The trouble with the idea of measurement is its seeming clarity, its obviousness, its implicit claim to finality in any inquisotory discourse. Its status in philosophy of science is taken to be utterly primitive; hence the difficulties it embodies, if any, tend to escape detection and scrutiny. Yet it cannot be primitive in the sense of being exempt from analysis; for if it were every measurement would require to be simply accepted as a protocol of truth, and one should never (...) ask which of two conflicting measurements is correct, or preferable. Such questions are continually being asked, and their propriety in science indicates that even measurement, with its implication of simplicity and adroitness, points beyond itself to other matters of importance on which it relies for validation. (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)

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)