On the Physical Realizability of Bell Test Assumptions: A Challenge from Information-Theoretic Constraints

Preprint paper abstract: We argue that Bell tests, while mathematically rigorous within their stated assumptions, operate in a regime that is fundamentally inconsistent with established physical principles including the Heisenberg Uncertainty Principle, the unattainability of zero entropy, and the Bekenstein bound. Specifically, we contend that the assumption of single-valued measurement outcomes—a cornerstone of Bell’s methodology—requires perfect localization of information that these principles forbid. We propose that physical measurements inherently produce multi-valued outcomes representable as sets of eigenvalues rather than single scalars. This multi-valued structure lacks a rigorously defined correlation product in current mathematics, analogous to the undefined product of kets |a⟩|b⟩. Consequently, Bell test conclusions regarding the incompatibility of locality and realism may be artifacts of imposing an inappropriate mathematical structure on physical reality. We outline the theoretical gap and suggest that experimental implementations using interference-based or other quantum hardware might physically realize the needed “set product” operations, enabling a new class of Bell-type experiments that probe correlations in the multi-valued regime. This work aims to stimulate discussion about whether current Bell tests address the correct mathematical framework for analyzing quantum correlations.