Analysis of Wallace’s Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects

Foundations of Physics 48 (7):751-782 (2018)

Abstract
To solve the probability problem of the Many Worlds Interpretation of Quantum Mechanics, D. Wallace has presented a formal proof of the Born rule via decision theory, as proposed by D. Deutsch. The idea is to get subjective probabilities from rational decisions related to quantum measurements, showing the non-probabilistic parts of the quantum formalism, plus some rational constraints, ensure the squared modulus of quantum amplitudes play the role of such probabilities. We provide a new presentation of Wallace’s proof, reorganized to simplify some arguments, and analyze it from a formal perspective. Similarities with classical decision theory are made explicit, to clarify its structure and main ideas. A simpler notation is used, and details are filled in, making it easier to follow and verify. Some problems have been identified, and we suggest possible corrections.
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DOI 10.1007/s10701-018-0179-7
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References found in this work BETA

The Foundations of Statistics.Leonard J. Savage - 1954 - Philosophy of Science 23 (2):166-166.
Understanding Deutsch's Probability in a Deterministic Universe.Hilary Greaves - 2004 - Studies in History and Philosophy of Modern Physics 35 (3):423-456.
Quantum Probability From Subjective Likelihood: Improving on Deutsch's Proof of the Probability Rule.David Wallace - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):311-332.

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Probability in Two Deterministic Universes.Mateus Araújo - 2019 - Foundations of Physics 49 (3):202-231.

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