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The Philosophical Significance of the Concept of Probability in Quantum Mechanics

Published online by Cambridge University Press:  14 March 2022

F. S. C. Northrop
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Extract

A striking characteristic of contemporary science is its emphasis upon probability. This is especially notable in quantum mechanics.

There is a respect in which probability is the same for all scientific theories. Verifiability requires that any theory predict certain numbers which can be compared with the numbers gained by actual operations of measuring. In actual practice these numbers, which we shall term theoretical measurables and operative measurables respectively, never correspond. It becomes necessary, therefore, for the scientist to specify when the deviation between them is such that verification occurs. These specifications are defined by the theory of errors in which the concept of probability has an essential place and a specific meaning. But the theory of errors is the same for all applications; hence, probability as defined by the theory of errors is the same for all scientific theories.

Type
Research Article
Information
Philosophy of Science , Volume 3 , Issue 2 , April 1936 , pp. 215 - 232
Copyright
Copyright © Philosophy of Science Association 1936

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References

1 The Foundations of Physics, R. B. Lindsay and H. Margenau, New York, 1936.

2 I.e. a body of abstract purely logical or mathematical forms, devoid of material content; sometimes called a system form or a doctrinal function.

3 The postulates of F′ could have been included in those of the system function F. I have separated them in order to distinguish very general properties from more restricted and technical ones; also, for reasons of emphasis which will appear later.

4 Ibid., p. 403.

5 Ibid., pp. 404–5.

6 Strictly speaking, this theorem is not true unless certain additional assumptions are made. Great aid in concentrating attention upon the crucial factors, and no weakening of our final conclusion results from our omission of such technical details, for, as the reader will see in the end, our conclusions would be reinforced rather than weakened were these additional assumptions included.

7 Ibid., p. 405.

8 I.e., an aggregate of theoretical measurables each with its correlated probability. This aggregate composed of theoretical measurables must not be confused with the quite different aggregate composed of measurements to which it is related in the a posteriori definition of probability. Since only the former type of aggregate enters into this paper it is not necessary for us to use some other word than aggregate to designate one of these two classes of things, as von Mises and Lindsay and Margenau have done. It happens that they have reserved the expression “probability aggregate” for the class of measurements, and use the expression “probability distribution” for what we have termed a “theoretical probability aggregate.”

9 Ibid., p. 470.

10 Philosophy of Science, 1934, pp. 133 ff.

11 See Lindsay and Margenau, pp. 404–411.