Universität zu Köln

Araujo, Mateus (2019). Probability in Two Deterministic Universes. Found. Phys., 49 (3). S. 202 - 232. NEW YORK: SPRINGER. ISSN 1572-9516

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Abstract

How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with relative frequencies matching their objective probabilities. To address the first question, we generalise the Deutsch-Wallace theorem to a wide class of many-world theories, and show that the subjective probabilities are given by a norm that depends on the dynamics of the theory: the 2-norm in the usual Many-Worlds interpretation of quantum mechanics, and the 1-norm in a classical many-worlds theory known as Kent's universe. To address the second question, we show that if one takes the objective probability of an event to be the proportion of worlds in which this event is realised, then in most worlds the relative frequencies will approximate well the objective probabilities. This suggests that the task of determining the objective probabilities in a many-worlds theory reduces to the task of determining how to assign a measure to the worlds.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Araujo, Mateus UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-155051
DOI:	10.1007/s10701-019-00241-7
Journal or Publication Title:	Found. Phys.
Volume:	49
Number:	3
Page Range:	S. 202 - 232
Date:	2019
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1572-9516
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language QUANTUM PROBABILITY; MECHANICS; PROOF; DECOHERENCE; EVERETT Multiple languages Physics, Multidisciplinary Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/15505