Quote by A. Neumaier
They are dealing with standard situations, and take them as proof of quantumness. The papers speak for themselves, but my lectures used them just as examples  the main message is quite independent of these details

I don't know what you mean by "standard situations" though. The "situations" that Bell was considering very specifically dealt with measurements made at a spacelike separation, I don't think he would have said any "proof of quantumness" (in the sense of violating the 'local causality' he was concerned with) can be found in other types of experiments.
Quote by A. Neumaier
The papers speak for themselves, but my lectures used them just as examples  the main message is quite independent of these details.

I found
one of the papers, but without knowing much about quantum optics, and without being able to read the theoretical proposal that led to this experiment, I don't think I can understand it (I can't even see anywhere in the paper where they compare quantum predictions with some inequality derived from local realism, it seems like all the equations deal exclusively with the quantum predictions and the reader is expected to know which ones violate some Bell inequality). Can you just tell me whether these experiments demonstrating "single photon nonlocality" involve looking at correlations between results at two or more detectors, results which experimenters in the neighborhood of each detector could in principle write down before learning anything about the result at the other detector?
Quote by A. Neumaier
The standard CHSH inequality (but also any other inequality or equality of this kind) is simply an inequality about states of pairs of independent observations, and has nothing per se to do with contexts or locality.

That's true, but a derivation of the claim that violations of the CHSH inequality are incompatible with local realism does require some assumption about measurements made at a spacelike separation.
Quote by A. Neumaier
I don't remember the details since I lost interest in these kind of arguments and experiments after having understood that they just probe certain wave aspects of QM, and tell (me at least) nothing of importance about hidden variables. It is obvious that QM is a wave theory, and that it therefore conflicts with simplified classical models that do not take this into account.

When you say "nothing of importance about hidden variables", are you denying that experiments of the type envisioned by Bell could definitively rule out any theory of
local hidden variables (where the value of a given local variable cannot be causally influenced by anything outside of its past light cone), or do you just not consider that "important", perhaps because you weren't interested in local hidden variable theories in the first place?
Quote by A. Neumaier
If these observations are nonlocal observations about identically prepared single photons they are violated by the interpretation in terms of the Maxwell equations (no matter what the detailed setup or the precise inequality tested) as long as the setting interpreted by standard QM violates these conditions.
So what? It just says that QM is correct, whatever it predicts, and that a classical interpretation would have to match these predictions. That such an interpretation must be more complex that a simple classical description is clear since QM has much more degrees of freedom. But I don't think it poses essential difficulties for a classical field theory if one makes the fields complex enough. Whether such a classical interpretation is warranted is another matter  I don't think it adds any value to the usefulness of QM.

But what does "complex enough" mean? A local theory of the type I described could have arbitrarily complicated values at each point in spacetime (for example the values might be tensors rather than vectors, or any other type of mathematical object), as long as the values at each point were not causally influenced by anything outside the past light cone of that point. Maybe you're talking about a nonlocal theory where the values of the field aren't associated with particular points in spacetime, or where FTL causal influences can occur? I'm not sure I would still call either of those a "classical" field theory, I don't know if that term has a standard definition though.