A century of mathematics in America. by Peter Duren

By Peter Duren

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Bohr applies the term ‘complementary’ also to the pieces of information on, or kinds of “evidence” of, such complementary phenomena (PWNB, 2:40; cf. 4:3). That is: “Information regarding the behaviour of an atomic object obtained under definite experimental conditions may [. ] be adequately characterized as complementary to any information about the same object obtained by some other experimental arrangement excluding the fulfilment of the first conditions” (PWNB, 2:26; cf. 54 With the series of terminological and conceptual changes outlined so far in mind, we can briefly summarize Bohr’s ‘middle’-period complementarity argument with regard to quantum theory as follows.

He does not, however, elaborate the meanings of these terms, nor does he always use them in a clear-cut manner. On the one hand, he speaks of “analysis” and “synthesis” as corresponding to the two meanings of complementarity, “mutual exclusion” and joint completion, respectively (PWNB, 4:125). On the other, he also uses the term ‘analysis’ when characterizing the “individuality of quantum effects” as the impossibility of analysis (PWNB, 2:62; cf. 19, 4:128, 134; NBCW, 10:59). ). , and 4:88–91. ).

For all such expressions “imply a departure from basic conventions of language which [. ’ Rather, he argues generally against speaking as if the observer “influence[d] the events which may appear under the conditions he has arranged,” 47 This is worth comparing with his later, more ‘modest’ expression (from 1956): “a revision of the foundation for the unambiguous application of some of our most elementary concepts” (PWNB, 4:171). 48 During World War II, Bohr’s writings on complementarity and related subjects are naturally rather scarce.

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