Everettian probabilities, the Deutsch-Wallace theorem and the Principal Principle

TL;DR

This paper critically examines the role of the Deutsch-Wallace theorem in Everettian quantum mechanics, questioning its justification of the Principal Principle and analyzing its implications for the nature of probability in physics.

Contribution

It provides a critical analysis of the Deutsch-Wallace theorem, arguing it does not justify the Principal Principle and discusses the implications for understanding probability in quantum mechanics.

Findings

The DW theorem does not justify the Principal Principle.

Probabilities in Everettian quantum mechanics are more complex than the theorem suggests.

Recent claims suggest the DW theorem may be redundant in explaining quantum probabilities.

Abstract

This paper is concerned with the nature of probability in physics, and in quantum mechanics in particular. It starts with a brief discussion of the evolution of Itamar Pitowsky's thinking about probability in quantum theory from 1994 to 2008, and the role of Gleason's 1957 theorem in his derivation of the Born Rule. Pitowsky's defence of probability therein as a logic of partial belief leads us into a broader discussion of probability in physics, in which the existence of objective "chances" is questioned, and the status of David Lewis' influential Principal Principle is critically examined. This is followed by a sketch of the work by David Deutsch and David Wallace which resulted in the Deutsch-Wallace (DW) theorem in Everettian quantum mechanics. It is noteworthy that the authors of this important decision-theoretic derivation of the Born Rule have different views concerning the meaning of probability. The theorem, which was the subject of a 2007 critique by Meir Hemmo and Pitowsky, is critically examined, along with recent related work by John Earman. Here our main argument is that the DW theorem does not provide a justification of the Principal Principle, contrary to claims by Wallace and Simon Saunders. A final section analyses recent claims to the effect that that the DW theorem is redundant, a conclusion that seems to be reinforced by consideration of probabilities in "deviant' branches in the Everettian multiverse.