The objective of this project is to evaluate the Deutsch-Wallace strategy for recovering standard quantum probabilities within the many-worlds theory. The many-worlds theory is a proposed solution to the measurement problem in quantum mechanics--the problem that there is nothing in the quantum mechanical state of a system after a measurement corresponding to the (unique) outcome. The many-worlds solution to the measurement problem says that each term in the post-measurement state corresponds to a world, and the explanation of the fact that observers get unique measurement results is that each world contains an observer who sees exactly one result. The main challenge facing the many-worlds theory concerns probability; it is not clear that probabilities can be ascribed to measurement results in a theory in which every measurement result actually occurs, or if probabilities can be ascribed, that they will be identical to those of standard quantum mechanics. Deutsch and Wallace have developed a decision-theoretic program for resolving these problems; they argue that innocuous axioms of rationality constrain an agent to ascribe the usual quantum probabilities to outcomes in the many-worlds case. However, the program, while influential, remains controversial, in large part because it is hard to evaluate the assumptions on which the arguments are based in the unfamiliar context of the many-worlds theory. The research strategy will be to exploit a structural similarity between the many-worlds theory and the much-analyzed Sleeping Beauty problem in epistemology to evaluate the underlying assumptions of the Deutsch-Wallace strategy. In particular, the investigation will focus on the extent to which recent research on the axioms of rationality appropriate to cases of temporal self-location carry over to the less familiar case of self-location in the branching structure of quantum worlds.
Intellectual merit: The many-worlds theory is the most popular quantum mechanical theory among philosophically inclined physicists, and the problem of probability is a serious obstacle facing that theory. The Deutsch-Wallace program is the most promising strategy for solving the problem, but despite much recent work, there is no consensus on whether it works. The structural similarities between the Sleeping Beauty case and many-worlds branching have been noted in the literature, and there is growing recognition that these similarities could be exploited to increase our understanding of rationality, uncertainty and probability in the many-worlds case. But no systematic exploration of the role of self-locating belief in many-worlds theories has yet been attempted.
Broader impacts: The implications of this research reach beyond the confines of academic philosophy and physics. Quantum mechanics, and especially the many-worlds theory of quantum mechanics, involves significant revisions in our view of the nature of the world and the nature of the human person (the "observer"). These revolutionary views catch the popular imagination, and there is considerable appetite in the community for presentations and discussions on quantum mechanics, branching persons and the like. Consequently, aspects of this research will be presented, as appropriate, to community groups. Through teaching Ph.D. students about the foundations of quantum mechanics, and by example, about how to teach the foundations of quantum mechanics, the results of this research will affect the next generation of academic educators and researchers.
