Hi Richard
Thank you for the advice and comments. It is early days for me in integrating retrocausality into entanglement swapping. I am afraid that I work very slowly and it is not that long since I (wrongly) thought that all this entanglement area was rubbish. This thread includes information about our aims, aspirations etc. so I will say some general points.
I have already shown mathematically that retrocausality can bypass Bell's inequalities. This is also easy to visualise in Costa de Beauregard's W shaped trajectories of particles in time. My own model, however, has particles which never zigzag but their influences do so. But now I want to try to understand QM better by adding retrocausality into more models to try and get QM results.
First, I should say that I accept QM's results but do not believe in ontological particle pairs instantly affecting one another. So, I accept that QM excellently describes our state of knowledge about the pairs of particles but does not describe their reality or ontology. I have thought about this more since reading Inge's ideas a few months back. This is comparable to the Monty Hall problem. Is the prize in box #3? We can perform calculations to find the best strategy to win the prize but the prize is fixed in one of the boxes even though our knowledge of the probability can vary during the game.
This is IMO very much like what is happening in entangled pairs. Because of retrocausality I can separate the states of the two particles (ontologically, or more ontological than using shared states) and still bypass the BI. So while the QM probabilities may get more and more complicated (as in a quantum computer) the reality for the particle itself always remains very simple as in the Monty Hall scenario. Any particle has a polarisation vector and a phase (in my classical gyroscope model) at any one time, but our knowledge of it can get very complicated to calculate. I have no reason at present not to fully accept the QM calculations as probabilities.
There is always a contradiction. My retrocausality retains locality and shuns action at a distance within the particle trajectories. So it is local for the particles themselves. But from Alice and Bob's viewpoint there is non-locality and action at a distance. This is very much like special relativity where Alice and Bob are on a train and Charlie is at a station watching them pass. A is moving wrt C, but is not moving wrt B. So yes, there is non-locality and action at a distance in the lab but the particles themselves are moving locally in their own frames.
I have modeled Malus's Law using a classical gyroscope. This gives S-G outcomes which can also be found using QM. QM can give the 0.707 correlation exceeding the Bell limit in a Bell experiment. My classical gyroscope on the other hand can give the intensity equivalent to a Bell 0.707 correlation in an S-G measurement but it cannot give 0.707 in a Bell experiment. But if I add in retrocausality, then my gyroscope model also allows a Bell experiment to give the 0.707 correlation, in addition to already giving Malus Law and S-G outcomes. I ask myself why do I need to add retrocausality to my classical gyroscope model when QM does not need to do so?
Ahranov uses the TSVF which takes a QM calculation and tweaks it/ re-orders it/ to add in what look to me like advanced and retarded (in time) waves. So does QM already have retrocausality embedded within it. Re Feynman and Wheeler etc etc. in QED.
So at the moment I am suspicious of entanglement swapping. I believe it is happening, but is it always possible to swap for any given pairs of entangled particles. I am working on it ...