[gus_massa]

Exactly, something like that.

(Note for others: This is not an implementation of the OP method, it's another paper with a somewhat similar topic.)

It's an interesting model, but I don't like some details.

It generates a pair of (not entangled) photons with the same polarization (actually, +pi/2). Then it has two detectors.

In each detector the first secret parameter is equivalent to the usual calculation of the probability that a photon that has a polarization that is not aligned with the polarizer pass. If you can buy perfect/magical detectors that has the second secret parameter equal to zero, then this is just equivalent to the usual model with non entangled photons. And it should not break the Bell inequality.

The second secret parameter of each detector tries to model that the detectors sometimes miss a photon. I still don't like the model they are using, but it's not my specialty. Anyway, usually noise and fluky detectors make the result look more like classic results, so I expect that this second parameter makes the result not break the Bell inequality.

The problem is that it is possible to make very careful experiments that break the Bell inequality, so I don't understand what their model tries to show.

[GistNoesis]

Kupczynski is in the list of the reference pointed by OP method.

>The problem is that it is possible to make very careful experiments that break the Bell inequality, so I don't understand what their model tries to show.

Their plausible and local model aim to (and does!) reproduce the QM probabilities observed by experimenters (for all alpha and beta settings) and therefore does violate Bell inequality.

>It generates a pair of (not entangled) photons with the same polarization (actually, +pi/2)

The photon pair is entangled. The polarization is definite (and with a pi/2 offset between the pair) but unknown to the observer which is therefore measuring a distribution, that the key point. It's proposing an explanation of what entanglement is.

[gus_massa]

Looking more carefully at the paper you posted is that the filter is filtering too much.

If alpha=beta or alpha=beta+90°, then the number of coincidences is approximately 500,000 (of the 20,000,000 tries)

If alpha=beta+45°, then the number of coincidences is only 1,500. i.e. like 300 times smaller.

Such a difference is would be very easy to see experimentally, and it is not the case. The number of coincidences independent of the angle between the sensors (with some noise, as always).

This filter is picking only the photons that have an angle phi that is very close to (alpha+beta)/2 or (alpha+beta)/2+90°.

[GistNoesis]

This is a good point, but it's not as clear cut. The free parameter V helps trade-off this.

For example if you have V=9.0 for alpha=beta+90° you have nbselected = 5622861 and for alpha=beta+45° nbselected = 1527848 That's only 3.7 times smaller.

But the main point of the paper is to have a really simple model to highlight the pointlessness of Bell theorem rather than point to a specific mistakes by experimenters.

[gus_massa]

But if you use V=9.0, now the result of the simulation is not longer equal to the experimental result. For example with alpha=0, beta=90, V=9, if I run the simulation 10 times I get

  0.9536987797308330
  0.9540514229678816
  0.9534108516112525
  0.9540204547111079
  0.9535252821469831
  0.9538811736228740
  0.9541386030170054
  0.9534090666514868
  0.9538249532069655
  0.9535418321159825

That is pretty consistently like 0.045 less than the expected result that is 1.0.

(It is weird, but if alpha=0, and V=9, and you change beta, then the error is very close to (45-beta)/1000, where beta is in degrees. It's probably not exactly 1000, because using a number in degrees is weird, but it's similar.)

The problem is not to find an alternative algorithm that predicts one of the results, the problem is finding one that predicts correctly all the results.

[GistNoesis]

Yep that's normal, that's why it's a trade-off.

It smoothly deforms the distribution between classical and QM, and the results look less like theoretical QM, and more like a experimental QM (in practice it's hard to observe 2.0*sqrt(2.0) theoretical violation of BI).

There is quite a lot of modelling freedom, to hide the distribution into the noise.

The whole question is what's more likely between experimenters missing photon pairs to the noise due to a systemic misconception in a complex experimental setup, or have the universe be non-local.

>The problem is not to find an alternative algorithm that predicts one of the results, the problem is finding one that predicts correctly all the results.

A model which predict all the results (Hint : Fields), will be more complex and even less likely to convince anyone.

Bell's theorem is a mathematical version of those onceyouseeit images ( https://twitter.com/TimKietzmann/status/1390405523430850562 ) where you realize that there is in fact nothing to see.

[gus_massa]

> The whole question is what's more likely between experimenters missing photon pairs to the noise due to a systemic misconception in a complex experimental setup, or have the universe be non-local.

It's not about what is more likely or which model I prefer. It's about which model gives accurate prediction that agree with the experimental results. (Or if you want to be more technical, which one has not been falsified.)