Foad Dizadji-Bahmani (California State University, Los Angeles)
The main challenge for the Everett interpretation of quantum mechanics (EQM) is the Probability Problem': If every possible outcome is actualized in some branch, how can EQM make sense of the probability of a single outcome as given by the Born rule?
Advocates of EQM have sought to make conceptual room for epistemic probabilities in one of two ways: the decision-theoretic approach (Deutsch (1999), Greaves (2004), Wallace (2012)) and the self-location uncertainty approach (Vaidman (1998; 2011), Sebens and Carroll (2016)).
Both approaches aim to show that faced with branching one is required to set one's credences as per the Born rule. In the first, the result is variously proved from a set of decision-theoretic axioms, which encode what it is to be rational. In the second, Sebens and Carrol prove the result from a single principle, their "Epistemic Separability Principle" (ESP).
Prima facie, the right way to set one's credences in an Everettian multiverse is by "Branch Counting" (BC): the credence a rational agent ought to have in a particular quantum measurement outcome is equal to the ratio of the number of branches in which that (kind of) outcome is actualized to the total number of branches because each branch is equally real.
BC is at odds with the Born rule and thus advocates of EQM have sought to argue against it in various ways. The aim of this paper is to show that these arguments are not persuasive, and that, therefore, the probability problem in EQM has not been solved. I consider two different arguments against BC: that BC is not rational because 1) there is no such thing as the number of branches in EQM; and 2) at least in some salient cases, it conflicts with a more fundamental principle of rationality, namely the aforementioned ESP.
Apropos 1: Wallace (2003, 2007, 2012) has argued that BC is irrational because there is no such thing as the number of branches. I draw a distinction between the following: that the number of branches is indeterminate (metaphysical) and that the number of branches is indeterminable (epistemological). It is there argued that neither claim is justifiable.
Apropos 2: The Sebens and Carrol (2016) self-location uncertainty approach turns on ESP, which requires that the "credence one should assign to being any one of several observers having identical experiences is independent of the state of the environment." They proffer a thought experiment called 'Once-Or-Twice' and show that BC is inconsistent with ESP in this case, and they advocate adopting the latter. I argue contra this that A) BC is a far more intuitive principle than ESP in the given context and that B) a crucial move in their argument — taking equivalent mathematical expressions as representing identical physical situations — is B1) inconsistent in methodology (because in setting up their framework they need to assume that equivalent mathematical expressions do not necessarily represent identical physical situations) and B2) is unjustified in the given thought experiment.
