Implications of Bell Violation in Classical Optics for Local Realism A recent set of articles (one in Nature, a second in Entropy, a third in the Journal of Physics B) declared that BCHSH violations by themselves do not rule out the possibility of constructing local-realistic models. Andrei Khrennikov has even constructed a completion of QM with classical random fields: "The message of PCSFT in a nutshell is that (i) quantum systems may be mapped on classical stochastic systems even if they are capable of nontrivial quantum manifestations, and that (ii) this shows that the aforesaid phenomena should be regarded more classical than it is commonly believed." Doesn't violating Bell inequalities in a local contextual framework change the discussion away from Bell loopholes? I thought this was particularly intriguing after seeing the confirmation of QTT back in 2019 and the work done in hydrodynamic QFT. I'm astonished so little has been made of these developments. Long live local realism or at least local reality without realism?
 A: First of all, that 2017 article is not a Nature paper.  It is a paper from Scientific Reports, an open-access journal published by the publisher of Nature.  Scientific Reports, like many online-only journals, it does not reject any papers for being insufficient important; papers are judged for publication solely based on whether they are correct.
However, even that standard may have been be too generously applied to that paper.  The paper does not, so far as I can discern, show anything that is actually relevant to Bell's conclusions.  Had I been asked to review it as a manuscript, I would have probably recommended that it be rejected outright as fundamentally misguided.
Much of the paper is written in marginal English, so at times it is difficult to tell what it is claiming.  However, this excerpt from the abstract seems to accurately express, more or less, what the paper does show:

We present a local-realistic model that reproduces quantum predictions concerning Bell tests. We claim that local-realism is fully compatible with correlations that are not of the Bell type and therefore lie outside the scope of Bell’s theorem.

The paper simply studies different quantities than the usual correlations that are used in Bell's Theorem.  It posits that the expressions that Bell worked with are, for some unexplained reason, not the correct ones for describing real observables.  It tries to tie this into the concept of signed measures, which is looks very concerning to me, since an immediate consequence of the replacement of a probability measure with a nontrivially signed measure is the existence of negative-measure events.  (The most important theorem about signed measures is that every signed measure can be written as a difference of two standard measures.)  Needless to say, if negative-probability events are allowed to contribute to contribute to expectation values, all sorts of nonstandard behavior becomes possible.  However, the paper does not, in the end, provide any actual reason to believe that it is proposing a mathematically consistent formalism—much less a physically correct one.
The paper by Andrei Khrennikov does something different, but it does not represent an overthrow of quantum indeterminacy either.  It claims that a certain classical stochastic process can duplicate Bell's correlation.  (I have not checked over whether the calculations are correct, but that is not actually important to the overall conclusion here.)  This does not conflict with anything we already knew, because it introduces fundamental classical randomness to the system.  That a sufficiently noisy channel can produce results that look nothing like clean measurements is no surprise; this is not a hidden variable theory, because the classical randomness is irreducible, and truly identically prepared systems will not produce the same outputs in successive experiments.
Another way to view this is that the classical randomness tilts the system in a way that prefers showing quantum-mechanical-like correlations, even if there is no underlying quantum element.  The model explicitly uses detectors with explicit thresholds, so events may sometimes go undetected.  The combination of these two elements constitutes a clear violation of fair sampling, and it is well known that without a substantial degree of fair sampling, Bell-type correlations do not necessarily point to quantum indeterminacy.
