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arXiv · 1504.05259

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

André L. G. Mandolesi
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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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André L. G. Mandolesi. 2017-11-07. Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects. https://doi.org/10.1007/s10701-018-0179-7

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