Some CHSH tests suppose that the reduction of the sum of transmitted and reflected photons in polarizing beam splitter cubes including the interference filters had no effect on CHSH-tests. In my view this may a good approximation in case of unentangled photons but not for entangled ones. I do not mean coincidences but only photons that have any entangled partner. Do you know any investigation about this aspect?
Where else would they go? (modulo a small possibility of absorption or scatter at the non-perfect surfaces). Compared to unentangled photons, entangled photons often show different correlations between reflected and transmitted paths. However, the number must be conserved. If you add up the total number reflected and the total number transmitted they must add up to the total number entering. There is just no other thing that can happen.
They could be absorbed or scattered anywhere. We don't know and I just do not want to use any theory about that aspect. I NEED measurements for it. In my view the probability of reflection and transmittance cannot overlap for entangled photons (see picture)
I believe you may be thinking about this wrong. A real polarizing beam splitter will have some degree of imperfection that will allow some absorption or scattering, but I don’t think that is what you want to discuss. In the limit of perfection (and real splitters aren’t far from it). There will be no absorption. Single unentangled photons won’t absorb and entangled pairs won’t absorb. There certainly won‘t be any special extra absorption due to entanglement which is what you seem to be suggesting.
Also, your diagram on the left is incorrect. A single photon will always have the diagram on the right. Their history doesn’t matter. If I make entangled pairs and bring each to a polarizer each of them analyzed separately will follow the diagram on the right. For example a photon with 45 degree polarization will reflect half the time. This is true of both photons at both polarizers, just like the diagram shows regardless of whether or not they are entangled.
What is interesting is when you look at the correlation of the two measurements. For example, if the entanglement produces pairs with orthogonal linear polarization, then whatever the first photon is seen to do at the first polarizer the second photon must do the opposite at the second polarizer. For example if they are each at 45 degrees to the polarizer, a photon may transmit or reflect. In a single entangled pair the other must do the opposite. over time each polarizer will see photons randomly reflecting or transmitting 50% of the time. But each individual pair will be seen to make opposite choices every time. Over many pairs, the resulting polarization appears to be random at each polarizer, but within each pair the results are 100% correlated.
That's the point. I know the theory about the entanglement and I send you my document how I see it. It's sounds really crazy and you should have the patience to read until the end. To say it in advance: I agree with John Bell, CHSH and so on. In all practical tests I find the beam splitters but also two interference filters that could have any additional effect. And I do not find any prove that entangled photons are just the same than unentangled ones.....
Oleg Petrov's article https://www.researchgate.net/publication/331041475_Information_Interpretation_of_Heisenberg_Uncertainty_Relation
proposes a fundamental principle, which, among other things, allows predicting the behavior of entangled photons. Perhaps it can help in this situation.
First draft of the document "Entanglement without spooky action at a distance" added. Simulation codes included.
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