dialectica

The Principle of Anomaly in Quantum Mechanics

Hans Reichenbach

Published Jan 1, 1948• 42 citations

Abstract

The following two questions are examined: 1o Do the unobservable parameters possess precise, though unknown, values ? 2o If these unobservable values were known, would it be possible to make precise predictions of the reults of later measurements ? The answer is shown to be negative; the questions, therefore, are not meaningless, being capable of a falsification. The inquiry leads to the establishment of a principle of anomaly, more precisely speaking, of causal anomaly, which is to be added to Heisenberg's principle of indeterminacy. This principle states that the principle of action by contact is violated whenever definite values are assigned to the unobserved quantities, i. e., when an exhaustive interpretation of quantum mechanics is used. The two most important exhaustive interpretations are given by the corpuscle and the wave interpretation; each leads to causal anomalies, though for different places. The causal anomalies can be eliminated by the use of a restrictive interpretation, which separates statements about unobserved quantities, as a third propositional class, from true or false statements. Bohr and Heisenberg have called such statements meaningless, without being able to eliminate them completely; these statements arte thus merely shifted into the metalanguage. In another version of the restrictive interpretation such statements are assigned a third truth value, the value indeterminate, and quantum mechanics is then presented in the form of a three-valued logic. The inquiry is carried through without the presupposition of any philosophical conception; every interpretation is examined with respect to the consequences to which it leads. - H. R.'

DOI: 10.1111/j.1746-8361.1948.tb00707.x

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