Correlation estimates are not unique fingerprints of physical systems: an example of non-uniqueness in model identification

Abstract

A study in inverse model identification. Using only pre-quantum physics (analogue mixer, low-pass filtering, Malus's law, Pearson correlation), we build a deterministic local coherent-detection model whose raw correlations are Bell-compliant (|S_raw| = √2/4). Pearson normalisation yields −cos(a−b), and the CHSH polynomial on these coefficients gives 2√2 (scale-invariant). This C_Pearson is not a Bell correlator and no Bell violation is claimed. The point: the value 2√2, taken from normalised correlation data alone (blind test), does not uniquely identify the generating mechanism — an explicit classical pre-image of the same data is exhibited. Bell-CHSH is used only as an extreme illustration.