CHAPTER 3 Nonseparability and Bell’s Theorem

Alyssa Ney

Abstract This chapter presents the argument for wave function realism that it is the only realist interpretation of quantum theories that can maintain a fundamentally separable and local metaphysics. It is commonly seen as a consequence of entanglement and Bell’s Theorem that quantum mechanics entails quantum nonseparability and nonlocality. Yet although all rival realist ontological interpretations of quantum mechanics involve either a nonseparable or a nonlocal fundamental metaphysics, the metaphysics of wave function realism is fundamentally both separable and local, although the view also makes room for nonfundamental nonseparability and nonlocality. The chapter considers several arguments that could explain why one should prefer interpretations of quantum theories that are separable and local, and concludes with a defense of intuitions in quantum interpretation.

Bernard d’Espagnat

This chapter stresses what may be called conventional or standard textbook quantum mechanics, that is, to the working hypothesis that quantum mechanics is complete. Some remarkable features of the general quantum formalism, often grouped under the general name "nonseparability," rather drastically limit the domain of validity of the idea. The two notions referred to in the title of this chapter are therefore, in a way, antagonistic. The state operator concept is of some use for investigating the properties of ensembles of subsystems of larger systems, sometimes uttered claim that its introduction makes it possible to remove "nondivisibility by thought" from quantum physics is definitely erroneous. When J. S. Bell's theorem appeared it was immediately clear that some expressions had to be comed in order to express in words its bearing and significance.

Abner Shimony

Darrin W.S. Belousek

We first examine Howard's analysis of the Bell factorizability condition in terms of ‘separability’ and ‘locality’ and then consider his claims that the violations of Bell's inequality by the statistical predictions of quantum mechanics should be interpreted in terms of ‘nonseparability’ rather than ‘nonlocality’ and that ‘nonseparability’ implies the failure of spacetime as a principle of individuation for quantum-mechanical systems. We will argue that his argument for the first claim is less than compelling and that any argument for the second claim will be interpretation-dependent and, hence, not generally valid.