Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-27T17:49:35.732Z Has data issue: false hasContentIssue false
  • English
  • Français

Reciprocity in the Uncertainty Relations

Published online by Cambridge University Press:  14 March 2022

Peter Kirschenmann
Peter Kirschenmann*
Affiliation:
Wayne State University
Get access Rights & Permissions [Opens in a new window]

Abstract

A philosophical interpretation of quantum mechanics presupposes a clear understanding of what is asserted by this theory. The aim of this paper is to help clarify one specific theorem of quantum mechanics, namely the so-called uncertainty relations. The surprisingly wide spread belief that these relations generally imply a reciprocal or inversely proportional relationship between the respective uncertainties is shown to be mistaken. Several reasons why this mistaken belief has been embraced are suggested. The conditions under which one could say that the uncertainty relations imply an inversely proportional relationship between uncertainties are specified.

Type
Research Article
Information
Philosophy of Science , Volume 40 , Issue 1 , March 1973 , pp. 52 - 58
Copyright
Copyright © 1973 by The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

A considerable part of this paper was worked out during the academic year 1970–71 while I was on a leave of absence from Wayne State University and had a grant from the Canada Council. I should like to thank Prof. M. Bunge, director of the Foundations and Philosophy of Science Unit at McGill University for his hospitality and helpful discussions.

References

REFERENCES

[1] Ballentine, L. E. “The Statistical Interpretation of Quantum Mechanics.” Reviews of Modern Physics 42 (1970): 358–381.10.1103/RevModPhys.42.358CrossRefGoogle Scholar
[2] Bunge, M. Foundations of Physics. New York: Springer, 1967.10.1007/978-3-642-49287-7CrossRefGoogle Scholar
[3] Carruthers, P. and Nieto, M. M. “Phase Angle Variables in Quantum Mechanics.” Reviews of Modern Physics 40 (1968): 411–440.10.1103/RevModPhys.40.411CrossRefGoogle Scholar
[4] Heisenberg, W. “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik.” Zeitschrift für Physik 43 (1927): 172–198.10.1007/BF01397280CrossRefGoogle Scholar
[5] Heisenberg, W. Die physikalischen Prinzipien der Quantentheorie. Stuttgart: Hirzel, 1930. (Transi, of The Physical Principles of the Quantum Theory. Chicago: University of Chicago Press, 1930.)Google Scholar
[6] Heisenberg, W. Der Teil und das Ganze—Gespräche im Umkreis der Atomphysik. München: Piper, 1969. (Transl. as Physics and Beyond: Encounters and Conversations. New York: Harper & Row, 1971.)Google Scholar
[7] Hill, E. L. “Classical Mechanics as a Limiting Form of Quantum Mechanics.” Mind, Matter, and Method. Edited by Feyerabend, P. K. and Maxwell, G. Minneapolis: University of Minnesota Press, 1966. Pages 430–448.Google Scholar
[8] Jammer, M. The Conceptual Development of Quantum Mechanics. New York: McGraw-Hill, 1966.Google Scholar
[9] Juhos, B. Die erkenntnislogischen Grundlagen der modernen Physik. Berlin: Duncker & Humboldt, 1967.Google Scholar
[10] Margenau, H. and Cohen, L. “Probabilities in Quantum Mechanics.” Quantum Theory and Reality. Edited by Bunge, M. New York: Springer, 1967. Pages 71–89.10.1007/978-3-642-88026-1_5CrossRefGoogle Scholar