Non-Inertial Response of Correlations: From Scalar Bell Observables to an Extended Correlation Tensor

A standard Bell observable is a scalar correlation associated with a selectedpair of local measurement directions. We formulate it as a projection of acomplete two-particle correlation tensor and distinguish two angular sectors.The central result is a reversal of the sign multiplying the cosine law: forcoincident calibrated settings, the Bell observable is positive for photonsand negative for a fermionic singlet. This distinction provides an operationalcriterion for experimental identification. For photons, the positive signfollows from averaging two projection amplitudes over the completenon-inertial phase interval; the fermionic sign follows from the negativeexchange holonomy of the phase--momentum sector. Mapping phase directions tolinear-polarizer axes produces the corresponding double-angle dependence. Thephoton Stokes tensor has positive linear-polarization components and a negativecircular-polarization component, whereas the fermionic singlet has anisotropic negative tensor. We introduce a motion-dependent extended tensor anda frequency-dependent non-inertial susceptibility. A phase-synchronoustwo-arm experiment combines optical modulation, rotation, and seededmultiaxial piezoelectric vibration. Independent motion measurements separatecommon and differential components and allow controlled variation fromcorrelated to independent and oppositely driven motion; a single rigidplatform is the simpler common-frame limit. Bell-setting and state-correlationvectors express the sign reversal as a scalar projection. The constructionyields binary joint probabilities and recovers the Tsirelson bound withoppositely signed optimal CHSH combinations.