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"Quantitative measure of correlation," minipaper, 1955

Hugh Everett

Published May 20, 2011• 0 citations
OpenAlex

Abstract

Before writing a first draft of the long thesis, Hugh Everett wrote three short papers, often refered to as his minipapers, for John Wheeler to review. This minipaper, called "Quantitative measure of correlation," lays some groundwork for the application of information theory as a measure of the degree of quantum correlation or entanglement. From very early in the project, Everett thought that Shannon information theory would provide insight into pure wave mechanics. While statistical measures, such as standard deviation, would have sufficed, Everett developed information-theoretic measures to represent such things as the width of distributions and the degree of correlation between the states of multiple systems. He thought that the standard quantum uncertainty relations were best expressed in an information theoretic way. The present document is the typed version of the minipaper that Wheeler would have seen and commented on.

Related papers

"On the Foundations of Quantum Mechanics," short thesis as defended, 1957

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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 \\emph{Reviews of Modern Physics} in July 1957 as "The `Relative State' Formulation of Quantum Mechanics.'' This document is Everett's short thesis, as submitted to Princeton for his degree.

•Jan 1, 1957•0 citations

"2. Information and Correlation in Quantum Mechanics," handwritten draft, circa 1956

Everett, Hugh

Among Hugh Everett's files were a number of handwritten documents related to the writing of his thesis. Many of them were drafts of material that ultimately appeared in the long thesis. This document, titled "2 Information and Correlation in Quantum Mechanics" by Everett, was found in a file labeled "Recent Drafts," which consisted of documents that match closely with the final version of the long thesis.

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Notes on possible thesis titles, circa 1955

Everett, Hugh

Among Hugh Everett's files were a number of handwritten documents related to the writing of his thesis. Some of them were early notes on ideas and material that ultimately appeared in the long thesis. This document, found loose among Everett's papers, includes brainstorming notes on possible titles for the long thesis. He originally settled on The Theory of the Universal Wave Function, but then changed it to Quantum Mechanics without Probability before distributing drafts to Bohr and others.

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The Everett interpretation of quantum mechanics

Bryce Seligman DeWitt

Introduction In the July 1957 issue of the Reviews of Modern Physics: Hugh Everett iii put forward a new interpretation of quantum mechanics (Everett 1957). John Wheeler, Everett's thesis adviser, published, in the same issue, an accompanying paper supporting Everett's views (Wheeler 1957). Everett's aim was to cut through the fuzzy thinking displayed by many authors, some of them quite prominent, who in previous years had written incredibly dull papers on how they understood quantum mechanics. Everett's idea was simply to assume that quantum mechanics provides a description of reality in exactly the same sense as classical mechanics was once thought to do. This is a shocking idea, for it leads to a multiplicity of “realities.” Few physicists in 1957 were prepared to accept it. And yet it can be shown to work. It is the purpose of this article to expand on Everett's original demonstration and to reveal the courage John Wheeler displayed in betting that his student was right. Classical theory of measurement System, apparatus, coupling Our starting point is the standard theory of measurement, which we shall first examine classically. In its simplest form a measurement involves just two dynamical entities: a system and an apparatus . It is the role of the apparatus to record the value of some system observable s . For this purpose system and apparatus must be coupled together for a certain period of time, which will be taken to be finite.

Cambridge University Press eBooks•Apr 22, 2004•26 citations

"III. Quantum mechanics of composite systems," handwritten draft, circa 1956

Everett, Hugh

Among Hugh Everett's files were a number of handwritten documents related to the writing of his thesis. Many of them were drafts of material that ultimately appeared in the long thesis. This document, titled " III Quantum mechanics of composite systems" by Everett, was found in a file labeled "Recent Drafts," which consisted of documents that match closely with the final version of the long thesis.

•Jan 1, 1956•0 citations

"III. Quantum Mechanics," handwritten draft, circa 1955

Everett, Hugh

Among Hugh Everett's files were a number of handwritten documents related to the writing of his thesis. Many of them were drafts of material that ultimately appeared in the long thesis. This single page, titled "III Quantum Mechanics" by Everett, was found in a file labeled "Early drafts".

•Jan 1, 1955•0 citations
Before writing a first draft of the long thesis, Hugh Everett wrote three short papers, often refered to as his minipapers, for John Wheeler to review. This minipaper, called "Quantitative measure of correlation," lays some groundwork for the application of information theory as a measure of the degree of quantum correlation or entanglement. From very early in the project, Everett thought that Shannon information theory would provide insight into pure wave mechanics. While statistical measures, such as standard deviation, would have sufficed, Everett developed information-theoretic measures to represent such things as the width of distributions and the degree of correlation between the states of multiple systems. He thought that the standard quantum uncertainty relations were best expressed in an information theoretic way. The present document is the typed version of the minipaper that Wheeler would have seen and commented on.
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 \\emph{Reviews of Modern Physics} in July 1957 as "The `Relative State' Formulation of Quantum Mechanics.'' This document is Everett's short thesis, as submitted to Princeton for his degree.
Among Hugh Everett's files were a number of handwritten documents related to the writing of his thesis. Some of them were early notes on ideas and material that ultimately appeared in the long thesis. This document, found loose among Everett's papers, includes brainstorming notes on possible titles for the long thesis. He originally settled on The Theory of the Universal Wave Function, but then changed it to Quantum Mechanics without Probability before distributing drafts to Bohr and others.
Introduction In the July 1957 issue of the Reviews of Modern Physics: Hugh Everett iii put forward a new interpretation of quantum mechanics (Everett 1957). John Wheeler, Everett's thesis adviser, published, in the same issue, an accompanying paper supporting Everett's views (Wheeler 1957). Everett's aim was to cut through the fuzzy thinking displayed by many authors, some of them quite prominent, who in previous years had written incredibly dull papers on how they understood quantum mechanics. Everett's idea was simply to assume that quantum mechanics provides a description of reality in exactly the same sense as classical mechanics was once thought to do. This is a shocking idea, for it leads to a multiplicity of “realities.” Few physicists in 1957 were prepared to accept it. And yet it can be shown to work. It is the purpose of this article to expand on Everett's original demonstration and to reveal the courage John Wheeler displayed in betting that his student was right. Classical theory of measurement System, apparatus, coupling Our starting point is the standard theory of measurement, which we shall first examine classically. In its simplest form a measurement involves just two dynamical entities: a system and an apparatus . It is the role of the apparatus to record the value of some system observable s . For this purpose system and apparatus must be coupled together for a certain period of time, which will be taken to be finite.