Can you split photons into 3?
You can split photons into 2 lower energy photons, but can you split them into 3? If you can, I can show you why Entanglement is really a bogus filtering effect (your "filter for photons that are successfully entangled", as you put it in that Delft "loophole free proof of entanglement").
Split a photon into 3, P1,P2,P3. By definition they are entangled, but you always add an extra filtering step before your Bells test... you filter for photons with one or two identical properties ("CheckProperties") as proof of successful entanglement, then you measure the other properties ("ProofProperties") and "hey presto" those are the same, so the act of measuring the properties must have set them, you claim.
So, we have 3 "successful" entangled photons, filter for the photons such that CheckProperties(P1) == CheckProperties(P2), ok, so now we have the triplet of entangled photons. If entanglement worked as claimed, then P3 is also entangled, and there is no need to filter for CheckProperties(P3) == CheckProperties(P1) or CheckProperties(P3) == CheckProperties(P2), ProofProperties(P3) will equal ProofProperties(P1) and ProofProperties(P2).
BUT IT WOULD NOT WORK. You would indeed have to filter also for the subset of photons P3 whose CheckProperties(P3) also match CheckProperties(P1) or CheckProperties(P2)....
You do not set the state of photon (or matter), simply by measuring it, and as if by magic the interactions it had in the past, which now are defined, fix themselves up to work with the newly known state, and in turn, the photons/matter that *those* secondary photons/matter interacted with are also partly know, so they change too, and so on propagating throughout the universe, faster than light, backwards in time.... just because you took a measurement, the universe changed to fix itself such that your result would now be correct. When I put it that way doesn't it sound ridiculous?
So what's happening?
You are not measuring the properties of P1, you are measuring the properties of the net effect between detector D1 and the photon P1, between D2 and its photon P2, and between D3 and its photon P3.
It honestly should be obvious to you, that two oscillatory components form a spin, and 3 form a translational 'waddle' ('velocity'), and that you're ignoring the motions in the detector when assuming those properties are solely properties of the 'entangled' photons. You already know from red shift the detector and photons are some sort of net effect, you are ignore that.
It is true that P1, P2 and P3 are in a defined connected state, because you split them from 1 photon. But the detectors are *not* in a unified state. When you filter for CheckProperties(p1) == CheckProperties(p2), you are actually filtering for CheckProperties(net(p1,d1)) == CheckProperties(net(p2,d2)), ensuring that the detector's relationship to the photon is the same for P1 and P2.
The unknown remaining for P3 is D3, or rather net(P3,D3).
That is why you still need to filter for P3 (as measured by detected D3).
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If you cannot split photons into 3, split them into 2 and 2 again to get P1, P2, P3, and P4. Filter to ensure entanglement for P1 to P2 and P2 to P3, then run your ProofProperties against P4 vs the rest.... it won't work. It's just a bit more complicated, and gives you more room to self-delude.
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You can deduce a lot, if you stop simply parroting the falsehood you learned to parrot. Electric must be an oscillating force, all forces must be oscillating because they take time to propagate, time = oscillations of the underlying field. The universe cannot be uniform, and particles, if you could ever see one, (and not just the net effect between them), would be close to specific orientations in that field. Think of a half spin, the F2 flip of that is from the electric field, not the particle. There cannot be 3 independant dimensions, because the 3 dimensions we preceive are 3 net effects. The underlying single force must propagate infinitely fast (H0), and 'mass' must be a repeating pattern that moves net zero in a field relative to an observer.
See those particles apparently spinning backwards in time, as observed in a cloud chamber? Merely shutter effects. The net interaction between the oscillating field and particle. Well seriously, did you never question why those go back in time?
So much is there right in front of you, but first, set aside Schroedinger.