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

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, showi...

Full description

Saved in:
Bibliographic Details
Published in:Foundations of physics 2018-07, Vol.48 (7), p.751-782
Main Author: Mandolesi, André L. G.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Classical Mechanics
Decision analysis
Decision theory
History and Philosophical Foundations of Physics
Philosophy of Science
Physics
Physics and Astronomy
Quantum mechanics
Quantum Physics
Relativity Theory
Statistical analysis
Statistical Physics and Dynamical Systems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-018-0179-7