Joy wrote: " ... your argument falls apart for the case of entangled neutrinos."
I think this underscores the importance of our being able to show that strong quantum correlations do not differ from weak classical correlations, given any case of particles sharing an initial condition.
A classical correlation -- such as the prediction that a fair die producing one value correlates perfectly to one of five other values -- is as dependent on perfect information (i.e., knowledge of the complete state of the die's six faces) as the probabilistic quantum mechanics. The trouble with QM, though, is that by assigning perfect information (by the equally likely hypothesis) to an incomplete state, nonlocality sneaks in the back door as a fundamental physical principle. One then leaps to the assumption that "the experiment not performed" has no basis in reality, and then takes the short step to conclude that we live in an observer-created world.
This nonconstructive argument (and its proof) neglects that the equally likely hypothesis applied to incomplete information is a shot in the dark. One is reminded of the parody:
"I shot an arrow into the air;
It fell to Earth I know just where.
Though aimed at a buck who stood afar,
It pierced the radiator of my car."
(No idea of whom to attribute this dimly remembered ditty.)
Point is, QM brings the target to the arrow. Whatever probability the arrow has of hitting the car when the bow is drawn, the probability is 100% that it hit the target.
Classically, the arrow either hit the target or missed (the outcome is heads or tails) -- and whether or not it hit or missed, there is a lot of complicated but local physics between the state preparation (drawing of the bowstring) and the measurement result. In QM, state preparation is disconnected from the measured outcome; Bell-Aspect type experiments only end up proving what they assumed in the first place, i.e., that correlated events remain correlated to infinity. The explanation: nonlocality. That's like saying that because EM and gravitational field influences are infinite, physical laws on one side of the universe do not differ from those on the other side -- true, but trivial.
What QT proponents *really* want from entanglement, is to be able to show that quantum correlations are independent of classical correlations .
Vlatko Vedral never replied to my response to his challenge, though some time ago in these FQXi forums he said he was willing to bet a bottle of Bollinger champagne that quantum entanglement would remain a part of fundamental physics. I am willing to take that bet.
Tom