Dear Jochen,
Thank you for the reply and the interest in my mentioned papers. In the one with the representation of the wavefunction on space or spacetime, the representation, albeit complicated, is just like a classical field theory, with infinite-dimensional vector fields satisfying some global gauge symmetry. But once we put aside the differences in the complexity of the theory, as I said, we see it's just a classical field theory. This as long as no collapse takes place. I'm not sure if David Albert would find this at odds to his proposal to teach QM and explains how it differs from classical mechanics based on the fact that the wavefunction lives on the configuration space. Now we see that this was only a representation, and the things are as classical as it gets, including being local. The difference occurs if there is a collapse. Collapse, for taking place everywhere in space simultaneously, introduces nonlocality, and because of collapse, entanglement leads to Bell correlations. Now, one can say, "assuming that your representation is true". It is true, I mean a correct representation, and maybe there can be simpler or more natural ones. But both mine and the wavefunction on the configuration space are just representations. Mine, as opposed to the wavefunction one, (1) makes explicit locality and when exactly it's violated, and (2) is consistent with the idea of "ontology on space or spacetime". So there is no need to appeal to ontology on configuration space, not that this was a problem, but I submit that this is NOT the characteristic of quantum mechanics, since there is no difference here. The key difference is brought in by collapse.
Now, about collapse, the paper I attached to my previous comment can be taken as independent on the Phys Rev one I linked in the same comment. But to me they are related. The one about the post-determined block universe makes use of the fact that the ontology of the representation of the wavefunction is on space or rather spacetime. But it's not only this, it proposes an interpretation of QM where there is no collapse and the outcomes are still definite (so it's not MWI, it's just unitary single worlds). But earlier I stated that the key difference between QM and classical is isolated in the collapse. And in the other paper, that collapse is not necessary, it can happen unitarily. And in fact, if there would be discontinuous collapse, it would be undesirable, like breaking conservation laws, relativity of simultaneity, the evolution law, and is in tension with the Wigner-Bragmann derivation of the wavefunction for any spin and its dynamics for free particles, from the Poincaré symmetry. And locality. Now, most people think that all these are a small price to pay. For me, since I care about relativity too, it's a too big price.
OK, so back to isolating quantumness. How can I say that quantumness is not in unitary evolution, since it is equivalent to a classical one, but also say that the collapse may not exist? Isn't there a contradiction between these? Indeed, from the post-determined BU paper follows that the difference is not in the collapse either, at least in my interpretation without discontinuous collapse. The key difference, I think, is deeper, and need to be found, but I hint in that paper that it has to do with some topological constraints which can prevent most of the local solutions to extend globally, leaving to a zero-measure set of solutions which look as fine-tuned to go around Bell's theorem while still being local. Now, you may disagree with the post-determined BU, since I didn't prove that this is the case yet, but at least the paper with the representation on 3d space can only be refuted if some mistake is found in my proof. So at least for now the best way to isolate the quantumness is in the collapse, more precisely, the fact that it takes place globally on all of the degrees of freedom of the fields on 3d which I use to represent the wavefunction. And this can have the same effect on classical fields too, as we can see if we take as example my representation.
Thanks again for the comments,
Cheers,
Cristi