Complementarity, Chance, and Probability

Abstract

This chapter addresses the peculiar, arguably uniquely peculiar, character of chance and probability in quantum mechanics, at least in certain interpretations of it, such as Bohr’s complementarity. Since, accordingly, the argument of this chapter depends on a particular (type of) interpretation of quantum mechanics and on the epistemology (fundamentally nonrealist in character) that this interpretation entails, this epistemology, as developed in this study, inevitably remains my equally primary subject here. Importantly, this particular view of chance and probability only pertains to the physical behavior of the systems considered and is defined by suspending causality even at the level of the individual entities involved, as against the view usually adopted in classical statistical physics, whereby the behavior of the individual entities comprising the multiplicities considered statistically is assumed to be causal. (As explained throughout this study, in Bohr’s interpretation, these entities are not quantum objects themselves but instead certain individual experimental situations manifest in measuring instruments impacted by their interactions with quantum objects.) By contrast, the mathematics deployed for estimating the probabilities involved is not essentially different, which fact may indeed be seen as adding to the peculiarity of the situation that we encounter in quantum mechanics. I would like to begin by establishing the key terms of my discussion, including the most basic ones, such as “chance” and “probability,” in part because their meanings vary in the discussions of quantum mechanics and their unspecified use may lead to confusion.