local wrote:Fred, joint and separated measurement are physically different, so you need different derivations. There is no single "the" prediction. That is the whole point of Graft's analysis.
Gill is just giving joint derivations for joint measurement. If you form a tensor product of a and b for a single measurement you have illegitimately combined knowledge of a and b for that measurement. In separated EPRB there are two independent measurements, each having access to only its own setting. Gill has not provided a derivation for separated measurement. Apparently he denies the distinction between joint and separated measurement. He also incorrectly states (if I read him correctly) that you can obtain a joint distribution from the marginal distributions. That is wrong. There would be no need for copula theory if that were true, and the marginal expectations for EPRB are 0 in any case. He can believe what he wants, but don't you be fooled.
Fred, I just told you the formulas which you got from Jay and rewrote in Mathematica. You asked how to get the separate probabilities of the four possible joint outcomes, and I politely answered your question. How to also get the joint probabilities as well as the correlation, following the same, standard, methodology. The standard approach for joint measurement of two commuting observables on one system, when the system is modelled using the standard tensor product approach, out of two subsystems which can be measured separately.
I am telling you the conventional way to get those probabilities. I am using the same joint state as Jay uses (the singlet state). You may want to argue that the state of the two electrons when they reach the two measurement devices is not the same state they had when they left the source.
I’m not saying the computations are correct. I’m not saying you should believe them. I do not attempt to distinguish between joint and separate measurement. I’m telling you the standard way to get the usual formulas for joint measurement of spin on two spin half systems, together prepared in the singlet state. The formulas which Joy wrote down, the ones which Jay wrote down.
Donald Graft (and many before him) have argued that entanglement is not maintained as the particles separate.
If that were the case, we would not observe violation of Bell inequalities. This is what Caroline Thompson argued, for years. She argued that the Aspect analysis, and the Weihs analysis, were wrong. That they got violation by cheating; by making untestable assumptions about the non-detections. That is why the experimenters gave us the 2015 experiments. But they do not find the singlet correlations. They don’t try to.