The Non-Signalling theorem in generalizations of Bell's theorem

Abstract: Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including even nonlocal hidden-variables theories such as de Broglie-Bohm theory. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic quantum theories. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational interpretation of the non-signalling theorem. We here argue that the non-signalling theorem must instead be viewed as an epistemic, phenomenological, or operational theorem i.e. one that refers exclusively to what epistemic agents can, or rather cannot, do. That is, we emphasize that the non-signalling theorem is a theorem about the operational inability of epistemic agents, e.g. human observers, to signal information. A major reason in favor of our conclusion is that any definition of signalling or of non-signalling invariably requires a reference to epistemic agents, and what these agents can actually measure and report; otherwise, the non-signalling theorem would equal a general "no-influence" theorem.