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The British Journal for the Philosophy of Science

Epistemology Quantized: circumstances in which we should come to believe in the Everett interpretation

David Wallace

Published Dec 1, 2006• 105 citations

Abstract

I consider exactly what is involved in a solution to the probability problem of the Everett interpretation, in the light of recent work on applying considerations from decision theory to that problem. I suggest an overall framework for understanding probability in a physical theory, and conclude that this framework, when applied to the Everett interpretation, yields the result that that interpretation satisfactorily solves the measurement problem. 1. Introduction 2. What is probability? 2.1Objective probability and the Principal Principle 2.2Three ways of satisfying the functional definition 2.3Cautious functionalism 2.4Is the functional definition complete? 3. The Everett interpretation and subjective uncertainty 3.1Interpreting quantum mechanics 3.2The need for subjective uncertainty 3.3Saunders' argument for subjective uncertainty 3.4Objections to Saunders' argument 3.5Subjective uncertainty again: arguments from interpretative charity 3.6Quantum weights and the functional definition of probability 4. Rejecting subjective uncertainty 4.1The fission program 4.2Against the fission program 5. Justifying the axioms of decision theory 5.1The primitive status of the decision-theoretic axioms 5.2Holistic scepticism 5.3The role of an explanation of decision theory 6. Conclusion

DOI: 10.1093/bjps/axl023

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I consider exactly what is involved in a solution to the probability problem of the Everett interpretation, in the light of recent work on applying considerations from decision theory to that problem. I suggest an overall framework for understanding probability in a physical theory, and conclude that this framework, when applied to the Everett interpretation, yields the result that that interpretation satisfactorily solves the measurement problem. 1. Introduction 2. What is probability? 2.1Objective probability and the Principal Principle 2.2Three ways of satisfying the functional definition 2.3Cautious functionalism 2.4Is the functional definition complete? 3. The Everett interpretation and subjective uncertainty 3.1Interpreting quantum mechanics 3.2The need for subjective uncertainty 3.3Saunders' argument for subjective uncertainty 3.4Objections to Saunders' argument 3.5Subjective uncertainty again: arguments from interpretative charity 3.6Quantum weights and the functional definition of probability 4. Rejecting subjective uncertainty 4.1The fission program 4.2Against the fission program 5. Justifying the axioms of decision theory 5.1The primitive status of the decision-theoretic axioms 5.2Holistic scepticism 5.3The role of an explanation of decision theory 6. Conclusion

Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track objective ones. But it is shown that if probability only arises with decoherence, then they must be given by the Born rule. That further, on the Everett interpretation, we have a clear statement of what probabilities are, in terms of purely categorical physical properties; and finally, along lines laid out by Deutsch and Wallace, that there is a clear basis in the axioms of decision theory as to why subjective probabilities should track these objective ones. These results hinge critically on the absence of hidden-variables or any other mechanism (such as state-reduction) from the physical interpretation of the theory. The account of probability has traditionally been considered the principal weakness of the Everett interpretation; on the contrary it emerges as one of its principal strengths.

Abstract This chapter discusses what would need to be done to address the epistemic difficulties associated with the Everett interpretation, then considers a number of putative solutions to the Everettian probability problem and assesses whether these approaches succeed in solving the epistemic aspects of that problem. The discussion covers naïve branch counting and Saunders’ sophisticated branch counting; Vaidman’s ‘measure of existence’ approach; the Deutsch-Wallce decision-theoretic approach; and the Sebens-Carroll and Vaidman-McQueen self-locating uncertainty approaches.

The Everett interpretation of quantum mechanics is an increasingly popular alternative to the traditional Copenhagen interpretation, but there are a few major issues that prevent the widespread adoption. One of these issues is the origin of probabilities in the Everett interpretation, which this thesis will attempt to survey. The most successful resolution of the probability problem thus far is the decision-theoretic program, which attempts to frame probabilities as outcomes of rational decision making. This marks a departure from orthodox interpretations of probabilities in the physical sciences, where probabilities are thought to be objective, stemming from symmetry considerations. This thesis will attempt to offer evaluations on the decision-theoretic program.

This paper analyses an attempt to reintroduce the probabilistic predictions of quantum mechanics into the Everett interpretation. An overview of the measurement problem and the Everett interpretation are first given, with particular attention paid to the issue of probability within a deterministic theory. An argument is put forth that observers in an Everettian multiverse generically experience a period of post-measurement uncertainty in regards to their location. It is further argued that this uncertainty allows pre-measurement to observers to act as if they are uncertain about future outcomes. This is then the justification for attaching probabilities to the squared moduli of the wave function. It is also noted that there is an assumption of typicality present in discussions of probability within Everett and some arguments to justify this assumption are considered.