Locating the many worlds.

Graham P. Collins

Lev Vaidman A

The growing interest in the concept of probability of self-location of a conscious agent has created multiple controversies. Considering David Albert's setup in which he described his worries about consistency of the concept, I identify the sources of these controversies and argue that defining "self" in an operational way provides a satisfactory meaning for the probability of self-location of an agent in a quantum world. It keeps the nontrivial feature of having subjective ignorance of self-location without ignorance about the state of the universe. It also allows defining the Born rule in the many-worlds interpretation of quantum mechanics and proving it from some natural assumptions.

Jacob Alkow

Peter J. Lewis

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: (1) If probability can be applied at all to measurement outcomes, it must function as a measure of an agent's self-location uncertainty. (2) Such probabilities typically violate reflection. (3) Many-worlds branching does not have sufficient structure to admit self-location probabilities. (4) Decision-theoretic arguments do not solve this problem.

Benjamin Bähr, Boris Lemmer, Rina Piccolo

Charles T. Sebens

There appear to be multiple mathematically and physically distinct theories that successfully reproduce the empirical predictions of quantum mechanics, so-called "interpretations" of quantum mechanics. This dissertation uses the tools of formal epistemology (prominently, the concept of self-locating uncertainty) to investigate which of the theories that have been put forward really are empirically adequate and what alternatives can be devised. The first chapter introduces a novel theory that incorporates aspects of two well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. The quantum wave function can be represented as a field on configuration space, the space of possible ways particles can be arranged. According to Bohmian mechanics a single point in this space is special; it represents the way all of the particles actually are arranged. The newly introduced theory holds that many of the points in configuration space are special; for each, there is a world in which particles are arranged that way. In general, there will be multiple worlds that are so similar that an agent cannot tell directly from experience which they are in; self-locating uncertainty is unavoidable. The next chapter argues for the empirical adequacy of the many-worlds interpretation. In this version of quantum mechanics, processes like quantum measurements cause agents to split into multiple copies and enter periods of self-locating uncertainty. An epistemic principle demarcating which facts about the world one's credences might reasonably depend on (only facts about what's happening around here) is used to derive probabilistic predictions from the many-worlds interpretation. In the third chapter self-locating uncertainty is employed in evaluating another version of quantum mechanics, Ghirardi-Rimini-Weber theory. In this theory, random collapse events prevent our world from splitting into many. If the collapse events are rare, this prevention fails. Other worlds have time to form but most are short-lived. Our survival provides evidence against that kind of theory. The final chapter is an original introduction to relativistic quantum field theory which lays groundwork for evaluating the prospects of extending various interpretations of quantum mechanics to this more sophisticated theory.