Clarify the implications of Bell–Wigner inequality violations

Determine the actual implications of quantum-mechanical violations of the Bell–Wigner inequality, derived under local hidden-variable assumptions for measurements on entangled two-spin-1/2 singlet states, and rigorously characterize what such violations imply for the interpretation of observed correlations in quantum mechanics.

Background

The Bell–Wigner inequality is derived by assuming local hidden variables that predetermine outcomes for measurements along three possible directions. Under these assumptions, certain probability inequalities must hold. Quantum mechanics predicts, and simulations confirm, parameter regimes where the inequality is violated for entangled spin-1/2 pairs in the singlet state.

The section discusses how such violations challenge local realism by showing that spin components along non-orthogonal directions cannot be treated as simultaneous elements of physical reality. However, the authors explicitly note that the broader interpretational consequences of these violations remain unsettled in the literature, indicating an open debate about what can be definitively concluded from Bell–Wigner violations about locality, realism, and the foundations of quantum mechanics.