JK
That looks quite brilliant, but the details were a little beyond me as I'm no mathematician (though scored top on Wigner with red/green lined socks in 2015!)
I hope you can help. It looks to me as if you have an algorithmic solution to non-linear classical 'quantum' interactions. That's of great interest as my essay describes a full ontology (and scaled up experiment) achieving what I think is 'impossible', a geometrical solution for the same problem, reproducing QM's predictions free of weirdness. You'll be one of a few here qualified to check it. I Analyse 'OAM/QAM' more closely & in essence do the following;
Assume pairs retain anti-parallel polar axes but random x,y,z for each pair.
Assume physical particle OR wavefront/fermion interaction as absorption & momentum exchange at some tangent point on the Bloch sphere.
Start the pairs with Maxwell's FOUR states, inc. 'curl' (polar N/S) AND equatorial (0 curl but max +/- linear) momentum. QAM is then just spherical rotation.
Identify from Geophysics that the momentum distribution of both pairs is inverse and by Cos latitude (as 'surface speed' but for any diameter within the field fermion (theta set by A,B)
Take polarised/modulated 'requantized' Cos values (also now theta dependent) to the (2 channel) photomultiplier fields for further orthogonal interactions and 2nd requantization, squaring the Cos values (Borns Law).
Working with all 3 degrees of freedom and detections only above a certain energy threshold at each angle (subject to phase) the mechanism provides the outputs which (when collated and misunderstood statistically!) fully reproduce QM's predictions! Actually just as John Bell predicted, and a Bayesian distribution.
Few can grasp the ontology. Declan Traill's short essay provides the computer code and plot supporting the mechanism, including meeting CHSH >2 and the 'Steering Inequality' >1 test closing the 'detector loophole'.
Non-integer spins emerge from y,z rotations and non-locality isn't required!
What I'm unable to do (simple incompetence I think) is find the Hamiltonian. I'll also of course be unable to convince the academic community it's no joke.
I'd greatly appreciate your advice and perhaps help.
Thanks for your own inspiring insights which I'm sure are connected.
Very best
Peter J