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This question is about the justification for the CHSH assumption of indeterminate photons in the proof of spooky quantum entanglement.

CHSH assumes that the photons have indeterminate polarization with strange justification. It is generally agreed that one Barium borate oxide crystal (BBO) cannot produce photons that have indeterminate polarization. CHSH puts 2 BBOs together with one that produces vertically polarized photons and one that produces horizontally polarized photons and assumes that makes the photons indeterminate. That seems like saying, with one guy throwing tomatoes at an actor and when another guy starts throwing eggs, the tomatoes become half tomato and half egg. The CHSH experiments slow the generation of photon pairs from one BBO so that at least 25ns separates the pairs in time. That seems to make the state of the polarization known, not indeterminate. When one of the detectors is set to match vertical polarization, one of its counters registers vertical polarization and the other registers horizontal polarization so everything is known about the polarization of the photons and which BBO they came from. What is indeterminate in this experiment?

Addition: If there is nothing indeterminate, the CHSH experiments are worthless. How about answering the question?

Addition: The indeterminacy is a big loophole.

Another fatal mistake in the CHSH experiments is that Bell’s inequality would not violate without erroneously setting up the inequality.

It turns out that 3 of the 4 CHSH tests are really the same test. That means that they do not fit Bell’s Inequality test that CHSH uses to “prove” its case. Both quantum predictions and the physical tests show that the only angle the results depend on is the angle between the polarizers. CHSH uses the actual angles of the polarizers. When both polarizers are turned the same amount, that does not change the results. One of the tests usually has a difference of 67.5 degrees and the other 3 tests all have a difference of 22.5 degrees.

Bell’s Inequality is P(A,B) - P(A,B’) + P(A’,B) + P(A’,B’) >= 2.
CHSH would be P(A,B) - P(A,B’) + P(A,B) + P(A,B) which is certainly not the same.
The experiment does not violate Bell’s inequality or even test it.

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The experiment using two barium borate oxide crystals to produce polarization-entangled photons is described in Paul Kwiat et al's paper Ultrabright source of polarization-entangled photons. A non-paywalled version can be found on the arXiv.

This idea that you have one guy throwing eggs at an actor and another throwing tomatoes, and you end up with half-egg half-tomatoes, is a misleading analogy. That seems to imply that there are two photon sources. This really wouldn't work in practice, because you couldn't make the two sources coherent.

What is going on is that the same laser beam is going through two barium borate oxide crystals with different orientations. When a laser beam goes through a single BBO crystal, some of the photons get turned into two photons of half the frequency, but with definite polarizations. When it goes through two BBO crystals one after another, you can't a priori tell which BBO crystal it underwent downconversion in, so the two different polarizations resulting from the two different BBO crystals are entangled. When you measure them using a diagonal filter which doesn't reveal which BBO crystal they came from, the two paths corresponding to the two BBO crystals interfere. This is entirely analogous to the two-slit experiment, where you have interference caused by the two slits that the photon could have gone through.

So continuing with the analogy, what is happening is you have one guy throwing custard pies. There are two magic force fields (BBO crystals), one of which turns some of the custard pies into tomatoes, and one which turns some of the custard pies into eggs.

After a custard pie goes through both force fields, it is still mostly custard pie, but partly egg and partly tomato. You can ignore the custard pie part, because those are the non-down-converted photons—these have a different frequency that is filtered out in the experiment. And after filtering out the custard pie part, you really are left with half-egg, half-tomato photons.

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Certainly not all CHSH inequality violation experiments are done with barium borate odixide crystals, so you have to give a link to the experiment you refere to, otherwise it's hard to know what you are talking about. Anyways, to proof experimentally that there is something "spooky" that violates the CHSH inequality NO correct EXPLAINATION of the process leading to this violation is needed. Quantum mechanics gives A explanation but not necessarily THE explanation. All you have to make sure is that the loopholes are "filled" (?). If what you say was right and there was no entanglement between these photons but still the CHSH inequality is experimentally violated then it would follow that QM is wrong, not the experiment.

Addition: "If there is nothing indeterminate, the CHSH experiments are worthless. How about answering the question?" ... That's is no question, that's a wrong statement.

Addition: "The indeterminacy is a big loophole." ... That's is no question, that's a wrong statement.

Addition: Bell inequality reads: |P(A,B)-P(A,C)| <= 1 + P(B,C) and CHSH inequality reads: |E(A,B) - E(A,B')| - |E(A',B')-E(A',B)| <= 2 (please refere to the original publications) ... not what you wrote. ... and yes, they're not the same.

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