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Analysis

Reply to Papineau and Dura-Vila

P. J. Lewis

Published Jan 1, 2009• 11 citations
Publisher

Abstract

I have argued (Lewis 2007) that anyone who adopts the Everettian approach to the foundations of quantum mechanics must also accept the (unpopular) ‘halfer’ solution to the Sleeping Beauty puzzle. Papineau and Durà-Vilà (2009) have responded with an argument that it is perfectly cogent both to be an Everettian and to accept the (popular) ‘thirder’ solution to Sleeping Beauty. Here I attempt to rebut their argument, and to clarify my original position. My argument depends on the claim that there are strong structural parallels between the Everettian treatment of a simple spin measurement and a simplified version of the Sleeping Beauty puzzle. The simple spin measurement is a measurement of the x-spin of a spin-1/2 particle whose state is an eigenstate of z-spin. The simplified Sleeping Beauty scenario is one in which Sleeping Beauty is told that she will (definitely) be woken on Monday and on Tuesday, with memory erasure in between. In each case, the agent's subjective experience has a branching structure, and she becomes uncertain about her location in this structure. On the basis of this analogy, I argue that the same subjective probability assignment is appropriate in each case to quantify the agent's uncertainty. But the accepted assignment in the Sleeping Beauty case does not allow for pre-measurement probabilities other than 1 when applied to the Everettian case, and the required assignment in the Everettian case entails the problematic halfer assignment when applied to the Sleeping Beauty case.

DOI
10.1093/analys/ann013

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Reply to Lewis: metaphysics versus epistemology

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Peter J. Lewis (2007) has argued that the Everettian interpretation of quantum mechanics implies the unpopular halfer position in the Sleeping Beauty debate. We retorted that it is perfectly coherent to be an Everettian and an ordinary thirder (Papineau and Durà-Vilà 2009). In a recent reply to our paper Lewis (2009) further clarifies the basis for his thinking. We think this brings out nicely where he goes wrong: he underestimates the importance of metaphysical considerations in determining rational credences. Lewis's original argument hinged on the epistemic parallels between (a) an Everettian scenario where the x-spin of an electron in an eigenstate of z-spin is measured, with the result hidden from an observer and (b) a simplified Sleeping Beauty scenario where Sleeping Beauty is told that she will be woken on Monday and on Tuesday, with memory erasure in between. Lewis (2007: 60) pointed out that in both cases the agent's subjective experience has the same branching structure, with the agent becoming uncertain about her location therein. He concluded that the agent should adopt the same credences in both cases. Given that Everettians are committed in the spin case to assigning pre-measurement credences of 1/2 to ‘up’ and ‘down’, Lewis infers that the Everettian interpretation implies that Sleeping Beauty should similarly assign pre-sleeping credences of 1/2 to waking on Monday and waking on Tuesday. But this would of course be very bad for the Everettian interpretation, since Sleeping Beauty's credences here should clearly be 1.

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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 mechanics1 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’ (2007a) 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.

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I have argued (Lewis 2007) that anyone who adopts the Everettian approach to the foundations of quantum mechanics must also accept the (unpopular) ‘halfer’ solution to the Sleeping Beauty puzzle. Papineau and Durà-Vilà (2009) have responded with an argument that it is perfectly cogent both to be an Everettian and to accept the (popular) ‘thirder’ solution to Sleeping Beauty. Here I attempt to rebut their argument, and to clarify my original position. My argument depends on the claim that there are strong structural parallels between the Everettian treatment of a simple spin measurement and a simplified version of the Sleeping Beauty puzzle. The simple spin measurement is a measurement of the x-spin of a spin-1/2 particle whose state is an eigenstate of z-spin. The simplified Sleeping Beauty scenario is one in which Sleeping Beauty is told that she will (definitely) be woken on Monday and on Tuesday, with memory erasure in between. In each case, the agent's subjective experience has a branching structure, and she becomes uncertain about her location in this structure. On the basis of this analogy, I argue that the same subjective probability assignment is appropriate in each case to quantify the agent's uncertainty. But the accepted assignment in the Sleeping Beauty case does not allow for pre-measurement probabilities other than 1 when applied to the Everettian case, and the required assignment in the Everettian case entails the problematic halfer assignment when applied to the Sleeping Beauty case.
Peter J. Lewis (2007) has argued that the Everettian interpretation of quantum mechanics implies the unpopular halfer position in the Sleeping Beauty debate. We retorted that it is perfectly coherent to be an Everettian and an ordinary thirder (Papineau and Durà-Vilà 2009). In a recent reply to our paper Lewis (2009) further clarifies the basis for his thinking. We think this brings out nicely where he goes wrong: he underestimates the importance of metaphysical considerations in determining rational credences. Lewis's original argument hinged on the epistemic parallels between (a) an Everettian scenario where the x-spin of an electron in an eigenstate of z-spin is measured, with the result hidden from an observer and (b) a simplified Sleeping Beauty scenario where Sleeping Beauty is told that she will be woken on Monday and on Tuesday, with memory erasure in between. Lewis (2007: 60) pointed out that in both cases the agent's subjective experience has the same branching structure, with the agent becoming uncertain about her location therein. He concluded that the agent should adopt the same credences in both cases. Given that Everettians are committed in the spin case to assigning pre-measurement credences of 1/2 to ‘up’ and ‘down’, Lewis infers that the Everettian interpretation implies that Sleeping Beauty should similarly assign pre-sleeping credences of 1/2 to waking on Monday and waking on Tuesday. But this would of course be very bad for the Everettian interpretation, since Sleeping Beauty's credences here should clearly be 1.
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 mechanics1 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’ (2007a) 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.
In Bradley ([2011b]), I offered an analysis of Sleeping Beauty and the Everettian interpretation of quantum mechanics (EQM). I argued that one can avoid a kind of easy confirmation of EQM by paying attention to observation selection effects, that halfers are right about Sleeping Beauty, and that thirders cannot avoid easy confirmation for the truth of EQM. Wilson ([forthcoming]) agrees with my analysis of observation selection effects in EQM, but goes on to, first, defend Elga’s ([2000]) thirder argument on Sleeping Beauty and, second, argue that the analogy I draw between Sleeping Beauty and EQM fails. I will argue that neither point succeeds. 1 Introduction2 Background3 Wilson’s Argument for ⅓ in Sleeping Beauty4 Reply: Explaining Away the Crazy5 Wilson's Argument for the Breakdown of the Analogy6 Reply: The Irrelevance of Chance7 Conclusion
Darren Bradley has recently appealed to observation selection effects to argue that conditionalization presents no special problem for Everettian quantum mechanics, and to defend the ‘halfer’ answer to the puzzle of Sleeping Beauty. I assess Bradley’s arguments and conclude that while he is right about confirmation in Everettian quantum mechanics, he is wrong about Sleeping Beauty. This result is doubly good news for Everettians: they can endorse Bayesian confirmation theory without qualification, but they are not thereby compelled to adopt the unpopular ‘halfer’ answer in Sleeping Beauty. These considerations suggest that objective chance is playing an important and under-appreciated role in Sleeping Beauty. 1 Introduction 2 Confirmation in Everettian Quantum Mechanics 3 Sleeping Beauty 4 The Selection Model 5 Bradley’s Argument 6 The Right Route to ⅓ 7 The Breakdown of the Analogy 8 Alternative Diagnoses 9 God’s Gambling Game 10 Non-chancy Sleeping Beauty Cases 11 Conclusion
The Sleeping Beauty paradox in epistemology and the many-worlds interpretation of quantum mechanics both raise problems concerning subjective probability assignments. Furthermore, there are striking parallels between the two cases; in both cases personal experience has a branching structure, and in both cases the agent loses herself among the branches. However, the treatment of probability is very different in the two cases, for no good reason that I can see. Suppose, then, that we adopt the same treatment of probability in each case. Then the dominant ‘thirder’ solution to the Sleeping Beauty paradox becomes incompatible with the tenability of the many-worlds interpretation.
I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of considering that some balls in the Entanglement urn have ontologically different properties form normal ones. In this context, considering a Monday-waking (drawing a red ball) leads to two different situations that are assigned each a different probability. This leads to a two-sided account of the Sleeping Beauty problem. On the one hand, the first situation is handled by the argument for 1/3. On the other hand, the second situation corresponds to a reasoning that echoes the argument for 1/2 but that leads however, to different conclusions.