This is the second, mathematically more detailed part of a paper consisting of two articles, the first having appeared in the immediately preceding issue of this Journal. It shows that a measurement converts a pure case into a mixture with reducible probabilities. The measurement as such permits no inference whatever as to the state of the physical system subjected to measurement after the measurement has been performed. But because the probabilities after the act are classical and therefore reducible, it is (...) often possible to adjust them so that Von Neumann's projection postulate is true. Among the more specific features dealt with in Part II is the occurrence of negative joint probabilities for the measurement of non-commuting operators in certain (not all!) quantum states. The general conclusions reached are stated at the end of the article. (shrink)
Although there is a complete consensus among working physicists with respect to the practical and operational meanings of quantum states, and also a rather loosely formulated general philosophic view called the Copenhagen interpretation, a great deal of confusion and divergence of opinions exist as to the details of the measurement process and its effects upon quantum states. This paper reviews the current expositions of the measurement problem, limiting itself for lack of space primarily to the writings of physicists; it calls (...) attention to inconsistencies and proposes resolutions. Except for a summary of the properties of statistical matrices which are needed in Part II, the first part is non-mathematical and deals largely with two kinds of probability, reducible and irreducible probabilities, which need to be distinguished for a proper understanding of the measurement act. (shrink)
In a recent paper, Prugovečki offered a theory of simultaneous measurements based upon an axiomatic description of the measurement act which excludes certain illustrations of simultaneous measurement previously discussed by the present writers. In this article, the fundamental conceptions of state preparation, state determination, and measurement which underlie our research are compared to Prugovečki's interpretations of the analogous constructs in his theory of measurement.
This paper is the forerunner of an extensive logical analysis of the relativity idea, in which an axiomatic structure based upon the principles of topology is developed. It is meant to expose the manner in which relativity stretches from the pole of pure conception to that of factual observation, from the a priori to the a posteriori. We take pains to show, in connection with special relativity, precisely which elements are postulational and which are verifiable empirically. Our attempt can be (...) somewhat naively characterized as an effort to show how misguided it is to "derive" relativity from such experimental facts as the Michelson-Morley experiment--as so many textbooks profess to do. (shrink)
A definition of causality, somewhat general but clear, is given early in the book. Two ideas which in the popular use of the term "cause" are often intermingled and hidden from view, are exhibited and distinguished; they are antecedence and contiguity. Born's definition of causality is sufficiently wide to include both of them.