Bell Meets General Philosophers of Science : Reassessing Measurement Independence

TL;DR

This paper reassesses Bell-type measurement independence by contrasting the nonfactorizable position with superdeterminism through three philosophy-of-science frameworks: de Regt's notion of scientific understanding, Kuhn's theory-choice criteria, and Lakatos's methodology of scientific research programmes. It argues that the nonfactorizable position currently offers greater intelligibility, explanatory power, and progressive potential, particularly as demonstrated by quantum teleportation and related quantum-information advances. The work further introduces a spectrum of intermediate positions quantified by mutual information $C_{MD}$, showing how partial violations of measurement independence can still account for CHSH violations and suggesting new avenues for theory development in quantum foundations. Collectively, the analysis reframes the Bell debate as a multi-dimensional appraisal problem and illustrates how information-theoretic tools can enrich philosophical assessments of foundational physics.

Abstract

Bell's inequality is derived from three assumptions: measurement independence, outcome independence, and parameter independence. Among these, measurement independence, often taken for granted, holds that hidden variables are statistically uncorrelated with measurement settings. Under this assumption, the violation of Bell's inequality implies that either outcome independence or parameter independence fails to hold, meaning that local hidden variables do not exist. In this paper, we refer to this interpretive stance as the nonfactorizable position. In contrast, superdeterminism represents the view that measurement independence does not hold. Despite its foundational role, this assumption has received relatively little philosophical scrutiny. This paper offers a philosophical reassessment of measurement independence through three major frameworks in the philosophy of science: de Regt's contextual theory of scientific understanding, Kuhn's criteria for theory choice, and Lakatos's methodology of scientific research programmes. Using these lenses, we evaluate the two major responses to the violation of Bell's inequality, the nonfactorizable position and superdeterminism, and argue that the nonfactorizable position currently fares better across all three criteria. Beyond this binary, we introduce a spectrum of intermediate positions that allow for partial violations of measurement independence, modeled via mutual information. These positions modify the ``positive heuristic'' of superdeterminism, a crucial component in Lakatos's definition of research programmes, offering avenues for progressive research. This analysis reframes the debate surrounding Bell's inequality and illustrates how methodological tools can effectively guide theory evaluation in physics.