Joy Christian wrote:***

I have worked out the correct eigenvalue of the operator (R + S + T - U) relevant for the Bell's implicit assumption [cf. eq. (16) or (29) of this paper: https://arxiv.org/abs/1704.02876].

The correct eigenvalue of the operator (R + S + T - U) is

(1) ,

where , and l, m, n, o, p, and q are the eigenvalues of the operators L = RS - SR, M = RT - TR, N = TS - ST, O = US - SU, P = UR - RU, and Q = UT - TU, respectively.

Now, implementing what they think is the demand of local realism, Bell and his followers assume that the eigenvalue of the operator (R + S + T - U) is (r + s + t - u). But that is true if and only if the operators R, S, T, and U commute with each other. This is easy to see from the above eq. (1). When R, S, T, and U all commute with each other, then z = 0 and the eigenvalue reduces to (r + s + t - u). But in the Bell-test experiments the operators R, S, T, and U do not commute with each other because they correspond to different detections made at mutually exclusive measurement directions. So Bell and his followers assume a wrong eigenvalue of the operator (R + S + T - U) and thus incorrectly implement Einstein's notion of local realism. It is a simple mathematical mistake. And it invalidates the bounds of -2 and +2 on the CHSH correlator. The correct bounds follow if we use the correct eigenvalue (1) worked out above. The correct bounds work out to be and , exactly as those predicted by quantum mechanics. Thus there is no incompatibility between quantum mechanics and local realism.

There is a dishonest attempt by a Bell-believer to deflect from the above calculation. Note to other readers: Don't fall for that deflection. Concentrate on what I have presented above.

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