A formal proof of the Born rule from decision-theoretic assumptions

2009/06/15 by David Wallace, Wallace, David · 3 voices
Arts and Humanities · Physics and Astronomy · #FOS: Physical sciences #Philosophy and History of Science #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #quant-ph

paper · pdf · doi:10.48550/arxiv.0906.2718

openalex publication_date 2009/06/15 · arxiv published 2009/06/15 · arxiv updated 2009/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then prove it formally, and lastly consider a number of proposed ``counter-examples'' to show exactly which premises of the argument they violate.

Discussions

• The MWI is what you get if you take seriously the idea that the equations of motion of quantum theory describe reality. In classical physics the evolution of a physical quantity, such as the $x$ posit [stackexchange, 4 points]
• I mean, maybe? Either way I'm happy to use measure theory as a theory of our measurements. arxiv.org/abs/0906.2718 [bsky, 4 points, 2 comments]
• I don't remember enough of the details to get into a discussion, but does this 2009 paper by David Wallace do what you're looking for? arxiv.org/abs/0906.2718 [bsky, 2 points, 0 comments]

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