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Fluctuation and Noise Letters

Typicality in Pure Wave Mechanics

Jeffrey Alan Barrett

Published Aug 15, 2016• 5 citations
Publisher

Abstract

Hugh Everett III's pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett's argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship between the predictions of pure wave mechanics and the standard quantum probabilities.

DOI
10.1142/s0219477516400095

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Given Hugh Everett III's understanding of the proper cognitive status of physical theories, his relative-state formulation of pure wave mechanics arguably qualifies as an empirically acceptable physical theory. The argument turns on the precise nature of the relationship that Everett requires between the empirical substructure of an empirically faithful physical theory and experience. On this view, Everett provides a weak resolution to both the determinate record and the probability problems encountered by pure wave mechanics, and does so in a way that avoids unnecessary metaphysical complications. Taking Everett's goal to be showing the empirical faithfulness of the relative-state formulation agrees well with his characterization of his project as one of seeking a model for observation in the correlation structure described by pure wave mechanics and seeking a measure of typicality over this empirical substructure that covaries with our empirically warranted expectations. 1 Pure Wave Mechanics and Relative States 2 Everett and Frank 3 Everett on the Nature of Physical Theories 4 Conditions for Empirical Faithfulness 5 The Empirical Faithfulness of Pure Wave Mechanics 6 Conclusion

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Hugh Everett III's pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett's argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship between the predictions of pure wave mechanics and the standard quantum probabilities.
Given Hugh Everett III's understanding of the proper cognitive status of physical theories, his relative-state formulation of pure wave mechanics arguably qualifies as an empirically acceptable physical theory. The argument turns on the precise nature of the relationship that Everett requires between the empirical substructure of an empirically faithful physical theory and experience. On this view, Everett provides a weak resolution to both the determinate record and the probability problems encountered by pure wave mechanics, and does so in a way that avoids unnecessary metaphysical complications. Taking Everett's goal to be showing the empirical faithfulness of the relative-state formulation agrees well with his characterization of his project as one of seeking a model for observation in the correlation structure described by pure wave mechanics and seeking a measure of typicality over this empirical substructure that covaries with our empirically warranted expectations. 1 Pure Wave Mechanics and Relative States 2 Everett and Frank 3 Everett on the Nature of Physical Theories 4 Conditions for Empirical Faithfulness 5 The Empirical Faithfulness of Pure Wave Mechanics 6 Conclusion
Abstract Everett thought of the quantum measurement problem as one of providing a consistent description of nested measurement. He proposed solving the measurement problem by simply supposing that all physical systems whatsoever always obey the linear dynamics and hence never collapse. Dropping the collapse dynamics immediately solves the measurement problem, but it introduces two new problems: explaining determinate measurement records and explaining quantum probabilities. In addition to these, we also consider the problem of empirical coherence in the context of pure wave mechanics. We then discuss how Everett himself understood determinate records and probabilities in his relative-state formulation of pure wave mechanics. What he ultimately provided was an argument that his formulation of quantum mechanics was consistent and empirically faithful. We will see why this is a relative weak standard by which to judge the empirical adequacy of a physical theory.
Abstract We consider a number of radically different ways that Everett’s pure wave mechanics has been understood. Each of these reconstructions aims to provide a stronger variety of empirical adequacy than Everett’s own formulation of the theory. Among the alternative formulations of quantum mechanics we consider are splitting worlds, decohering worlds, many minds, many threads, and many maps. Each of these differs in its metaphysical commitments and, hence, in how it explains determinate measurement records and probabilities. We focus, in particular, on the problem of accounting for the standard quantum probabilities. To this end, we consider the relationship between typicality and probability and contrast synchronic and forward-looking probabilities. We conclude with a brief discussion of epistemological, pragmatic, and information-theoretic formulations of quantum mechanics. A recurring issue in this chapter concerns what it should mean for a physical theory to be empirically adequate.
Hugh Everett's long thesis was submitted to John Archibald Wheeler, his doctoral thesis advisor, in January 1956 under the title "Quantum Mechanics by the Method of the Universal Wave Function.'' It was retitled "Wave Mechanics Without Probability'' and circulated in April of that year to several prominent physicists, including Niels Bohr. Largely due to the criticism of the long thesis by the Copenhagen colleagues, Everett and his advisor John Wheeler rewrote Everett's thesis in the winter of 1957 to produce a much shorter version, which Everett subsequently defended for his Ph.D. under the title "On the Foundations of Quantum Mechanics.'' While the long thesis was organized around the quantum measurement problem and how it is best solved by pure wave mechanics, the short thesis presented Everett's relative-state formulation of pure wave mechanics more as a suitable theory for the development of quantum gravity, cosmology, and field theory. The short thesis no longer contains Everett's chapter on information theory and correlation, his survey of possible solutions to the measurement problem, or his extended discussion of the nature of physical theories. What remains is a distilled presentation of pure wave mechanics, his principle of the fundamental relativity of states, and his derivation of the standard quantum statistics. The short thesis was retitled for publication in Reviews of Modern Physics in July 1957 as "The 'Relative State' Formulation of Quantum Mechanics.'' The version below closely follows the Reviews of Modern Physics article. The long thesis itself was not published until 1973 in the DeWitt and Graham Princeton University Press anthology. It was published under the title "The Theory of the Universal Wave Function." Although Everett did not publish the long thesis, he nonetheless kept a copy of it, and appears to have returned to it periodically to make changes even after the short thesis appeared in print. This document is a scanned version of Everett's personal copy of his long thesis, with his collected comments and changes.
http://dx.doi.org/10.5007/1808-1711.2016v20n1p45Because of the conceptual difficulties it faces, quantum mechanics provides a salient example of how alternative metaphysical commitments may clarify our understanding of a physical theory and the explanations it provides. Here we will consider how postulating alternative quantum worlds in the context of Hugh Everett III’s pure wave mechanics may serve to explain determinate measurement records and the standard quantum statistics. We will focus on the properties of such worlds, then briefly consider other metaphysical options available for interpreting pure wave mechanics. These reflections will serve to illustrate both the nature and the limits of naturalized metaphysics.
Everett’s Relative State Formulation is one of the most famous and debated interpretations of Quantum Theory. Further deepening of the debates has been made possible by the discovery of his unpublished notes and manuscripts. \nMy purpose is to examine Everett’s ideas about physical theories, and show that his understanding of actual experience can be put into correspondence with the latest forms of constructive empiricism and empirical adequacy: the problem of ‘extra structure’, which is the reason for metaphysical interpretations, can be solved by using a pragmatic criterion to choose in which way the theory should correspond to empirical evidence. \nA quantitative justification for probabilities in Everettian context is given in terms of typicality.