Possible Worlds and Uncertainty Measures

Lubomír Skála, V. Kapsa, Martina Lužová

Toby Handfield

As we saw in the previous chapter, the Everett interpretation seems to dispense with probabilities in quantum mechanics. Instead of describing a world for which many things are possible, but only some of those possibilities are actualised, it suggests a world in which all possibilities actually happen . Moreover, this is something of which we can be absolutely certain . Obviously, this does not straightforwardly fit our experience. We do not see multiple possibilities becoming actual. Whenever we measure a superposed particle, we observe only one property or another. Moreover, we have a very useful probabilistic rule to help us to predict what we will see. How can the success of this probabilistic rule be explained, if an Everett world does not involve any uncertainty? There are two main moves that are employed in response to this challenge. The first – what I call Stage A – is to show that there is a relevant sort of uncertainty, even in a universe where we are certain that everything will happen. The second move – Stage B – is to try to vindicate the probability of the Born rule in particular. That is, to show that we should not merely be uncertain about the future, but that we have good reason to attach the particular probabilities dictated by the Born rule to the possible outcomes of a quantum experiment. We will consider these two stages in turn.

Pieter Kok

Paul Tappenden

The 2022 Tel Aviv conference on the many-worlds interpretation of quantum mechanics highlighted many differences between theorists. A very significant dichotomy is between Everettian fission (splitting) and Saunders–Wallace–Wilson divergence. For fission, an observer may have multiple futures, whereas for divergence they always have a single future. Divergence was explicitly introduced to resolve the problem of pre-measurement uncertainty for Everettian theory, which is universally believed to be absent for fission. Here I maintain that there is indeed pre-measurement uncertainty prior to fission, so long as objective probability is a property of Everettian branches. This is made possible if the universe is a set and branches are subsets with a probability measure. A universe that is a set of universes that are macroscopically isomorphic and span all possible configurations of local beäbles fulfills that role. If objective probability is a property of branches, then a successful Deutsch–Wallace decision-theoretic argument would justify the Principal Principle and be part of probability theory rather than specific to many-worlds theory. Any macroscopic object in our environment becomes a set of isomorphs with different microscopic configurations, each in an elemental universe (elemental in the set-theoretic sense). This is similar to the many-interacting-worlds theory, but the observer inhabits the set of worlds, not an individual world. An observer has many elemental bodies.

Walter Kauzmann

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.