Dear Jiri,
Three comments.
First, I disagree with your assertion that it is possible to derive Bell inequalities in the framework of quantum mechanics. This claim is widespread, but it ignores a key assumption made by Bell and his followers: the existence of classical hidden variables not described by the quantum Hilbert space. Once one insists that quantum mechanics employ Hilbert subspaces to represent properties the whole Bell argument falls apart. A detailed proof is in my article “Quantum Locality,” Found. Phys. 41 (2011) 705; arXiv:0908.2914, in which I demonstrate that a version of Einstein locality is fully consistent with quantum principles. No one has yet refuted the argument in that paper, which of course may mean that no one has read it, apart from the referee (David Mermin) who tried his best to poke a hole in it without success. For a gentler introduction see my “EPR, Bell, and Quantum Locality”, Am. J. Phys. 79 (2011) 954. arXiv:1007.4281.
Second. I am perplexed by your desire for a non-realist version of quantum mechanics. We physicists have become pretty well convinced, after a century of hard thought and careful experiments, that the reality which we probe with our experiments is quantum mechanical. Do you think that something has to follow the laws of classical physics to be “real”?
Third. What do you think you have gained by replacing ‘measurement’ by ‘observation’? This looks very much like the von Neumann chain, which many of us working in quantum foundations do not find very satisfactory.
Bob Griffiths
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