[Mentor's note: This thread has was forked off from another thread because it was a digression there.

This is false. Bell's theorem is based on a certain assumption (the statistical independence or free-will assumption). Some local and realistic theories that contradict this assumption exist. You can find such an example here:

"Explaining observed correlations" would mean giving a description of the causes, following Reichenbach's common cause principle. This would be impossible, because Einstein causality, in a version which supports Reichenbach's common cause, is sufficient to prove the Bell inequalities too.

So, all you can hope for is some minimal version of QT which explains nothing, but simply describes observable correlations.

I would also object to the use of the word "local". A theory where everything has some localization in space and the speed of information transfer is finite can be reasonable named "local", even if the limiting speed would be much greater than c. The better word would be Einstein-local. Not that important, maybe, but even if QT itself is non-local, you could approximate it by some local theory, and the difference would be observable only for measurements space-like in the version of "space-like" with the much higher limiting speed. The result of the actual naming convention is Orwellian - one would have to name theories which are local in the common sense meaning of the word "non-local".

I recognize some Q-bist ideas in your paper so I can answer quickly. I see two serious problems with this approach:

1. You claim that the brain is a localized object so observations are local events. The problem is that the brain is still an extended object and really huge as compared to the presumed size of particles around Planck unit. It might be that a conscious experience is non-local after all.

2. This approach leads to absurd conclusions. Assume that you are given a Klingon war-bird capable of going to the center of our galaxy and back within minutes. According to your theory there is still no proof of exceeding the speed of light because in the end you have nothing but some observations in the brain which, as you argued, are local. It seems to me that the price of such theory is the complete rejection of science. It becomes meaningless even to speak about locality. An observation implicitly require something to be observed. If nothing is observed the proper word is not "observation" but "illusion".

I don't the the point of your "Stochastic electrodynamics" paper, it refers for equivalence to Nelson, but Nelsonian stochastics is (beyond the one-particle case) non-local.

Maybe but I'm unable to see this from that paper. All I can find in this paper is "In the various phenomenological approaches to stochastic QM it has been shown that the integral of eqs. (4) and (5) with U = 0 References is entirely equivalent with the Schrodinger equation and its complex conjugate [4]." with [4] referring to Nelson. Thus, to hydrodynamic variables. But in hydrodynamic variables, the velocity as defined by the BM guiding equation has a physical interpretation. And it depends, for more than one particle, in a non-Einstein-local way on the global configuration. So, I'm unable to identify there any locality.

Unfortunately the forum rules require me to use only peer-reviewed papers and for some reason the admins are very quick to lock the threads I post or even delete my posts. Hopefully this time it will not happen. There is a consistent book, "The Emerging Quantum: The Physics Behind Quantum Mechanics" that can be found here:

The statistical independence or free-will assumption is required only for external parameters in Bell inequality tests. Do you suggest that there are theories that propose how outputs of different PRNG and QRNG can violate statistical independence?

The closest thing to "appearance of non-locality" in 8.3.3 I have seen in the fast overlook is "The single-particle quantum nonlocality, rather than an ontological property, appears thus as a semblance, an artifact of the reduced statistical description, which would dissolve by ...". So, it is about single-particle theory.

In 8.4 I see, at first, some sufficiently explicit formulas which support the non-local character. But then I see at p. 295 the following phrase:
"Nevertheless, considering for example that the Bohm particle that follows the trajectory xi(t) with a velocity vi = dxi /dt is not the real, physical particle, but rather a representative particle that at each point reproduces the statistical dynamics of the appropriate subensemble, the spooky-action problem disappears".

It does not make sense for me. Ok, in Nelsonian stochastics the dBB velocity is not a deterministic velocity but an average. But once even the average depends in a non-local way on something far away, this non-locality will not go away. (In the other direction, this may be possible. A theory with deterministic evolution and non-locality can, by averaging, loose the non-local character, with dBB in quantum equilibrium as an example. But a non-locality in some average which somehow disappears? Sorry, I don't believe.

And I don't see it in any explicit computations. Take the experiment known as "delayed choice", and compare the two scenarios where the which way measurement is done before resp. after the two ways intersect a second time. If the "which way" is already measured, the paths will be classical. If not, there will be interference, and the meeting point acts like a mirror. All you need to come to this conclusion is the possibility to identify correctly different parts of the beam which correspond to different positions of the far away second particle. So, if you would be able to see the microscopic picture, you could easily tell if the which way measurement far away has been already done (the particle moves straight) or not (the particle is mirrored). Only if you average over everything, and are unable to see any paths, this no longer makes a difference.

Yes, this is my claim. I am not familiar with PRNG and QRNG but I assume you mean random number generators.

Let's describe the experiment in accordance to classical electromagnetism. As all devices/people involved in this experiment are made out of atoms they can be represented as large groups of charged particles (electrons and nuclei). In order to calculate the trajectory of an electron at Bob's location you need to know the electric and magnetic fields there. Those fields are a function of position/momenta of all field sources (electrons and nuclei) not only at Bob's location but also at Alices' location and the location of the source of the entangled particles. It is therefore mathematically obvious that the evolution of the three subsystems (A - Alices' detector, B - Bob's detector and S - source) cannot be independent. So the assumption that the hidden variable, say the spin of the particles is independent of the state of the detectors is false.

Everything I said above is true regardless of how the experiment is performed. You may use people, computers, PRNG's, QRNG's, monkeys, whatever to set the detectors. It does not matter.

Now, I do not know if such mechanism is the real explanation behind the quantum correlations but my burden of proof does not require that. It is enough for me to show that the subsystems cannot have independent evolution so that Bell's assumption falls.

Let's look at setup where we use PRNG (Pseudorandom number generator) to set analyzer angles for Alice and Bob. PRNG produces it's output after entangled particles have left the source (it's the way how it is implemented in real loophole free experiments). So when entangled particles are produced at the source this dependence should be formulated in terms of the seed of PRNG. But then PRNG takes the seed and produces a number (bit) from the seed by strict mathematical algorithm that works regardless of wast number of the states of particles that make up the PRNG circuit.
So your hypothetical model has to take into account the state of the seed and very high level classical and quite complicated configuration of the circuit regardless of the combined state of wast number of particles. And at the same time the model has to be quite general. Sorry, but I don't see how you can claim something like that.

In other words, you cannot do any physics at all. Any prediction whatever made by some physical theory assumes, even if it does not explicitly tell you about this in every moment, that what is predicted is independent of a lot of things in the universe, in particular of those we simply don't know about.

This loophole simply does not make sense, because taking it seriously would be the end of science. Return to astrology, where we do not exclude the influence of Venus on our love stories or so.

I use a fundamental description of the experiment, focusing on the known physical interaction between fundamental particles. The output of PRNG emerges out of the motion of those fundamental particles. If the motion of fundamental particles at A is not independent of the motion of fundamental particles as B (and you don't deny this fact) then the output at A and B will not be independent. A detailed explanation of the dependency would require a computer simulation of such devices using classical EM applied to their internal particles, which is impossible to do at this time. But, at least qualitatively one can be sure that such dependency must exist. What are your arguments that the microscopic correlations cannot produce effects at macroscopic level?

No, this is false. Locality implies that one can treat a subsystem without taking into account the larger system (ultimately the entire universe). For example one can calculate a trajectory to go to the moon without taking the entire galaxy into account. You can even ignore the Sun to some extent. But this does not imply that the trajectory of the moon is independent of the evolution of the galaxy, on the contrary. So you are making a confusion between the possibility of describing a subsystem independently of some other subsystems with the claim that the subsystems are not correlated. Big mistake.

So, you can evolve A disregarding B (because the effect of A is present at B in the form of the local electric and magnetic fields originating at B) and you can evolve B disregarding A (because the effect of A is already present at B in the form of the fields originating at A), so you can do science just fine, but you are not justified in saying that the evolution of A is independent of the evolution of B.

You seem unable to actually attack my premises (the right way to deny an argument) so you seem to just make an appeal to emotion. If I am right it's bad. But you want everything to be OK so I must be wrong. Sorry, that's a fallacious way to argue. Anyway, I hope I have provided a satisfactory explanation why the "end of science" claim is unfounded.

I say that PRNG circuit is localy deterministic at macroscopic level and as such it is independent of remote site or source. So even if we allow some dependence before PRNG has transformed the seed into the output then after PRNG has done it's job any dependence should take into account that local deterministic process that randomizes the seed. And that local deterministic process is described by quite complicated (and somewhat arbitrary) mathematical algorithm that can't be included in some simple physical model.

No, Einstein-locality means some sort of independence, namely independence on everything outside the past light cone. And I'm quite justified in saying this, this is the very definition of Einstein causality/locality.
Then, don't confuse independence - which is a statistical property - with not being influenced. This statistical independence, also named freedom of choice of the experimenter, is something which can be easily constructed, by combining various influences considered to be as random or independent (combine information from light from far away galaxies with random number generator and some local quantum experiment and a classical dice and my own pressing some button). And if one doubts that this gives results independent from the experiment done, we cannot make science in a meaningful way. Which does not mean that some sound of the measured system has not influenced the dice used there and my button pressing too. This influence is simply irrelevant, because it is a random one which will not modify the statistics. So, you cannot use it to explain, or explain away some observable correlations.