The concepts of uncertainty in prediction and inference are introduced and illustrated using the diffraction of light as an example. The close relationship between the concepts of uncertainty in inference and resolving power is noted. A general quantitative measure of uncertainty in inference can be obtained by means of the so-called statistical distance between probability distributions. When applied to quantum mechanics, this distance leads to a measure of the distinguishability of quantum states, which essentially is the absolute value of the (...) matrix element between the states. The importance of this result to the quantum mechanical uncertainty principle is noted. The second part of the paper provides a derivation of the statistical distance on the basis of the so-called method of support. (shrink)

The life of Niels Bohr spanned times of revolutionary change in science itself as well as its impact on society. Along with Albert Einstein, Bohr can be considered to be this century's major driving force behind the new philosophical and mathematical descriptions of the structure of the atom and the nucleus. Abraham Pais, the acclaimed biogrpaher of Albert Einstein, here traces Bohr's progress from his well-to-do origins in late nineteenth-century Denmark to his position at centre stage in the world political (...) scene, particularly during the Second World War and the development of atomic weapons. Pais' description moves through the science as it was before Bohr, as it became because of Bohr, and thence to Bohr's scientific and philosophical legacy. That legacy is contained both in theory as it is now universally enshrined, as well as in its practice in such great Danish institutions as Riso. But more than that, Pais captures the essence of Bohr, the intensely private family figure who, despite appalling personal tragedy, became one of the most loved cultural figures of recent times. (shrink)