but then again a human twin as a classical object is well defined classically as well as its observable properties, but a one particle quantum system, described completely by a wave function or quantum state is not well defined in general in QM, meaning it is not an invariant as in the classical case.
My post was a reply to Demystifier's example, where they explicitly "translate" the human twins into Quantum particles and I was presenting a caveat in that translation.I don't understand that objection. Bell's theorem is not a statement about quantum mechanics, it is a statement about a class of (hypothetical) theories that aren't quantum mechanics but do make a particularly appealing (to the classically-minded) assumption about the probability distribution of the measurement results.
Maybe it's just me but when the theorem is seen derived in this simple form it is hard to fathom all the fuss and the mistery usually attributed to Bell's theorem. In a few words all it is saying is reality is not classical when probed with a quantum experiment, wich we already know since we check in a daily basis that the predictions of QM are correct. This can be easily realized just by acknowledging that the common sense inequalities derived using the twins properties, assume as it is common sense from a classical point of view, that all the observables properties commute, but precisely that common sense premise is the one QM proves wrong and therefore switches the Poisson bracket for the quantum commutator. In this particular case (2 dimensional Hilbert space) the commuting relations completely determine the quantum state in an invariant way.I am reading the popular-science book
A. Zeilinger, Dance of the Photons
In the Appendix I have found a surprisingly simple derivation of Bell's inequalities, which, I believe, many people here would like to see.
The setup using twins as the analogy is easy enough to understand... But how does the analogy continue when the Bell inequality is violated? That's the part I'd really like to read, as I haven't fully gotten to grips with that part yet.
The obvious example of non-locality explanation is the twins talking to each other about which property they each have measured, and remaining identical if it is the same property or shuffling it up if it is a different property on each of them.