Do EPR-Bohm experiments provide evidence for fuzzy quantum states?

The experimental data for EPR-Bohm experiments exclude hidden variable interpretations of quantum theory. What is less known that the experimental data for this kind of experiment (Phys. Rev. Lett. 81,23, p. 5039, 1998) indicates the possibility of an anomaly challenging quantum mechanics (I learned about this possibly anomaly from papers of Adenier and Khrennikov, see this and this. The obvious question is whether this anomaly might provide a test for the notion of fuzzy quantum logic inspired by the TGD based quantum measurement theory with finite measurement resolution.

The experimental situation involves emission of two photons from spin zero system so that photons have opposite spins. What is measured are polarizations of the two photons with respect to polarization axes which differ from standard choice of this axis by rotations around the axis of photon momentum characterized by angles α and β. The probabilities for observing polarizations (i,j), where i,j is taken Z₂ valued variable for a convenience of notation are P_ij(α,β), are predicted to be P₀₀= P₁₁=cos²(α-β)/2 and P₀₁= P₁₀= sin²(α-β)/2.

Consider now the discrepancies.

• One has four identities P_i,i+P_i,i+1=P_i,i+ P_i+1,i=1/2 having interpretation in terms of probability conservation. Experimental data of the experiment reported in Phys. Rev. Lett. 81,23, p. 5039, 1998 are not completely consistent with this prediction and this is identified as a possible anomaly .

• The QM prediction E(α,β)= ∑_i (P_i,i-P_i,i+1)= cos(2(α-β) is not satisfied neither: the maxima for the magnitude of E are scaled down by a factor ≈ .9. This deviation is not discussed by Adenier and Khrennikov.

Both these findings raise the possibility that QM might not be consistent with the data. It turns out that fuzzy quantum logic predicted by TGD and implying that the predictions for the probabilities and correlation must be replaced by ensemble averages, can explain anomaly b) but not anomaly a). A "mundane" explanation for anomaly a) can be imagined.

For details see the chapter Was von Neumann Right After All? . See also the article TGD: an Overview.