Bell's theorem and the measurement problem: reducing two mysteries to one?

Abstract

In light of a recent reformulation of Bell's theorem from causal principles by Howard Wiseman and the author, I argue that the conflict between quantum theory and relativity brought up by Bell's work can be softened by a revision of our classical notions of causation. I review some recent proposals for a quantum theory of causation that make great strides towards that end, but highlight a property that is shared by all those theories that would not have satisfied Bell's realist inclinations. They require (implicitly or explicitly) agent-centric notions such as "controllables" and "uncontrollables", or "observed" and "unobserved". Thus they relieve the tensions around Bell's theorem by highlighting an issue more often associated with another deep conceptual issue in quantum theory: the measurement problem. Rather than rejecting those terms, however, I argue that we should understand why they seem to be, at least at face-value, needed in order to reach compatibility between quantum theory and relativity. This seems to suggest that causation, and thus causal structure, are emergent phenomena, and lends support to the idea that a resolution of the conflict between quantum theory and relativity necessitates a solution to the measurement problem. arXiv:1602.07404v1 [quant-ph]

Classical Causal Models for Bell and Kochen-Specker Inequality Violations Require Fine-Tuning

“…A violation of a Bell inequality thus implies either a violation of relativistic causality, or of one or more of the assumptions underlying this framework for causality, such as Reichenbach's principle of common cause [12,13]. This second alternative has motivated a programme to extend the classical causal formalism to a framework of quantum causal models [13][14][15][16][17][18], opening the exciting prospect of a coherent understanding of the nature of causality in a quantum world, and a resolution of at least part of the puzzle of Bell's theorem [19]. * e.cavalcanti@griffith.edu.au Contextuality, on the other hand, is a priori unrelated to causality: it is not necessary that measurements are space-like separated, or that they involve separate subsystems at all.…”

Reply to Gillis's "On the Analysis of Bell's 1964 Paper by Wiseman, Cavalcanti, and Rieffel"

“…With that should come a yet deeper respect for Bell's substantial intellectual effort over many years to formalize localistic intuitions as local causality. Finally, we hope that Gillis and others may also come to appreciate, and even contribute to, recent efforts [10,25,3,26] to make further advances in solving "the problem of formulating [cause and effect] sharply in contemporary physical theory. "…”

Implications of Local Friendliness Violation for Quantum Causality

“…This is an interesting program, and it is making steps towards resolving what one of us called the "easy problem of Bell" [40], i.e., the problem of giving a causal explanation of Bell correlations. However, as previously argued by one of us in [40], quantum causal models (as currently formulated) cannot resolve the "hard problem of Bell", namely the measurement problem. In the next Section 4, we provide a proof of this assertion, based on the Local Friendliness theorem [2].…”