Peter,
"What I show about the 'statistical inference' of QM is that it's nonsense and doesn't even produce what many seem to think it does."
Since QM is derived from empirical results, that is a ridiculous claim. Richard is right -- you seem not to know, much less appreciate, the fundamentals of quantum mechanics and Bell's theorem.
Understand that your proposal is no less dependent on subjective choice (detector settings) than any Bell-Aspect type of experiment. The choice function -- which obviates a probabilistic measure that begs statistical inference -- lies outside that 'obvious' space effectively defined by inductive reason, and must lie outside of it. Even Bell proponents recognize this fact; that's why they say that results of the experiment not performed are nonlocal.
Opponents of the nonlocal interpretation of QM do not simply claim -- as you imply -- "Reality is local, so live with it." A locally real framework of quantum correlations is a deductive system independent of the experiment, whether performed or not.
We all intutively know that reality is "really real" only when it is local (the 'obvious space'.). That's not the point. The point is whether the "experiment not done" influences the experiment done locally. It's very easy to "prove" by colored cards or the "QRC" that we can't read each others' minds and that the classical limit of guessing is 50%.
To extrapolate that knowledge to quantum correlations -- say opponents of nonlocality -- is overreaching. Why? -- because the means by which one purports to "prove" that correlation are classical! That is, classical induction tells us for a sufficiently long run of fair coin tosses, heads will appear an equal number of times as tails. That's real. What's not real is the state of superposition of the opposite value when the one value is observed (this is one of the things on which I agree with Rob McEachern).
No matter how many ways they play the game, Bell's theorem proponents cannot escape the conundrum that they are using the rules of local reality to make a case for nonlocal reality. If everything is real, they say, then nothing is real -- Anton Zeilinger, et al, have taken this all the way to an anti-realist philosophy.
The problem is that of inductive inference. QM is empirical. As Bell noted in the "Bertlmann's Socks" paper, " ... when you see (Fig. 1)that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann, gives immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is not the EPR business just the same?"
Then one prepares "entangled" particles and sends them from the source on opposite vectors to show that the 'EPR business' is the same as the correlation of Bertlmann's socks. After that establishment of a classical expectation, one performs experiments to show that that classical expectation cannot be met for quantum correlations.
Is the "EPR business" the same as Bertlmann's socks, where we can assume the socks are entangled at the source and separated by Bertlmann's choice of what feet to wear them on? This is where Joy Christian found the error in Bell's reasoning; the classical expectation that he set up in his very first equation. That expectation is incomplete -- certainly one can say that the choice function is satisfied in Professor Bertlmann's decision of what sock to place on what foot -- the extrapolation of that function to Bob's and Alice's choices, though, leaves an unbridgeable gap of logic; i.e., it implies that Bob and Alice choose (by setting their detectors) which socks Bertlmann will wear rather than simply observing the result. The choice function has then been mystically transferred from a correlation in nature (Bertlmann's choice) to the creation of quantum states, by observer settings.
Restoring Bertlmann's choice demands deductive reasoning, from a mathematically complete framework. The inductive creation of quantum entanglement and nonlocality, however sophisticated, will always suffer the curse of proving its own assumptions.
Best,
Tom
