Any Bell Experiments Showing Inequality Violations in Purely Classical Systems and What this Would Mean If So? Are there any legitimate experiments/papers out there that have shown a violation of the Bell Inequalities in purely classical systems in which local realism couldn't sanely be called into question? I mean real-world objects - a deck of cards, a pair of gloves, etc. Things whose properties are constrained and correlated, yet completely intrinsic and knowable through simple observation, but which are then separated and independently measured, and the measurements are subequently compared to see if B.I. violations occurred.
There are a few papers on the Internet that claim to show this in one form or another, but I'm not really in a postiion to judge if they're legitimate, so I'd rather just hear from the experts on whether they know of any instances where violations have been truly shown in classical systems, or even genuine attempts to test this.
If this has been shown, or if it ever were to be shown, what would this mean? Would it just demote entanglement to little more than a statistical quirk? Or would it shake the foundation of our understanding of statistics and information theory?
I hope the last part isn't too philosophical, but what I'm anticipating is something along the lines of, "no we've never seen this, and we will never see it because it would defy the laws of math and lead to a universe-ending paradox if we did." Or, "yes we can observe this in classical systems but it doesn't say anything about quantum entanglement because ___".
Edit
I'm not sure the intent behind my question was clear based on some of the comments and responses, so let me ask it slightly differently.
I'm not questioning the Bell theorem or that quantum entanglement cannot be explained through any local HV model. What I'm asking is: ignoring the possibility of signaling or superdeterminism, are there any experiments testing whether macro/classical systems can ever behave in a way that would also contradict "realism" such that one could find violations of the BI without any quantum influences?
Again my understanding going into this is that the answer is no, but it would be very interesting indeed if it were yes.
Edit 2
I found a paper online by William McHarris, an apparently deceased former Michigan State University physics professor, entitled "Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes", which appears to be more legitimate than others and hasn't been mentioned yet, though it doesn't seem to be a peer-reviewed journal paper.
He says at page 7, "classical nonlinear systems are known to exhibit correlations, ranging from the directions of particles in tornadoes to the distribution of energies in cosmic rays — and at times these can be great enough to overlap with quantum correlations." (emphasis mine).
Is there any merit to this? Or am I misinterpreting what he's saying?
 A: There are no violations of Bell's inequality by classical, local systems. Bell proved it. That's the reason that the inequality is interesting.
Papers that claim a violation of Bell's inequality usually make the mistake of thinking that Bell's inequality is a general law like the uncertainty principle. It's actually a result about one particular experiment. Bell's goal was to prove that no local hidden variable theory can reproduce all predictions of quantum mechanics. To do that, it's sufficient to show that there exists one experiment for which no LHV theory can reproduce the QM prediction, and that's what Bell did.
Showing that LHV theories can match the QM prediction for a different experiment has no bearing on Bell's result. Of course many such experiments exist. Papers that make this mistake include "Disproof of Bell’s Theorem" by Joy Christian, which has appeared on the Physics SE before, and "Experimental Bell violations with classical, non-entangled optical ﬁelds" by Gonzales et al, published in Journal of Physics B, which I just found in a web search for such claims. Both of them describe experiments where the measurements have continuous-valued results. That might be interesting if they proved a Bell-like result for continuous variables, but they don't. They just replace Bell's correlation function with a different function and assume that the inequality remains valid, which it doesn't.
Bill Alsept's answer makes a similar mistake. He describes a knife-throwing experiment in which there is a sinusoidal dependence of the "knife detection rate" on the angle of each detector relative to the knife that encounters it. There is no theorem saying that that's classically impossible. If you treat the knives as hidden variables, Bell's inequality does imply for this experiment that there can't be a sinusoidal dependence of the correlation of the detection rate of the two detectors on the angle between the two detectors, and if you work out the details you'll find that there isn't.
The paper by William McHarris that is mentioned in the question makes a much more basic error. He says that Bell neglected to consider classical correlations between the particles (which is wrong), and in support of that he claims that Venn diagrams only work for statistically independent properties, and the borders of the diagram become fuzzy if there are correlations (his figure 3). In reality, showing such correlations is the whole point of Venn diagrams. The borders would only be fuzzy if the individual properties were fuzzily defined, which is not what he claims.
A: There's a lot of misinformation on this subject. Andrei Khrennikov and Peter W. Morgan point out that Bell violations can occur with classical random fields, and it seems that few physicists understand the subtleties of non-Kolmogorov probability. Khrennikov was a student under Kolmogorov. From a field point of view, you can certainly have reality without "realism", if you are prepared to abandon particles. The assumptions required to derive Bell inequalities are not usually satisfied for random field models if there are ANY thermal or quantum fluctuations. The field propagators are nonlocal in a trivial sense and not in a signaling sense.
It turns out that Bell inequalities can be violated by classical light, Brownian motion, and water waves. In a paper by Papatryfonos, an experiment was conducted with a hydrodynamic quantum analog, where experimenters adjusted well geometries to get Bell violations in a simple tank with water. The authors also hinted at creating Bell violations with memory, after isolating the two systems with a wall. Future experiments are forthcoming. In my view, the recent Nobels were awarded prematurely.
Here are the papers you should read to understand the present debate over so-called "nonlocality" and the completion of quantum mechanics:
The Straw Man of Quantum Physics
Bell Inequalities for Random Fields
Bell Test in a Classical Pilot-Wave System
Shifting the Quantum-Classical Boundary
Brownian Entanglement: 
https://arxiv.org/abs/quant-ph/0412132 
https://arxiv.org/abs/quant-ph/0310114 
https://arxiv.org/abs/quant-ph/0211033 
Classical Electrodynamics Can Violate Bell-type Inequalities
Apparent Violations of Bell-Boole Inequalities in Elastic Collision Experiments
The Chaotic Ball: An Intuitive Analogy for EPR Experiments
Violation of the Bell-Inequality in Supercorrelated Systems
Contextuality, Complementarity, Signaling, and Bell Tests
Comment on "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometers"
A: Bell's theorem/inequality states that any physical theory that incorporates local realism cannot reproduce all the predictions of quantum mechanics.
For the sake of discussion, I assume that “predictions of quantum mechanics” means Malus Law or cos2theta. After all, most articles on this subject come with an overlay diagram of linear and non-linear slopes depicting classical and QM predictions. These articles make the argument that physical models cannot reproduce the results of Malus Law.
But what if they could? What would be the repercussions if real (large enough to see objects) could be physically correlated to reproduce the same predictions as QM? Below I have described just such a situation (Not a theory) where the results do match. Although the objects described below are analogous in many ways to the Alice and Bob scenarios we all know, they are real. Read through the first half set up to appreciate the derivations in the second half.
In order to prove that particles can be physically correlated to match QM, I’ve gone to the extreme of choosing large ordinary objects. I could chose from many different objects but to make a point and to be specific, the objects I chose are ordinary throwing knives (please bare with me thanks). Each knife is twelve inch-long, one inch tall and 1/8” thick.
The two knives are correlated in a few was such as: (1) Every knife travels at the same speed and reaches a tester at the same time. (2) As they travel toward the testers, they all rotate vertically end over end at the same rpm. Some pairs begin rotating sooner than others and may or may not be pointing forward when they get there. They could be pointing any direction including sideways. We've all experienced that kind of target practicing. (3) The tester/analyzer is a wall with a one-inch wide slot. The wall can be rotated so the slit is anywhere from vertical to horizontal.
When the slot is set vertical, all the knives pass through but when the slot is set horizontal, no knife can pass. If you rotate the slot five degrees from vertical, most knives still make it through but now there’s a slim chance the rotating knife will make contact with one edge of the slot. With the slot set vertically, all knives make it through and at five degrees it’s obvious the odds have been slightly reduced.
Rotate the slot to 25 degrees and it becomes harder for a knife to pass. You can imagine if the knife is rotated correctly when it reaches the slot, it will make it through, but now vertically rotating knives could hit the edge of the slot. As a matter of fact, if you take the time to truly visualize this you will see that a number of new things come into play. The position of the knife’s rotation (similar to Feynman rotating clocks) which is analogues to amplitude, plays a big part, especially in relation to the knives proximity to the slots edges.
If the slit is rotated to 85 degrees from vertical (not quite horizontal) most likely a knife will not pass through but there is a very slim chance that if it’s pointed at the slot as it gets there, it will. The probability is low but still possible.
After throwing thousands of vertically rotating knives at various set points ranging from vertical to horizontal you accumulate the results. The results will show that the number of knives passing through is directly proportionate to the set angle of the slot. More interesting is that the proportional results are NOT LINEAR. Instead you’ll find that the results do match Malus Law and cos2theta.
The accumulated results are farther smoothed by the random release and rotating phases which may or may not let them pass through. This again is analogous to phase and coherency of photons.
Bell's inequality is an attempt to prove this cannot be done. But here we have a real situation (Not even a theory) where the results do match QM predictions and follow Malus Law perfectly.  Bell only considered polarization but particles have more variables than that. Perfect correlation would involve speed, direction, polarization, coherency, and frequency. He didn’t consider anything to do with rotation or frequency, which then brings linear dependency into the picture. Bell’s setup locks you into parameters such as vin diagrams. It’s a mathematical statement that does not apply to reality.
