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The ontology of CH is explained in some detail in . Fundamentally it is based on the assumption that physical properties can be represented by subspaces of a Hilbert space. This last is, indeed, a mathematical formalism, but it enables one to reason rationally about the physical world. If you want to address the question of whether it is shorter in distance to fly from New York to Los Angeles with an intermediate stop in Chicago or an intermediate stop in Dallas, you have to somehow translate this into an abstract formalism of distances on the surface of a sphere. However, I suspect your question may have a bit of the flavor of “Explain those correlations in intuitive terms that make good classical sense”, to which I have to respond that I don’t think there is such an explanation. In developing an intuition about the quantum world we have to pay attention to the way in which it differs from the world of classical physics. I agree that intuition, not just formalism, is needed in order to do good physics, and when I wrote Ch. 24 I hoped it would make a significant contribution to an intuitive understanding of some of the oddities of EPR-Bohm. That is why I construct various frameworks in Sec. 24.2 in order to deal with the conundrum stated in what I hope are understandable physical terms in Sec. 24.1. Working through them helped me gain some measure of intuitive understanding of what goes wrong with Mermin’s device, and I hope that it will serve this purpose for others–although someone else might be able to word it better than I have.
 R. B. Griffiths, “A Consistent Quantum Ontology”, Stud. Hist. Phil. Mod. Phys. 44 (2013) 93; arXiv:1105.3932