Allen Stairs

Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather aims to complement that work

I begin with an appeal to the GHZ/Mermin state to illustrate the allure of contextualism and value-definiteness. I then point out that standard contextualism, with its special status for non-degenerate operators, faces some embarrassing questions. Further, there is an alternative that apparently does not have the same problems. A modest re-pasting of Hilbert space makes the honors almost even between these two varieties. The paper closes with some reflections on the peculiarities of contextualism.

Emilio Santos has argued (Santos, Studies in History and Philosophy of Physics http: //arxiv-org/abs/quant-ph/0410193) that to date, no experiment has provided a loophole-free refutation of Bell’s inequalities. He believes that this provides strong evidence for the principle of local realism, and argues that we should reject this principle only if we have extremely strong evidence. However, recent work by Malley and Fine (Non-commuting observables and local realism, http: //arxiv-org/abs/quant-ph/0505016) appears to suggest that experiments refuting Bell’s inequalities could at most confirm that quantum mechanical quantities do not commute. They also suggest that experiments performed on a single system could refute local realism. In this paper, we develop a connection between the work of Malley and Fine and an argument by Bub from some years ago [Bub, The Interpretation of Quantum Mechanics, Chapter VI(Reidel, Dodrecht,1974)]. We also argue that the appearance of conflict between Santos on the one hand and Malley and Fine on the other is a result of differences in the way they understand local realism