de Ronde, Christian and Massri, Cesar
(2019)
Against the Tyranny of 'Pure States' in Quantum Theory.
[Preprint]
Abstract
In this paper we provide arguments against the dominant role played by the notion of pure sate within the orthodox account of quantum theory. Firstly, we will argue that the origin of this notion is intrinsically related to the widespread empirical-positivist understanding of physics according to which 'theories describe actual observations of subjects (or agents)'. Secondly, we will show how within the notion of pure state there is a scrambling of two mutually incompatible definitions. On the one hand, a contextual definition which attempts to provide an intuitive physical grasp in terms of the certain prediction of a measurement outcome; and on the other hand, a non- contextual purely abstract mathematical definition which has no clear physical content. We will then turn our attention to the way in which pure states and mixtures have been considered by two categorical approaches to QM, namely, the topos approach originally presented by Chris Isham and Jeremy Butterfield [27, 28, 29] and the more recent logos categorical approach presented by the authors of this article [11, 12]. While the first approach presents serious difficulties in order to produce an orthodox understanding of pure states and mixtures, the latter presents a new scheme in which the distinction between pure states and mixtures becomes completely irrelevant.
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