Transitions without connections: quantum states, from Bohr and Heisenberg to quantum information theory

In his recent paper, L. Freidel noted that instead of representing the motion of electrons in terms of oscillators and predicting their future states on the basis on this representation, as in the previous, classical, electron theory of H. Lorentz, quantum theory was, beginning nearly with its inception, concerned with the probabilities of transitions between states of electrons, without necessarily representing how these transitions come about. Taking N. Bohr’s and then W. Heisenberg’s thinking along these lines in, respectively, Bohr’s 1913 atomic theory and Heisenberg’s quantum mechanics of 1925 as a point of departure, this article reconsiders, from a nonrealist perspective (which suspends or even precludes this representation of the mechanism behind these transitions), the concept of quantum state, as a physical concept, in contradistinction to the mathematical concept of quantum state, a vector in the Hilbert-space formalism of quantum mechanics. Transitions between quantum states appear, from this perspective, as “transitions without connections,” because, while one can register the change from one quantum phenomena to another, observed in measuring instruments, we have no means of representing or possibly even conceiving of how this change comes about. The article will also discuss quantum field theory and, in closing, briefly quantum information theory as confirming, and giving additional dimensions to, these concepts of quantum state and transitions between them