Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-06T10:40:48.316Z Has data issue: false hasContentIssue false
  • English
  • Français

The Sum Rule is Well-Confirmed

Published online by Cambridge University Press:  01 April 2022

Clark Glymour
Clark Glymour*
Affiliation:
University of Oklahoma
Get access Rights & Permissions [Opens in a new window]

Extract

Simon Kochen and Ernst Specker's well-known argument ([6]) against hidden variable theories for quantum mechanics is also an argument against the possibility of quantum systems having, simultaneously, precise values for all of the dynamical quantities associated with such systems. Devices for defeating the argument were in the literature even before its publication, but recently Arthur Fine has raised a new difficulty ([4]). Fine points out that Kochen and Specker's argument requires the following principles:

Sum Rule: At all times, in all states, the value of the quantity with operator A + B is the sum of the values of the quantity with operator A and the quantity with operator B, provided A, B commute.

Product Rule: At all times, in all states, the value of the quantity with operator AB is the product of the values of the quantities with operators A and B, provided A, B commute.

Type
Discussion
Information
Philosophy of Science , Volume 44 , Issue 1 , March 1977 , pp. 86 - 94
Copyright
Copyright © 1977 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

†

I am indebted to Mr. Richard Healey and to Mr. James Van Aken for removing many of my confusions about the subject of this note.

References

REFERENCES

Bell, J. “On the Problem of Hidden Variables in Quantum Mechanics.” Reviews of Modern Physics 38 (1966): 447.CrossRefGoogle Scholar
Boyd, R. “Realism, Underdetermination, and a Causal Theory of Evidence.” Nous 7 (1973): 1.CrossRefGoogle Scholar
Cross, W. and Ramsey, N. “The Conservation of Energy and Momentum in Compton Scattering.” Physical Review 80 (1950): 929.CrossRefGoogle Scholar
Fine, A. “On the Completeness of Quantum Theory.” Synthese 29 (1974): 257.CrossRefGoogle Scholar
Glymour, C. “Relevant Evidence.” Journal of Philosophy 72 (1975): 403.CrossRefGoogle Scholar
Kochen, S. and Specker, E. “The Problem of Hidden Variables in Quantum Mechanics.” Journal of Mathematics and Mechanics 17 (1967): 59.Google Scholar
Stuewer, R. The Compton Effect. New York: Science History, 1975.Google Scholar
Williams, E. “Concerning the Scattering of Fast Electrons and of Cosmic Ray Particles.” Proceedings of the Royal Society 169 (1939): 531.Google Scholar
van Fraassen, B. “To Save the Phenomena.” unpublished manuscript. U. of Toronto, 1975.Google Scholar