The emergence of quantum behavior for two entangled particles

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When I submitted my manuscript to the journal Foundations of Physics, one of the referees was pointing out that
The positive model developed in this manuscript represents a lot of careful work, and exhibits a solid grasp on the foundational literature. To my mind, the fatal flaw is the failure to discuss multiparticle systems. It's a fatal flaw because the paper purports to develop a local realistic model of quantum phenomena. Well-known impediments to the empirical adequacy of such models (e.g. the Bell inequalities) arise in the presence of entanglement between particles. A revised version of the paper that shows how the model recovers standard QM's prediction of the violation of Bell-type inequalities would make a much stronger case that the model is worth taking seriously. (Such a recovery needn't entail extending the model to incorporate spin phenomena: the Bell-correlated observables needn't be spin observables.) [bold mine]
I therefore started incorporating momentum-entangled particles' behavior in my model, which I did not have in mind at the beginning (at least, not for that submission).

In a previous post, we have discussed the necessary extensions of the model for two entangled particles that share momentum preparation. We are now ready to evaluate the corresponding probability densities.



The joint pmf of the position of two entangled particles is denoted as ρ(x(I); x(II); t) and represents
the probability that both particles of the same emission arrive exactly at the indicated locations with
a timelife t. I won't repeat the mathematical derivations that are described in that paper. I prefer to reproduce them here, taking them from the 2018 companion arXiv paper:


So the key role is played here by the change-of-variable technique to transform the known pdf's of the source momentum v0 and phase φ (independent variables) into the sought joint pdf of the two detector locations.

Later in the same paper, I have shown the results of the simulation of a double-slit interferometer with entangled particles and retrieved quantum results including violation of Bell's inequalities. We shall discuss this important point in a future post.

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