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By Pauling L.

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Extra info for A New Crystal for Wave-Length Measurements of Soft X-Rays

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Clearly, not every observable on M^(VLy) need be the classical representative of a quantum observable. 3. The classical frame As already sketched in the previous section, the classical frame adopts for the set fi of pure states the structure of a measurable space, and all singletons {u>}, u> € fi, are assumed to be measurable. The set of all states, pure states and mixtures, is then identified with the convex set M+(fi) of all the cr-additive probability measures on fl. The pure states correspond 52 to the Dirac measures, namely the probability measures concentrated at a point of fi, to be denoted Su, w € ft.

Clearly it is uniquely determined by the subset F~l{X) of fi: in other words the events are represented by the elements of the Boolean algebra B(U) of all the measurable subsets of fi. With some abuse of notation the subset F~X(X) will be sometimes denoted by the pair (F, X). When we refer to elements of B{Q) without special attention to the random variable they come from we will write a, b,... and say that fi{a), (J, £ A/1+(fi), is the probability of occurrence of the event o when the state of the physical system is / j .

12). The process is described from a "phenomenological" point of view, that is without reference to any explanatory account. The concept may refer to classical as well as to quantum physics. An explicit reference to this concept within the treatments of foundations seems to appear only in the last decades and not by many authors: this absence has certainly not contributed to the clarification of the basic concepts 28 of theoretical physics. Ludwig has attached importance to this concept in a paper going back to 1961, 9 but he has not emphasized it in his later books.

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A New Crystal for Wave-Length Measurements of Soft X-Rays by Pauling L.

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