vanhees71 said:
But you didn't make the point clear! Unnikrishnan does. Even under the assumption of angular-momentum conservation on average, which is less than what's the case for QT, where angular-momentum conservation holds on an event-by-event basis, he can show that there's no local deterministic HV model which leads to the violation of Bell's inequality as predicted by QT. I've not read Mermin's paper, but I don't think it's necessary, because in Unnikrishnan's paper everything is clear.
What I had in the paper was just Unnikrishnan's summary paragraph. Obviously, I can't include all the explication he provides in his paper after that summary, but I didn't think it necessary since his summary was very clear to me. Apparently, it wasn't clear to you, so I revised the paper
here replacing his summary with my "no preferred reference frame" argument for his conservation of angular momentum on average. My argument is just another way of looking at his argument or just another way of looking at Boughn's argument
here. However you justify it, the key insight of Unnikrishnan is to use conservation of angular momentum on average to provide ##\overline{BA+}## and ##\overline{BA-}## in the correlation function (see post #386). That gives you the quantum correlation function without ever using quantum mechanics. This is akin to deriving the Lorentz transformations from the light postulate (in more ways than one, as I will point out).
As for articulating the fact that Unnikrishnan's result rules out "local HV theories," that's trivially clear from the fact that his conservation principle reproduces the quantum correlation function which rules out local HV theories (I have included that very statement in the paper). In the Mermin paper (had you bothered to read it), he goes to great lengths to explain how his "instruction sets" are the equivalent of any local HV theory. As with the Unnikrishnan paper, I can't include Mermin's entire paper in mine, so I must expect the reader to have read the Mermin paper. The Mermin device is a metaphor for the formalism of QM in this particular experimental set-up. So, when Mermin shows that his device cannot be explained with instruction sets, he's showing how QM rules out local HV theories. The conundrum of the Mermin device is then, "If it doesn't work via instruction sets, how the hell does it work?" Since Unnikrishnan's conservation principle gives the quantum correlation function responsible for the mysterious outcomes of the Mermin device, his conservation principle invoked as a constraint (as with the light postulate) then answers that question, i.e., resolves the conundrum of the Mermin device. However, ...
As I point out, Unnikrishnan's conservation principle only resolves the conundrum of the Mermin device if you can accept the conservation principle as a constraint on the distribution of outcomes in space and time with no `deeper mechanism' to account for the constraint proper. In other words, you have to accept the conservation principle as a constraint in and of itself without further explanation. Prima facie the conservation of angular momentum on average sounds like a perfectly reasonable constraint. But, this constraint does not provide a `deeper mechanism' at work on a trial-by-trial basis to account for the average conservation. So someone might still say, "But, what mechanism is responsible for the conservation? How do the particles `know' how to behave in each trial so as to contribute properly to the ensemble? Each particle has `no idea' what the outcomes were at both locations in preceding trials, nor does it `know' what the other device setting is in their particular trial. How the hell does this average conservation pattern in space and time get created?"
And that leads us to the other analogy with the light postulate. Even Michelson of the Michelson-Morley experiment said, "It must be admitted, these experiments are not sufficient to justify the hypothesis of an ether. But then, how can the negative result be explained?" In other words, even Michelson required some `deeper mechanism' to explain why "the speed of light c is the same in all reference frames." In general, if one cannot accept a constraint or postulate in and of itself as the fundamental explanans, that constraint or postulate is just as mysterious as the explanandum. That's the point of my paper and that is the point of our book, "Beyond the Dynamical Universe." So, my paper is just another argument for constraint-based explanation as fundamental to dynamical/causal explanation.