What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. Of course, the entangled system has spatial (I would call it "spatiotemporal") extent. And all the questions we have pertain to how we get perfect correlations from the expanded system WITHOUT some kind of FTL influence - since the measurements are made independently later (than your locally prepared solution).
If the two photons have a spacelike seperation when measured, the two photons were always spacelike seperated. The two photons produced by parametric down conversion have never interacted with each other.
I think the use of the term "non-local" is not helpful here. It is used inconsistently to mean different things in different articles.Since the entangled system itself has spatial extent and is therefore nonlocal from one spot to another, there is something "nonlocal" going on - which is termed "quantum nonlocality" (because we do not further understand the nature of the nonlocality).
Again, I don't think the use of "non-local" here means what you are trying to suggest.For other readers: the statements of vanhees71 are his opinion, and virtually all those studying Bell and QFT do not share his opinion.
To date, he has not produced a single quotation from any well respected source echoing his viewpoint - he just says it is "obvious" from QFT. On the other hand, the statements affirming the existence of "quantum nonlocality" are legion. 2022 Nobel winner Zeilinger: "The nonlocality is confirmed by observing a violation of Bell’s inequality by 4.5 standard deviations.
Why do you think the above implies what you have in brackets below?Thus, by demonstrating quantum nonlocality for photons that never interacted...
[and could therefore not have been prepared initially in the synchronized state vanhees71 imagines],
First, the use of synchronized here doesn't relate to the standard usage (as Einstein used it) of the word in which synchronization takes place via causal processes. The two photons are created with a spacelike seperation, so I don't know what synchronization means in that context.
The following article on parametric down conversion might be interesting:
To the OP: there is no paradox. Relativistic QM does not offer a local causal mechanism/explanation for Bell type entanglement, and does not offer an FTL signaling mechanism that would violate relativity. Quantum nonlocality coexists with relativity, they operate in different domains.
In an earlier post you mentioned "influences" as different from "cause."
How are those not synonymous here? In Bell's type experiments, the measurements are independant of each other, which by definition means the measurements are not causally connected.