Stefan,
"What do you mean by undecidable?" I mean inadequate information exists in any individual case. i.e; Does the equator spin clockwise or CCW?, and; what is the circumference of spin at a pole? or "is 'sand' closer to red or green." (+see below)
I'm not sure what you mean by 4 pairs of values, but I suspect you mean the 2nd order ('hyperfine') electron case. However the answer to your 1st question; 'are we using electrons' is No. For now we're considering just the photon spin 1 (polarity) until you've grasped the 1st order dynamics. I agree I need to fully specify details. Also show in Fig's. First the answers, which are 'Yes', except as below;
"two discrete possibilities of pole orientations - in relation to the two particles. Yes BUT; the approaching 'photons' are not really 'particles' but expanding wavefronts with surface helicity, so I prefer to minimise use of "particle" to avoid confusion with the 'field' electrons.
"..new spin axis again lying on its propagation axis. Right?" Hmmm. With CFS etc. it's an expanding wavefront again. The part on the propagation axis should then have elliptical polarity. Ellipticity is (common and) important! The peak energy, 'circular polarity' axis it seems, is 'deflected' proportional to field strength (voltage dependent in an electro optic analyser such as Weihs). In weak field cases the apparent net 'deflection' is low (a bit like 'curved space-time'!).
"Why should...The other particle's new spin...be then measured as *spin down*, for same settings and orientations of the magnets."? OK. Imagine a long bench with 20 identical detectors in line all set to the same spin. Now form a large ring with them on the floor. They'll all spin the same way, OK? Now take them all away apart from two adjacent ones. Now go round to the back of each and look in the output holes. You'll find one Clockwise and one CCWise! That's 'non mirror symmetry' of spin; an apparently peculiar fundamental truth about spin very poorly understood by man. Observer 'orientation' is everything!
"Is this wave energy identical with the OAM?" In the approaching wavefront, and to the 1st order, it seems Yes. But the OAM transferred ('measured') is 'RELATIVE', so a function of electron orientation, and also of wavelength.
If the electron field is also in lateral motion we also find "kinetic reverse refraction" due to charge asymmetry ('JM rotation') which has the same effect as the anomalous "stellar aberration". (Within the 'extinction distance' for the medium we also get 'multi refringence' and 'scintillation'). But don't worry about that lot for now!
Either of the 2 photomultipliers 'clicks' with varying probability related to the cosine value, so we've established that EACH (A or B) set of findings can be plotted to give it's own independent cosine curve distribution related to 'latitude' derived from electron orientation for each event.
We now have two independent 'sets of data' each producing cosine curves linked ('entangled') by the common propagation axis. The 'relative angle' case is an entirely NEW abstracted 'geometry'. As we only need relative information we must consider this as asking; "for every angle A, is angle B more 'similar' or more 'opposite', and how certain." Then we can plot the answers (using inverse values). Clearly a very small angle difference gives high certainty of "similar". Near 180 degrees gives high certainty "opposite". But AS 90o APPROACHES; CERTAINTY REDUCES non linearly, with the reversal around 90o.
In summary; Geometrically we only need to show how the cos distribution at each detector emerges. The 'relative' distribution re-emerges from that due to the common axis, as a non linear distribution of 'similarity', which may of course also be termed 'probability'.
My Essay 'end notes' Table 1 'Classroom Experiment' results (reproduced) describes that same question as; "Which colour is closest; Red or Green".
I do understand it takes some getting your head round. I didn't anticipate assimilation of DFM dynamics before 2020 so you're ahead of the game!
I'm racing round the world's biggest sailors graveyard on Sunday (Goodwin Sands) so if I don't come back it's all up to you!
Best wishes
Peter
PS. I attach the 'kit' for reproducing the subjective classroom experiment.Attachment #1: 9_Kit._FIG_5.jpg