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The Gibbs’ Paradox and the Distinguishability of Physical Systems

Published online by Cambridge University Press:  14 March 2022

Robert Rosen
Robert Rosen*
Affiliation:
The University of Chicago
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Abstract

The Gibbs’ Paradox is commonly explained by invoking some type of “principle of indistinguishability,” which asserts that the interchange of identical particles is not a real physical event, i.e., is operationally meaningless. However, if this principle is to provide a satisfactory resolution of the Paradox, it must be operationally possible to determine whether, in fact, two given systems are identical or not. That is, the assertion that the Gibbs’ Paradox is resolvable by an indistinguishability principle actually is an assertion that we can in principle possess a complete set of effective procedures for determining the identity or non-identity of arbitrary physical systems. We show that, in rather general situations, an assertion of this type is not well founded. It is further pointed out that a failure to recognize an incomplete set of “sameness criteria” can lead to serious blunders in physics and in biology.

Type
Research Article
Information
Philosophy of Science , Volume 31 , Issue 3 , July 1964 , pp. 232 - 236
Copyright
Copyright © 1964 by Philosophy of Science Association

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Footnotes

1

This work was supported in part by the United States Air Force Office of Scientific Research under Grant # AF-AFOSR-9-63, and in part by a USPHS Career Development Award.

References

[1] Gibbs, Josiah Willard, Collected Works, 1948, Vol. I. (Yale University Press), p. 167.Google Scholar
[2] Schrödinger, Erwin, Statistical Thermodynamics, 1948 (Cambridge).Google Scholar
[3] Kleene, S. C., Introduction to Metamathematics, 1952 (van Nostrand), p. 382 et seq.Google Scholar
[4] Rosen, Robert, Bull. Math. Biophysics, 24 (1962), 375–393.CrossRefGoogle Scholar
[5] Ling, Gilbert, A Physical Theory of the Living State, 1962 (Blaisdell).Google Scholar