> Im not sure we can fully disentangle the wave-equation for the photon from the equations for the splitters
That doesn't matter. The two sides of the experiment are space-like separated, and the splitters on each side are light-like separated. There is no place the information can possibly be other than in the photons.
...except non-local variables. Which is why I keep mentioning non-locality.
I don't think words are working and I'm not sure I understand your point fully. Could you draw a diagram? Specifically, the apparatus and where you think the requirement for information occurs.
I really do want to understand your point, because it's an interesting argument, even if I'm not sure I agree.
Could you point out what you think that has to do with locality?
It mentions it once, to assert it as a desired axiom (and incorrectly assert that QM can be local, which it can't be). I also would argue that GR supports non-local theories well enough, in that the actual geometry can appear macro-Euclidean (or other nice space) while containing micro-bridges which break the locality structure for the "nice" macro space.
A non-local value is any value which can impact things at super-luminal speed (generally, instantaneously). Of course, I would argue that the non-locality is only apparent, and we're simply seeing the shape of things very wrong because of how brains work, the information reaches us, etc.
> A non-local value is any value which can impact things at super-luminal speed
Ah. Those are ruled out by relativity. If you can send information faster than light, then you can send information backwards in time and violate causality.
That doesn't matter. The two sides of the experiment are space-like separated, and the splitters on each side are light-like separated. There is no place the information can possibly be other than in the photons.