of quantum mechanics require an interpretation if their claim to solve the measurement problem is to be vindicated. The most straightforward interpretation rule, the fuzzy link, generates a violation of common sense known as the counting anomaly. Recently, a consensus has developed that the mass density link provides an appropriate interpretation of spontaneous collapse theories that avoids the counting anomaly. In this paper, I argue that the mass density link violates common sense in just as striking a way as the fuzzy link, and hence should not be regarded as a problem-free alternative to the fuzzy link. Hence advocates of spontaneous collapse theories must accept some violation of common sense, although this is not necessarily fatal to their project.

In 1994, Maudlin proposed proposed an objection to the transactional interpretation, involving an absorber that changes location depending on the trajectory of the particle. Maudlin considered this objection fatal. However, the TI did not die; rather, a number of responses were developed, some attempting to accommodate Maudlin's example within the existing TI, and others modifying the TI. I argue that none of these responses is fully adequate. The reason, I submit, is that there are two aspects to Maudlin's objection; the more readily soluble aspect has received all the attention, but the more problematic aspect has gone unnoticed. I consider the prospects for developing a succesful version of the TI in light of this second aspect of the objection.

The call to supplement the quantum wave function with local beables is almost as old as quantum mechanics. But what exactly is the problem with the wave function as the representation of a quantum system? I canvass three potential problems with the wave function: the well-known problems of incompleteness and dimensionality, and the lesser known problem of non-locality introduced recently by Myrvold. Building on Myrvold's insight, I show that the standard ways of introducing local beables into quantum mechanics are unsuccessful. I consider whether we really need local beables, and assess the prospects for a new theory of local beables.

All parties to the Sleeping Beauty debate agree that it shows that some cherished principle of rationality has to go. Thirders think that it is Conditionalization and Reflection that must be given up or modified; halfers think that it is the Principal Principle. I offer an analysis of the Sleeping Beauty puzzle that allows us to retain all three principles. In brief, I argue that Sleeping Beauty’s credence in the uncentered proposition that the coin came up heads should be 1/2, but her credence in the centered proposition that the coin came up heads and it is Monday should be 1/3. I trace the source of the earlier mistakes to an unquestioned assumption in the debate, namely that an uncentered proposition is just a special kind of centered proposition. I argue that the falsity of this assumption is the real lesson of the Sleeping Beauty case.

It has long been recognized that a local hidden variable theory of quantum mechanics can in principle be constructed, provided one is willing to countenance pre-measurement correlations between the properties of measured systems and measuring devices. However, this ‘conspiratorial’ approach is typically dismissed out of hand. In this article I examine the justification for dismissing conspiracy theories of quantum mechanics. I consider the existing arguments against such theories, and find them to be less than conclusive. I suggest a more powerful argument against the leading strategy for constructing a conspiracy theory. Finally, I outline two alternative strategies for constructing conspiracy theories, both of which are immune to these arguments, but require one to either modify or reject the common cause principle. Introduction The incompleteness of quantum mechanics Hidden variables Hidden mechanism conspiracy theories Existing arguments against hidden mechanisms A new argument against hidden mechanisms Backwards-causal conspiracy theories Acausal conspiracy theories Conclusion.

This article provides an overview of the philosophical literature on the GRW theory of quantum mechanics, and argues for a particular position regarding that literature. Much of the literature is ontological; it attempts to defend a conception of what the world is like according to the GRW theory against perceived competitors. I argue that there is no real debate here, since these supposedly conflicting positions are better regarded as alternative and compatible ways of describing the world of the GRW theory.

There is an important sense in which an agent’s credences are universal: while they reflect an agent’s own judgments, those judgments apply equally to everyone’s bets. This point, while uncontentious, has been overlooked; people automatically assume that credences concern an agent’s own bets, perhaps just because of the name “subjective” that is typically applied to this account of belief. This oversight has had unfortunate consequences for recent epistemology, in particular concerning the Sleeping Beauty case and its myriad variants.

The world looks three-dimensional unless one looks closely, when it looks 3N-dimensional. But which appearance is veridical, and which the illusion? Albert contends that the three-dimensionality of the everyday world is illusory, and that 3N-dimensional wavefunction one discerns in quantum phenomena is the reality behind the illusion. What I try to do here is to argue for the converse of Albert's position; the world really is three dimensional, and the 3N-dimensional appearance of quantum phenomena is the theoretical analog of an illusion; we represent quantum reality to ourselves as 3N-dimensional in order to more readily visualize the correlations between wave packets.

A few years ago, I argued that according to spontaneous collapse theories of quantum mechanics, arithmetic applies to macroscopic objects only as an approximation. Several authors have written articles defending spontaneous collapse theories against this charge, including Bassi and Ghirardi, Clifton and Monton, and now Frigg. The arguments of these authors are all different and all ingenious, but in the end I think that none of them succeeds, for reasons I elaborate here. I suggest a fourth line of response, based on an analogy with epistemic paradoxes, which I think is the best way to defend spontaneous collapse theories, and which leaves my main thesis intact.

The Transactional Interpretation of quantum mechanics is a promising way of fulfilling Einstein’s vision of a completed quantum mechanics. However, it has received forceful criticism from Maudlin. Indeed, I shall argue that the force of Maudlin’s criticisms has been underestimated, and that none of the extant responses are adequate. An adequate response, I contend, requires reconceptualizing the kinds of explanations the Transactional Interpretation gives. I sketch such a reinterpretation and argue that it does not fall prey to Maudlin’s objections. However, there remain significant obstacles in the way of formulating a fully adequate version of the Transactional Interpretation.

A major problem facing no-collapse interpretations of quantum mechanics in the tradition of Everett is how to understand the probabilistic axiom of quantum mechanics (the Born rule) in the context of a deterministic theory in which every outcome of a measurement occurs. Deutsch claims to derive a decision-theoretic analogue of the Born rule from the non-probabilistic part of quantum mechanics and some non-probabilistic axioms of classical decision theory, and hence concludes that no probabilistic axiom is needed. I argue that Deutsch’s derivation begs the question.

According to a recent paper by Tim Maudlin, Bell’s theorem has nothing to tell us about realism or the descriptive completeness of quantum mechanics. What it shows is that quantum mechanics is non-local, no more and no less. What I intend to do in this paper is to challenge Maudlin’s assertion about the import of Bell’s proof. There is much that I agree with in the paper; in particular, it does us the valuable service of demonstrating that Einstein’s objections to quantum mechanics have nothing to do with its indeterminism. But I do think that Maudlin’s conclusion is overly cut-and-dried. Quantum mechanics is far from a unified edifice, and what Bell’s theorem shows depends on what version of quantum mechanics you look at. In particular, I’ll try to make the case that there’s an interesting, if ultimately uncompelling anti-realist construal of the import of Bell’s theorem. And I also want to suggest that locality isn’t quite as decisively defeated as Maudlin claims.