Bell Theorem and probabilty theory

[mn4j]

On the other hand, there is no existing candidate LR theory on the table to compare to QM at this time.

You are mischaracterizing the debate as one between LR and QM. It is NOT.

Stochastic Mechanics (Marshall, Santos) is an example of a field of research in that regard, but every candidate SM model is found to have problems and is quickly modified again. And since such models do not predict anything useful, there is no incentive to study them further. We already have a very useful model - QM - and the experiments supporting it are in the thousands. Something useful from the field of study would go a long way towards convincing the scientific community.

So yes, I think quantity does matter, and I think utility matters. And I think the history of the area does matter as well, including when a theory (QM) is supported by improving technology.

The utility of a theory says nothing about it's correctness. The system of epicycles was very useful in the dark ages but you won't claim it as a correct theory. Technology always precedes theoretical understanding.

Why should you need to close every loophole simultaneously if you can close each separately? If a prisoner cannot escape from the first lock by itself, and cannot escape from the second lock by itself, how can he escape when both locks are present?

You answer your own question. The papers you mentioned are just prisoners claiming to have escaped because they were able to open one of seven locks. Unless you can open all seven locks you can't reasonably claim to have escaped, even if you change your name to Houdini.

I don't disagree with a desire to close all loopholes simultaneously; but I think that is a standard that is being applied to Bell tests which is applied nowhere else in science. Surely you must have noticed this as well.

It is common sense. The standard is demanded by the claims made by Bell. Extraordinary claims require extraordinary evidence. If you claim there is no green stone on Jupiter, you better get your ducks together and be sure you have combed every micrometer of the planet before you can say your experiment proves the claim. Yet if you claim there is a white stone in Alabama, all you have to do is find one white stone anywhere in Alabama to prove your claim. Bell says NO LR can violate his inequality.

 

[DrChinese]

Three points. First. I'm not an expert in Bell tests and loopholes issue, so can't really comment on that on the detailed level. I know that there's for example "time-coincidence" loophole (http://arxiv.org/abs/quant-ph/0312035), which is apparently exactly the loophole de Raedt is exploiting (http://arxiv.org/abs/quant-ph/0703120, the link I already gave). I'm not sure that all known loopholes were already closed even separately, though this might be true. In particular, I just don't know any details about this "entanglement" studies that you cite (and don't have time at the moment to start reading them). Do they test Bell inequalities after this entanglement "swapping"? Or how else these findings prove LR false?

Second. I guess that I slightly disagree with you about different standards of tests. Of course there are super-precise tests of GR still being done. But to test GR you need to observe something that is predicted by GR, like light deflection or whatnot. When this is observed, nobody claims that there's a "loophole" in this experiment, and the results can be interpreted such that light is not deflected. It's evident: nobody heard of any loopholes in GR tests. On the other hand, to test QM versus LR one needs to show that the Bell's inequalities are violated. And all the attempts to show it still have some loopholes that allow alternative explanations.

Third. Nobody in his right mind claims that QM is "wrong". For de Raedt, QM is a correct mathematical model working well on the ensemble level only, without saying anything about single events. He is not trying to show that QM is wrong, he is trying to show that it can be completed in a LR way. Well, we know that it's impossible due to Bell. But de Raedt obviously disagrees. And it doesn't make a lot of sense for me to defend de Raedt, but he is most definitely not a crackpot (he has done a huge amount of "real" work in computer simulations of different physical models, including decoherence etc.). I believe (as you do) that his reasoning about Bell is flawed, but he certainly does not try to obscure anything on purpose: I'm quite sure that he is honest.

A couple of comments, and by the way I doubt our positions are very different overall.

Any theory, including GR, can be attacked as lacking loophole free experimental support by a sufficiently motivated scientist. The concept would be to deny an essential element of the theory, and then try to show that somehow the experiment "could" be wrong even if the evidence is convincing by normal scientific standards. What if GR readings are not a fair sample? Maybe Newtonian physics is correct instead because there is a built-in sample bias. (I am only kidding of course.)

The entanglement swapping issue is really just another aspect of the hurdles any LR theory must explain. Two independently created photon pairs A1/A2 and B1/B2 are created. By performing a suitable partial Bell State Measurement (BSM) on one of each pair (A1 & B1), their partners A2 and B2 are now partially entangled (as to time bin). (So in this particular case, polarization is not swapped but that has been done as well by Pan, Zeilinger et al.) So the question is: how do the local hidden variables guiding A2 and B2 - which have never been in causal contact - manage to be correlated? That's not even a process that a non-local Bohmian (dBB) type theory has an easy time with.

As to intellectual honesty: no assertion being made to the negative. I just ask why someone in that position wouldn't make the source of the delta between LR model and QM be obvious? That is the first thing we all look for. And yet I always find myself reading a lecture on the wrongs of Bell while looking for that little detail I know is there somewhere. The author, I would think, would know what that detail is.

I always ask myself: what would Einstein have thought about Bell or Aspect? If he were alive today, I think he would be well convinced and would cede the essential point.

 

[DrChinese]

The utility of a theory says nothing about it's correctness. The system of epicycles was very useful in the dark ages but you won't claim it as a correct theory. Technology always precedes theoretical understanding.

That's wrong: how are theories judged correct? There is no such standard. Theories can have experimental support, and theories can make predictions that can be tested. And that is how they are judged. Correctness implies black and white, right or wrong. Theories can be better or worse depending on their application. But I cannot meaningfully say a theory is correct.

As to technology preceding theory: that makes no sense at all. Sometimes it does, sometimes it doesn't. There is no historical absolute on this. So again, meaningless.

 

[kobak]

Thanks for replying. In the beginning I started answering and addressing all the points where we disagree, but this is getting too huge and difficult to handle (so I'll concentrate on the main issue). But let me first say one thing. I'm not a "hostile audience", because I sincerely try to understand what de Raedt is saying. But it's extremely difficult to talk with you because you're constantly being very sloppy. Here's an example:

If you say Raedt's modes are not examples of LR, I repeat once again: YES THEY ARE. You see this kind of discussions takes us no where. Explain why they are not.

Are you joking? I have been saying all the way that I think that de Raedt's models are LR. Well, I think that you just miswrote something here, but it's quite difficult to try to decipher you sometimes. Another example:

2) That Bell's inequality is not a correct representation of local reality.
Now for some reason, Bell's followers ALWAYS gravitate towards (1). Do you agree that (2) is also a possibility

What on Earth is this second option supposed to mean at all? "Bell's inequality is not a representation of local reality"? Eh? I guess that what you mean here is that BLR is not LR. But it's really a pain to guess what you meant all the time.

Now, it's clear that the *MAIN POINT* is that you think there are LR theories that are not BLR. And you think that de Raedt's model is an example. I don't see why it's not BLR, I think it's absolutely BLR, and I think that I never saw any LR-but-not-BLR suggestion. And without an example I won't believe that that's possible. Here's your objection:

If de Raedt's model is BLR then how do you explain the fact that the model violates the inequality, when according to Bell it is impossible.

Well, my answer is simple: it does not violate the inequality. The inequality "seems" to be violated in the particular experimental setup because the certain post-selection procedure is applied. It's possible to create correlation by post-selecting, that's what this whole coincidence loophole is about!

You have no idea what you are talking about. Even ardent Bell believers have shown that not all LR are accounted for in BLR. See http://arxiv.org/abs/quant-ph/0205016 for one example.

Thanks for giving this link, it's actually interesting. I don't see though how it proves your point. Authors clearly write that "memory loophole" that they're describing can be avoided in experiment. If it's avoided along with other loopholes -- goodbye LR.

You claimed that some photons were lost in their double slit simulation. This is wrong! All photons reach the detector and affect the outcome of the experiment. Maybe what you were trying to say is that in t heir model, not all photons result in a click. In any case, do you have experimental evidence proving that all photons leaving the source MUST result in a click at the detector in a double slit experiment?

Yes, I meant exactly this: not all photons result in a click. I don't have an evidence, but it could be obtained. I described two experiments that could check this model. Take a look at the second. De Raedt says that if the screen is moved back and forth, the interference picture will get smeared. If this experiment is done and interference is NOT smeared, then de Raedt himself said that he would "retire", which I guess means that he will admit that his models are totally wrong and give up. And what would you say in this case?

 

[kobak]

DrChinese, yes, I think that our position regarding the main points here is the same. And I must say that I myself have also wondered many times about what "would Einstein have thought about Bell or Aspect"...

 

[Pio2001]

No. I disagree. So long as Bell's inequalities purport to make claims about reality, the correspondence between those inequalities and reality MUST be independently validated by experiments before any claims they make about reality can be said to be proven.

In photons' polarisation experiments, the correspondance between Bell's inequality and reality are that a detection is noted 1 and an absence of detection is noted 0, and also that nothing that is done outside the past light-cone of an event has any observable consequence on this event, which corresponds to the fact that in Bell's theorem, A does not depend on beta and that B does not depend on alpha.

The second correspondance is validated by experiments that show that nothing can go faster than light.
The first correspondance has not to be experimentally validated. You don't have to prove that you set 1 for a detection and 0 otherwise. We believe you !

Agreed without prejudice. Note that every loop-hole found to date is a hidden assumption in Bell's proof. I do not claim by agreeing to the above that all loop-holes have been found.

Action of the detector on the source, disproven by Aspect with ultra-fast switch, was not a hidden assumption, it was the explicit assumption that A did not depend on beta and conversely.
Fair sampling loophole was not either. Bell's theorem applies to the means of all measurments, not only some of them.
Statistics loophole have been filled with the GHZ evidence.

I've not studied all this, but not all loopholes were hidden assumptions in Bell's theorem. Actually, it seems to me that most loopholes claimed to be found in Bell's theorem rather than in experiments were unfounded. The CHSH generalisation of Bell's theorem makes things more clear : it takes into account anything that can happen around the measurment as hidden variable.

If you say Raedt's modes are not examples of LR which are not accounted for by Bell's LR, I repeat once again: YES THEY ARE. You see this kind of discussions takes us no where. Explain why they are not.

They violate Bell's inequality because Cxy depends on both t(n,1) and t(n,2) (equation 3), which is not the case in Bell's theorem. In Bell's theorem, Cxy depends only on the product of the measurments results (the Kronecker deltas in equation 3).

The role of t(n,1) and t(n,2) is to introduce a measurable individual dependence on the measurment angles, while they have no effect on the individual spin results.

Technically, it makes Cxy not being Bell's coincidence rate anymore. It has more to do with "what we measure" than with "what is locality".

That is a very narrow reading of de Raedt's work. Did you completely fail to understand the importance of the Deterministic Learning Machine model of de Raedt's?

De Raedt's pseudorandom model works without any Deterministic Learning Machine, and perfectly predicts Bell's inequality violation ! DLM are not involved in this step.
DLM are there to restore determinism, after the prevous step has restored locality.

Moreover, I'm not sure of it, but it seems to me that DLM would be accounted for as hidden variables in the general CHSH proof of Bell's theorem of 1969 :
This generalisation attributes hidden variables not only to the particles, but also to the measurment devices. For this purpose, the result A, function of the hidden variable lambda, and of the angle alpha, with the value -1 or +1, is replaced by the average value of A, function of alpha and lambda, on all hidden variables of the measurment device, and we start with
|average of A| <= 1. (respectively for B...)

Violation of Bell's inequality in any experiment has two possible explanations, not just one.
1) That Bell's inequality is a correct representation of local reality and the experiment is either not real or not local or both
2) That Bell's inequality is not a correct representation of local reality.

Now for some reason, Bell's followers ALWAYS gravitate towards (1). Do you agree that (2) is also a possibility and MUST be considered together with (1) when interpreting the results of these experiments? Please, I need a specific answer to this question.

I myself agree, but case 2 deals with what we do, while case 1 deals with what we get.

In De Raedt's simulation, Cxy is not the coincidence rate defined in Bell's theorem. That's how Bell's inequality does not represents what's going on in the simulation.
If the simulation is a good representation of reality, then the experiment can be modified so as to make W big enough compared to |t(n,1) - t(n,2)| in equation 3, so that the Heaviside function is always equal to 1, and Cxy tends to Bell's definition of the measurments product.
This way, we get back the experiment in adequation with Bell's theorem (case 2 is discarded), and we can test local determinism.

Another, sad, example : Joy Christian's use of Clifford algebra to prove Bell wrong ( http://arxiv.org/abs/quant-ph/0703179 ). Christian uses the half spin model, where Bell's theorem is applied setting spin down = -1, and spin up = +1.
He starts from the hypothesis that spin down and spin up are not real numbers, but numbers from Clifford algebra. He then shows that S can be equal to more than 2.

Since Bell's theorem says nothing else than if the possible results are -1 or 1, then S<=2, Christian's result is trivial and useless !

 

[mn4j]

That's wrong: how are theories judged correct? There is no such standard. Theories can have experimental support, and theories can make predictions that can be tested. And that is how they are judged. Correctness implies black and white, right or wrong. Theories can be better or worse depending on their application. But I cannot meaningfully say a theory is correct.

As to technology preceding theory: that makes no sense at all. Sometimes it does, sometimes it doesn't. There is no historical absolute on this. So again, meaningless.

I guess then you believe the system of epicycles is an accurate representation of the solar system and the motion of the planets!

 

[mn4j]

What on Earth is this second option supposed to mean at all? "Bell's inequality is not a representation of local reality"? Eh? I guess that what you mean here is that BLR is not LR. But it's really a pain to guess what you meant all the time.

If you have thought it through clearly enough you will know what the second option means. Let me put it to you in layman terms.

A man was depressed to the point he believed he was dead. No matter the efforts of his family he kept saying he was dead. A smart doctor tried to convince him that dead men do not bleed. After a significant effort he accepted. But at that moment, the doctor pierced him with a needle and he started bleeding. Can you guess what his next statement was? The doctor had hoped he would say "I am alive". Instead he said "Oops, I guess dead men bleed afterall".

The violation of Bell's inequality only proves that that the assumptions used in deriving the inequality do not apply to the experiment in question. Do you agree? Please give me a specific answer to this.

Those assumptions include assumptions about the way probabilities of local realist variables are supposed to be calculated. So in effect, Bell has an untested presentation of how local realist theories are supposed to behave. Yet when the inequalities are violated, instead of re-evaluating those assumptions, Bell proponents screem "I guess dead mean bleed after all".

Now, it's clear that the *MAIN POINT* is that you think there are LR theories that are not BLR. And you think that de Raedt's model is an example. I don't see why it's not BLR, I think it's absolutely BLR, and I think that I never saw any LR-but-not-BLR suggestion. And without an example I won't believe that that's possible.

I already mentioned why this is not a constructive criticism. I also explained in my previous post to you why de Raedt's mode is not accounted for by Bell. The article I presented by a pro-Bellist clearly states that Bell's model does not account for models like de Raedt's which have memory effects, notwithstanding the conclusion of that paper. Also your claim that you never saw any suggestion that Bell's representation of LR was not exhaustive is surprising because it is numerous in the literature. This thread was started by one such, Hess has presented a few, Joy Christian has presented a few. Are you serious?

Well, my answer is simple: it does not violate the inequality. The inequality "seems" to be violated in the particular experimental setup because the certain post-selection procedure is applied. It's possible to create correlation by post-selecting, that's what this whole coincidence loophole is about!

What experiment setup, it is a simulation. What aspect of the simulation do you claim deviates from how real experiments are actually performed.

Thanks for giving this link, it's actually interesting. I don't see though how it proves your point.

Do you agree that according to this article, Bell's theory does not account for models with memory effects. The authors state as much even though they end up dismissing it's importance. At least they were honest to admit that Bell's theory does not account for such local realist theories, which you apparently are still unwilling to do.

Authors clearly write that "memory loophole" that they're describing can be avoided in experiment. If it's avoided along with other loopholes -- goodbye LR.

That is beside the point. Do they or do they not state that Bell's model of LR does not apply to situations in which there are memory effects? Please answer this question.

Yes, I meant exactly this: not all photons result in a click. I don't have an evidence, but it could be obtained. I described two experiments that could check this model.

You don't have evidence, yet you are ready and willing to proclaim proudly that de Raedt's model is wrong on this basis? Isn't it more prudent to wait until you have obtained such evidence before you make such claims?

Take a look at the second. De Raedt says that if the screen is moved back and forth, the interference picture will get smeared. If this experiment is done and interference is NOT smeared, then de Raedt himself said that he would "retire", which I guess means that he will admit that his models are totally wrong and give up. And what would you say in this case?

Do you believe, the interference will get smeared if the slits are moved back and forth? What about the source?

 

[DrChinese]

I guess then you believe the system of epicycles is an accurate representation of the solar system and the motion of the planets!

The map is not the territory, my friend. Theory is always a model (map). And some are better than others.

 

[kobak]

Hello again, mn4j,
I suggest that if we continue this discussion at all, let's try to concentrate on the most important points only and also try avoid nitpicking each other (like what "scientific consensus" really means etc.). I'm quite sure that we won't reach an agreement, but we can at least pinpoint our disagreements.

The violation of Bell's inequality only proves that that the assumptions used in deriving the inequality do not apply to the experiment in question. Do you agree? Please give me a specific answer to this.

Yes, certainly.

Those assumptions include assumptions about the way probabilities of local realist variables are supposed to be calculated. So in effect, Bell has an untested presentation of how local realist theories are supposed to behave.

Well, let me put it a bit differently. I've been always repeating here that "local realism" is not a well-defined term. So strictly speaking you're right: it might not be fully correct to say (without any additional clarifications) that Bell's theorem proves that all LR theories should obey Bell's inequality. I hope you'll be happy that I agree with you here.

However, here's my main point: Bell derives his technical assumption about probabilities distribution by providing some particular *physical* intuition. This technical assumption that he uses is certainly always true and absolutely uncontroversial in all areas of classical (meaning non-quantum) physics. It's just the plain fact, that in all classical physics the outcome of Bob's experiment can never be statistically dependent on Alice's choice of experimental setup etc., so Bell's assumption holds. So let me drop the issue of "local realism" and make the following claim instead: Bell's theorem shows that *assuming "classicality"* -- his inequality has to be true.

Do you agree to such a statement? Note, that even if de Raedt model turns out to (a) be not BLR, (b) violate Bell's inequalities, (c) be just right (I still strongly disagree that it's possible, but even if it's like that), -- then this is certainly not a "classical" model. In classical physics apparata do not learn. The same goes for Christian's models: if they are right, then ok, spin measurements form a Clifford algebra (whatever this means), and this is again certainly not a "classical" model.

So, to recapitulate: do you agree that Bell's technical assumptions about correlations are completely well motivated, if we change the assumption of "local realism" to assumption of "classicality"? I very much hope that you will agree to that.

---------

Now, except of this, I see two main issues. First: I claim that de Raedt's model is BLR (and hence has to obey Bell's inequalities, and hence will not be able to hold anymore, after a loophole-free violation of inequalities is observed). You're saying that his model is not BLR, and your argument is that it's even stated in the Darrett-Popescu article. Well, I have to read it more carefully to answer you here. I will try to find the time for that and get back then, that's important.

Second point is that you also say that de Raedt model is not BLR because it violates Bell's inequalities. Here I disagree strongly, and I think that this shows that you don't really understand what a "coincidence loophole" is. Here's again, how I see it: 1. de Raedt's simulation does not deviate from real experiment of Weihs et al (you asked me, how it deviated; well, it doesn't). 2. The coincidence loophole (which this experiment did not avoid) means that it's possible to explain the apparent Bell's inequality violation by the fact that events are post-selected, and because of this post-selection the correlation is created out of nothing. 3. This is exactly what de Raedt is exploiting. 4. Bottomline of this analysis: de Raedt's model is BLR, it obeys Bell's inequalities, but in the non-perfect loopholed experiment it can LOOK like it violates them. This is the view expressed here: http://arxiv.org/abs/quant-ph/0703120 (see also http://arxiv.org/abs/quant-ph/0312035 about coincidence loophole). Do you understand this argumentation? You may disagree (please tell where exactly), but do you understand it?

Let me also ask for a clarification of your point of view. Do you think that Bell's inequalities are in reality NOT violated (and all experimental violations are only due to loopholes)? Or do you think that his inequalities in reality ARE violated (so that even ideal perfect experiment will find violations), but these violations can be explained by some LR theory which is not accounted by Bell's theorem? I guess that yours is the latter opinion. Which means that even a perfect loophole-free experiment will not prove anything to you, right? Why are you then arguing about loopholes and this "prisoners who can get out in different ways" at all?

---------

Finally, about double-slit paper.

You don't have evidence, yet you are ready and willing to proclaim proudly that de Raedt's model is wrong on this basis? Isn't it more prudent to wait until you have obtained such evidence before you make such claims?

It is. I don't proclaim that his model is wrong on this basis, I'm proposing a bet (let's put it that way). Imagine this experiment is done exactly as de Raedt himself proposed it (screen is jittered from left to right parallel to itself). Question: what will happen? My bet: interference pattern doesn't change. "de Raedt's" bet: interference pattern gets smeared, because "detectors" on the screen won't have enough time to "learn". Your bet?

And additionally: imagine that experiment is made and I win. What would that mean? I think that de Raedt thinks that it will prove his model false, and he certainly does not believe that this outcome is possible AT ALL. What do you think?

Please don't ask questions about different experimental setups, I'm interested only in this one, that is defined absolutely precisely.

 

[sirchasm]

A comment on "the map is not the territory".
I believe this implies we can only simulate "territory" as in QM simulations, fliud-dynamics on supercomputers. supernova and nuclear weapons simulations etc.

So the question has to be: when is a simulation 'exact'? And can we simulate the territory = construct a map, that is indistinguishable = identical to "the territory"?

 

[mn4j]

The map is not the territory, my friend. Theory is always a model (map). And some are better than others.

Yes you are right, all theories are valid , everything is relative, the map of China is a valid map of the US, just worse than the US map and the Earth is the center of the solar system, depending on your perspective.

 

[DrChinese]

So the question has to be: when is a simulation 'exact'? And can we simulate the territory = construct a map, that is indistinguishable = identical to "the territory"?

It is impossible, in principle, for any map to precisely model a territory other than for a limited (by assumption) scope. (The only way is if the map *IS* the territory, in which case it really doesn't qualify as a map anymore.) The reason I bring this up is that our natural desire is to use a map (i.e. a model) as a convenience. When you use a map, you assume it is accurate enough to be useful for your purposes. But most people know a map is a model; yet they have trouble seeing a theory as a model of reality too. Yet it is, and this is not merely a philosophical issue. As you can see from the discussion, some people think their model is "true" or "correct". Well, a map can be more useful or less useful (as in a relative way) but I don't see how any map can be absolutely and finally "true".

Take gravity, as an example: the acceleration due to gravity on Earth is about 9.8 meters per second. And yet there are only a few objects on the planet that are actually accelerating (relative to the earth) at that rate. Most are at rest or moving according to other forces acting on the object. So obviously, no theory of gravity can describe the movement of objects on earth. You must instead expand your description to include numerous other variables on a case by case basis.

...Which defeats the point of our original map, and shows it to be absolutely wrong - if we insist on calling the map itself absolutely correct. If we acknowledge it as only a useful tool, the problem disappears. That is why I believe it is unfair to criticize QM as a tool. Because as a tool, it is useful and fulfills the reasonable demands we place on it. Only when someone tries to ask if it is "correct" does a problem arise. Instead, I think we need only ask if a better tool can be found. EPR asked if a more complete specification of a quantum system was possible, and they believed it was. But the subsequent evidence (Bell+Aspect et al) is that it is not. But I do not believe that makes QM true, it just means it is a good - or perhaps best - map.

 

[DrChinese]

Yes you are right, all theories are valid , everything is relative, the map of China is a valid map of the US, just worse than the US map and the Earth is the center of the solar system, depending on your perspective.

Sorry, didn't mean to divert you from your distinctly more interesting discussion with kobak. But I think your statement pretty well proves my point of what happens when people think their model IS reality. They freak out because they find out they are not in Kansas any more. I will bow out for a while on this thread and let you continue. Later,

 

[mn4j]

Well, let me put it a bit differently. I've been always repeating here that "local realism" is not a well-defined term. So strictly speaking you're right: it might not be fully correct to say (without any additional clarifications) that Bell's theorem proves that all LR theories should obey Bell's inequality. I hope you'll be happy that I agree with you here.

Yes I'm happy, thank you.

However, here's my main point: Bell derives his technical assumption about probabilities distribution by providing some particular *physical* intuition. This technical assumption that he uses is certainly always true and absolutely uncontroversial in all areas of classical (meaning non-quantum) physics.

And here is my main point: The above statement is False for the following reasons:
1) Bell's particular *physical* intuition does not account for the most interesting class of local hidden variables, the types Einstein and Schrödinger would have liked to see.
2) The technical assumptions he uses are not always true, for reasons I have explained here. The effect is that this introduces further hidden assumptions -- at the very least, the assumption that those technical assumptions are always true for local hidden variables. Without independent validation of this assumption, the possibility that this assumption is false will never go away, even if 99% of the scientists believe it.
3) Those technical assumptions are not uncontroversial in all areas of classical physics. In fact violation of Bell's inequalities is not limited to quantum systems. Take a look at de Raedt's recent paper for an example in which there is violation of Bell's inequality for a voting game with three human players.

It's just the plain fact, that in all classical physics the outcome of Bob's experiment can never be statistically dependent on Alice's choice of experimental setup etc., so Bell's assumption holds. So let me drop the issue of "local realism" and make the following claim instead: Bell's theorem shows that *assuming "classicality"* -- his inequality has to be true.

This is false. I have already explained in this thread that any two time varying harmonic systems are correlated and as such their probabilities are not disjoint. Unless you want to claim that two pendulums or clocks on opposite sites of the globe are not classical.

Note, that even if de Raedt model turns out to (a) be not BLR, (b) violate Bell's inequalities, (c) be just right (I still strongly disagree that it's possible, but even if it's like that), -- then this is certainly not a "classical" model. In classical physics apparata do not learn.

This is false. Let's take two classical systems
1) Heat transfer in a gas: How does the heat go from one end to another? The molecules learn the velocity of the "hotter" molecules they collide with, and transfer this "knowledge" to other molecules they themselves collide with. This is exactly what a DLM is.
2) A billiard ball. The stationary ball, on collision with the moving ball, learns the momentum of the on-coming ball. That is a DLM.

DLMs are classical!

So, to recapitulate: do you agree that Bell's technical assumptions about correlations are completely well motivated, if we change the assumption of "local realism" to assumption of "classicality"? I very much hope that you will agree to that.

Sorry, I can not agree that. Because as I have explained repeatedly, I know of systems for which Bell's inequality does not apply, which can not be classified as non-classical. But also because I am not quite sure what you mean by classical.

Now, except of this, I see two main issues. First: I claim that de Raedt's model is BLR (and hence has to obey Bell's inequalities, and hence will not be able to hold anymore, after a loophole-free violation of inequalities is observed).

So then, even if you believe it is BLR, since de Raedt's model is also a simulation, not much different from a theoretical derivation, the fact that it violates Bell's inequalities either means Bell's mathematics is wrong, or de Raedt's mathematics is wrong. So again the issue boils down to whether "a bleeding man is alive" or "dead men bleed".

I will reply to your second point in a separate post as this is getting too long.

 

[mn4j]

Second point is that you also say that de Raedt model is not BLR because it violates Bell's inequalities. Here I disagree strongly, and I think that this shows that you don't really understand what a "coincidence loophole" is.

I think maybe you are the one who is not quite sure what it means. Do you deny the fact that de Raedt's model reproduces the QM result? Doesn't that mean it also violates the inequality. Please answer this question.

Here's again, how I see it: 1. de Raedt's simulation does not deviate from real experiment of Weihs et al (you asked me, how it deviated; well, it doesn't).

Does the real experiment deviate from Bell's inequality? Does the real experiment agree with QM? Does QM violate also violate the coincidence time loophole? (see http://arxiv.org/abs/0801.1776)

2. The coincidence loophole (which this experiment did not avoid) means that it's possible to explain the apparent Bell's inequality violation by the fact that events are post-selected, and because of this post-selection the correlation is created out of nothing.

Again you focus only on the "dead men bleed" part and completely ignore the fact that the coincidence time loophole can also mean Bell's inequality does not model the behaviour of all real local systems.

3. This is exactly what de Raedt is exploiting. 4. Bottomline of this analysis: de Raedt's model is BLR, it obeys Bell's inequalities but in the non-perfect loopholed experiment it can LOOK like it violates them. This is the view expressed here: http://arxiv.org/abs/quant-ph/0703120 (see also http://arxiv.org/abs/quant-ph/0312035 about coincidence loophole). Do you understand this argumentation? You may disagree (please tell where exactly), but do you understand it?

http://arxiv.org/abs/quant-ph/0703120 has been refuted by de Raedt (see http://arxiv.org/abs/0706.2957).
The bottom line is this: de Raedt's model satisfies the Einstein's conditions of local causality and exactly reproduce the single particle and two-particle expectation values of the singlet state.

Let me also ask for a clarification of your point of view. Do you think that Bell's inequalities are in reality NOT violated (and all experimental violations are only due to loopholes)? Or do you think that his inequalities in reality ARE violated (so that even ideal perfect experiment will find violations), but these violations can be explained by some LR theory which is not accounted by Bell's theorem?

My viewpoint is that it is possible to find a model that satisfies the Einstein's conditions of local causality and exactly reproduce the expectation values of the singlet state, contrary to Bell's claims. My viewpoint is that constructing Bell's inequalities in a manner which accounts for all possible real experiments like the ones performed so far will result in inequalities that are never violated. My viewpoint is that no experiment has ever been performed exactly as Bell modeled in his equations. Therefore Bell's theorem is currently an untested theorem, and when such such an experiment is performed, it will not violated the inequalities.

Which means that even a perfect loophole-free experiment will not prove anything to you, right?

Show me a loophole free experiment which violates Bell's inequalities and I will concede. My view is there will never be a loophole free experiment because the problem is not with the experiments but with the inequality. If a theory is so restrictive in scope that it has taken many talented experimentalists several decades to test it in vain, then maybe the answer is not that "dead men bleed afterall" or rather, that "we need more perfect experiments". The answer is that "the bleeding man is alive" or rather, that Bell's inequalities do not accurately represent real experiments that can be performed.

I don't proclaim that his model is wrong on this basis, I'm proposing a bet (let's put it that way). Imagine this experiment is done exactly as de Raedt himself proposed it (screen is jittered from left to right parallel to itself). Question: what will happen? My bet: interference pattern doesn't change. "de Raedt's" bet: interference pattern gets smeared, because "detectors" on the screen won't have enough time to "learn". Your bet?

Isn't it common sense that a moving camera takes smeared images? In case you did not know, this experiment has been performed many times over by lay people and you lost the bet already.

 

[kobak]

Well, I fear that I don't see how this discussion can lead to anything more. From what you've just said, I'm now sure that you don't understand what a coincidence time loophole is. This is crucial, so there's unfortunately no point in this discussion anymore.

I will briefly react to some points you made.

And here is my main point: The above statement is False for the following reasons:
1) Bell's particular *physical* intuition does not account for the most interesting class of local hidden variables <...>
2) The technical assumptions he uses are not always true, for reasons I have explained here. The effect is that this introduces further hidden assumptions -- at the very least, the assumption that those technical assumptions are always true for local hidden variables <...>
3) Those technical assumptions are not uncontroversial in all areas of classical physics. In fact violation of Bell's inequalities is not limited to quantum systems. Take a look at de Raedt's recent paper for an example in which there is violation of Bell's inequality for a voting game with three human players.

My statement was this: "in classical physics Bell's technical assumption was always uncontroversial and generally considered true". You're saying that this is false and give as an example some theories of hidden variables. I'm sorry, I was talking about CLASSICAL physics. So I disregard your points (1) and (2) here. The only meaningful response is your point (3). Well, I guess I should take a look on this de Raedt's example. But what I did already see, is the "Bernoulli urn" example from Jaynes, also repeated by de Raedt, -- and this example totally and completely misses the point. So I'm quite fed up by his examples.

This is false. I have already explained in this thread that any two time varying harmonic systems are correlated and as such their probabilities are not disjoint. Unless you want to claim that two pendulums or clocks on opposite sites of the globe are not classical.

I have seen your example with pendula. I don't see how this relates to the situation when two space-like separated measurements are performed and one result is statistically dependent on the choice of other experiment. I'm talking about this very situation (as described by EPR and Bell), not about some abstract correlation between something.

I think maybe you are the one who is not quite sure what it means. Do you deny the fact that de Raedt's model reproduces the QM result? Doesn't that mean it also violates the inequality. Please answer this question.

This is exactly the point where it becomes clear that you don't properly understand this loophole issue. de Raedt's model reproduces the QM result for THIS PARTICULAR experiment (Weihs et al.) which has loopholes. Because of this experimental flaws, it's possible for a BLR theory to give the impression that it violates Bell's inequalities. In the loophole-free experiment de Raedt's model will obey Bell's inequalities, unlike QM.

I really can't express this clearer (without giving technical arguments, that are anyway contained in the articles I cited).

http://arxiv.org/abs/quant-ph/0703120 has been refuted by de Raedt (see http://arxiv.org/abs/0706.2957).

Sure, I've seen this. I think his reply misses the point completely. Let me ask you something: did you actually read this critique of de Raedt and his reply? Or are you saying that it has been successfully refuted just because there exists an article claiming to be a refutation? I'm just curious.

Isn't it common sense that a moving camera takes smeared images? In case you did not know, this experiment has been performed many times over by lay people and you lost the bet already.

It's amazing how you keep avoiding answering my simple question for several postings already. I asked you what do you think about the outcome of double-slit interference when the screen is moved from left to right, and you're telling me something about cameras.

What on Earth has it to do with my question? If I project a movie on a white (ideal) screen with a projector and then start moving the screen from left to right with any frequency I want, the picture won't change, and all the viewers can still enjoy the movie. Now we're talking about double-slit interferometer instead of beamer. Screen is moved. Question: will the interference picture get smeared? If you say "yes" (like de Raedt does), here's the second question: assume, just assume for the sake of argument, that it's found NOT to change, exactly like the movie in the example above. What would be your conclusion? I remind here, that de Raedt said that in this case he would "retire".

I'm wondering whether you are again going to skip answering these two direct questions.

 

[mn4j]

My statement was this: "in classical physics Bell's technical assumption was always uncontroversial and generally considered true". You're saying that this is false and give as an example some theories of hidden variables. I'm sorry, I was talking about CLASSICAL physics. So I disregard your points (1) and (2) here. The only meaningful response is your point (3). Well, I guess I should take a look on this de Raedt's example. But what I did already see, is the "Bernoulli urn" example from Jaynes, also repeated by de Raedt, -- and this example totally and completely misses the point. So I'm quite fed up by his examples.

You did not define what you mean by classical physics.

I have seen your example with pendula. I don't see how this relates to the situation when two space-like separated measurements are performed and one result is statistically dependent on the choice of other experiment. I'm talking about this very situation (as described by EPR and Bell), not about some abstract correlation between something.

Is it unclassical for photons and electrons which make up all experimental apparatus to exhibit time-varying harmonic oscillation? I take it you do not understand the difference between logical dependence and physical causation. You see, when you calculate probabilities of systems which are known to be correlated, like harmonic systems, you MUST consider them to be logically dependent even if there is no physical effect transferred between them, otherwise you get paradoxical results.

This is exactly the point where it becomes clear that you don't properly understand this loophole issue. de Raedt's model reproduces the QM result for THIS PARTICULAR experiment (Weihs et al.) which has loopholes. Because of this experimental flaws, it's possible for a BLR theory to give the impression that it violates Bell's inequalities. In the loophole-free experiment de Raedt's model will obey Bell's inequalities, unlike QM.

You seem to have stuck on this one loophole and you can't get passed it. Your statement is wrong. For all your claims about talking to de Raedt, you have no idea what his model is all about evidently. In case you did not know, de Raedt's model agrees with QM in single-photon beam-splitter and Mach-Zehnder interferometer experiments, wheeler’s delayed choice experiment, quantum eraser, EPRB experiments with photons, EPRB experiments with non-orthogonal detection planes etc.

You did not tell me if you believe the QM formalism also suffers from the coincidence time loop-hole. I wonder why?

Sure, I've seen this. I think his reply misses the point completely. Let me ask you something: did you actually read this critique of de Raedt and his reply? Or are you saying that it has been successfully refuted just because there exists an article claiming to be a refutation? I'm just curious.

I have read every article I point you to. Have you read the ones you point me to? Did you bother reading de Raedt's reply? What exactly do you believe misses the point. Spell it out and I will explain why it is you who missed the point. We can go into technical detail if you prefer.

It's amazing how you keep avoiding answering my simple question for several postings already. I asked you what do you think about the outcome of double-slit interference when the screen is moved from left to right, and you're telling me something about cameras.

The answer is so blindingly obvious I did not expect that you were serious. De Raedt gave you the answer even. The pattern gets smeared! It is not an experiment you need to bother doing. It has been done many times! Do I really need to answer the second question? If you think I'm wrong, go do the experiment and bring your results, then we can talk.

What on Earth has it to do with my question? If I project a movie on a white (ideal) screen with a projector and then start moving the screen from left to right with any frequency I want, the picture won't change

That is a very naive look at the situation. You can't be serious? A movie screen is not a detector. A photographic film is. Try projecting a still image on a photographic film while moving the film from left to right and then develop the film and see if it is not smeared. Do you seriously believe the same will not happen if the detector in front of a double-slit is jiggled? Isn't the interference image whatever is recorded on the detector. Or maybe let's jiggle your head real fast, while you watch, since your eyes are the real detector in this case. Are you telling me you will enjoy the same quality of movie as an unjiggled pair of eyes? You can perform this experiment right now. Jiggle your head while you read this page and tell me whether the image does not get smeared.

I'm wondering whether you are again going to skip answering these two direct questions.

I can point to umpteen questions of mine you have not answered but then again I'm not keeping score.

Are you ready to concede that classical systems DO learn just like in de Raedt's model? Are you ready to concede that Bell's model does not account for systems which learn, like de Raedt's?

 

[kobak]

You did not define what you mean by classical physics.

That's easy: let's just say, that by classical physics in this case I mean all physics known before 1920. To make this comment self-contained, I repeat my claim: in classical physics Bell's technical assumption (that you and Jaynes and de Raedt keep saying is unjustified) is always true. You disagree. Well, it seems that to refute my claim one example would suffice. This example must be of the following (just to spell it out): two space-like separated experiments are done and the result of Alice's experiment "A" is NOT statistically independent from Bob's choice of experimental setup "b" or his outcome "B".

Maybe I miss something here, but I don't see how your harmonic oscillators can provide a counterexample to that. Please explain, if you think it can. And here's another consideration: if it were THAT easy to provide a counterexample to Bell (by just taking two harmonic oscillators), then why would all this story about deterministic learning machines be necessary? It seems to me that you make an oversimplification here. It's impossible to replicate QM correlations by just considering two oscillators or clocks, is it?

I take it you do not understand the difference between logical dependence and physical causation.

Just a short note: I think I do. It also seems to me that "logical dependence" is a term that you took from Jaynes (and de Raedt), because it's never being used in modern probability/statistics treatments. The precisely defined term that is usually used is "statistical dependence". Try googling this term, and your one. "Logical dependence" is used only in mathematical logic, but that's different.

You seem to have stuck on this one loophole and you can't get passed it.

Well, I'm sorry, but I believe that this is the most important and crucial point here.

You did not tell me if you believe the QM formalism also suffers from the coincidence time loop-hole. I wonder why?

Because I don't understand what your question means! How can a "formalism" suffer from a "loophole"? I think that this question gives another indication that you fail to understand the meaning of this loophole issue.

Let me give an analogy (it will be a rather silly one). Imagine we're trying to prove general relativity by observing gravitational waves. The opposing theory is Newtonian gravity, where there's no waves. So it the waves are observed, Newtonian theory is proved to be false. The experiment is done and experimental setup for some reason has to be located on the surface of the ocean. The gravitational waves are indeed observed. It may seem that GR is proven, but there's a subtlety: the whole apparatus was located in water and there were waves in water, so in principle it's possible to explain the apparent gravitational waves that were observed by just some influence from the water waves. So folks that don't believe in GR take this view. This experimental problem is called "water loophole" and experimenters are working hard to avoid it putting the setup on a hard ground, but they didn't succeed so far.

To spell it out: GR corresponds to QM, gravitational waves to the violation of Bell's inequalities, water loophole to coincidence-time loophole, explanation of how this faulty experiment can result in apparent detection of gravitational waves to de Raedt's explanation of how the faulty experiments can result in apparent violation of Bell's inequalities.

And now you come and ask, whether "the QM formalism also suffers from the coincidence time loop-hole". Analogy: does the general relativity suffer from the water loophole? This question just doesn't make any sense to me.

I have read every article I point you to. Have you read the ones you point me to? Did you bother reading de Raedt's reply? What exactly do you believe misses the point. Spell it out and I will explain why it is you who missed the point. We can go into technical detail if you prefer.

OK, I'm sorry for suspecting that you didn't read them. Yes, I also did. We could go into technical details, but it doesn't make any sense before we understand the issue of loophole in a similar way. Actually, when I read de Raedt's reply I was just lost several times. I think it misses the point, because it's unclear, and it is unclear because de Raedt apparently also does not understand this loophole issue. It's just that his reply doesn't really reply to what was said by Seevinck and Larsson. The critique is almost one page long and makes a clear point, while de Raedt writes a lengthy reply with all kind of beating around the bush.

Here's one particular example (maybe it's not the most important one. I don't remember any more, but I just have this written down anyway). Seevinck and Larsson say that in de Raedt's model \gamma is less then \gamma_0 which would be necessary to violate the inequality modified to take a loophole into account (and this equality is still violated by QM). de Raedt triumphally replies that they made a mistake in derivation, and then presents his own version of this derivation, which results in \gamma -> 0. Zero is clearly still less than \gamma_0, but he never comments on it.

The answer is so blindingly obvious I did not expect that you were serious. De Raedt gave you the answer even. The pattern gets smeared! <...> That is a very naive look at the situation. You can't be serious?

Oh, now I see that that's just a misunderstanding. Probably I didn't explain my experiment well enough, and now I checked and found that it's not described in arXiv version of the paper (http://arxiv.org/abs/0809.0616). It's just that when I asked de Raedt about this paper, he sent me a draft with a fuller version, and the experiment is described there. We're just talking about different experiments. You're right about yours, that's clear (and that "experiment" really is stupid and obvious, I agree).

Roughly speaking, what I meant is that screen is jittered, detection events are counted in individual detectors and then relocated with a computer program, that takes into account where the screen was at the moment of detection. Does it make more sense now? The crucial point is that de Raedt's detectors have first to learn before they start reproducing QM probabilities, and by jittering we prevent them from learning correctly (I quote de Raedt: "In other words, the experiment should address a time scale that is sufficiently short such that our detector models have not yet reached the stationary state").

He actually proposes a bit different setup, where only *single* detector is used, and it's slided back and forth along the "screen" line. The detection events are counted and then plotted versus the position of the detector at the moment of detection. If this detector is moved slowly (so that it reaches stationary state at every point) then the resulting plot will show the usual interference pattern. However if it's moved fast, then it would get smeared. Not because of this silly "moving camera" effect, but because detector doesn't have time to learn afresh at every single point.

Please tell me if this experiment now makes sense to you. If it does, then my questions remain the same. Do you think that interference pattern will change? What do you think is the prediction of the usual QM? What would you say if it actually doesn't change?

I can point to umpteen questions of mine you have not answered but then again I'm not keeping score. Are you ready to concede that classical systems DO learn just like in de Raedt's model? Are you ready to concede that Bell's model does not account for systems which learn, like de Raedt's?

First question: well, in the certain sense, yes. If the billiard ball getting kicked by another billiard ball counts for "learning", then yes. It's just that nobody in the times of classical physics would think that parts of the screen "learn" the phase of the incoming photons.

Second question: no, not yet. As I already said, here I should take a better look on the Popescu article. I didn't have time so far.

 

[mn4j]

Hi Kobak,
Sorry for the late response. I will try to be brief because every response just seems to be getting longer and longer. So I will not attempt to respond to every teeny-weenie point.

That's easy: let's just say, that by classical physics in this case I mean all physics known before 1920. To make this comment self-contained, I repeat my claim: in classical physics Bell's technical assumption (that you and Jaynes and de Raedt keep saying is unjustified) is always true. You disagree. Well, it seems that to refute my claim one example would suffice. This example must be of the following (just to spell it out): two space-like separated experiments are done and the result of Alice's experiment "A" is NOT statistically independent from Bob's choice of experimental setup "b" or his outcome "B".

I have given one example already in this thread. Bob and Alice each have a pendulum, and they are free to adjust the length of the string as they like. Coincidences are said to occur if both Bob and Alice's pendulum have swung to the same angular position at the same time. Bob's selection of the length is not ontologically dependent on Alice's length selection and they are free to select any length they want. In fact they are not even aware of the existence of each other until the experiment is complete and we are looking at the results. The results were recorded as a time tagged values of the deviation of the pendulum from the target position for a given duration after every change in settings.
1) Do you agree that these two experiments are local realist in the classical sense?
2) Do you agree that there will be a correlation between the results obtained by Bob and Alice?
3) If you agree to (2). Do you agree that this correlation or (statistical dependence as you call it) is not due to spooky-action at a distance or conspiracy?
4) Do you then agree that given a coincidence, if I (the external observer doing the calculations) were to know Bob's string length, the result Bob obtained and the result Alice obtained, I should be able to calculate a probability for Alice's string length which is higher than the maximum entropy value?

In case you don't understand the last point, let me explain: Given a fair coin, the maximum entropy probability for heads or tails is 0.5. This value tells you nothing about the ACTUAL result of the experiment you just performed by throwing a coin. However, if the coin throw was part of a bet in which you chose heads and I see you going of to buy a bear, I will be able to say the probability that the result was heads is higher than 0.5. Even though I did not see the actual result and I have no determinative proof that the coin used in the particular case was fair. As you can see from this example, probability is NOT JUST about frequencies of outcomes but about state of knowledge (Read up on Harold Jeffreys). Frequencies of outcomes is just a subset of the ways of updating the state of knowledge.

So then going back to point (4), you see that it is possible to obtain a probability for Alice's string length that is higher than the maximum entropy value, if I know Bob's string length. This is logical dependence and exists even for situations in which there is no communication or physical influence between Alice and Bob. If this doesn't make sense to you, then you can not even begin to understand my arguments in this thread, or Jayne's for that matter.

Maybe I miss something here, but I don't see how your harmonic oscillators can provide a counterexample to that.Please explain, if you think it can.

Consider the following harmonic oscillator equation.
<br /> y(t) = A sin(\omega t + \theta)<br />
in your favourite plotting package, generate a range of t values. Any range you choose. Using two random number generators, pick two sets of triplets (A, \omega, \theta)
use one set to calculate the corresponding y(t)_1 and the other set to calculate the corresponding y(t)_2 with the previously generate t values.
Plot y(t)_1 vs y(t)_2 and confirm that indeed there is a correlation between the two, no matter what values of (A, \omega, \theta) you used for each, however randomly you generated them.

In case you still think I did not understand what the coincidence time loophole is, let me point out to you that in this case, it has to do with which point in y(t)_1 is plotted against which point in y(t)_2. I won't go into much further detail than that here other than to say you can even introduce a constant offset (or time delay) between t values used in both cases without eliminating the correlation.

Because I don't understand what your question means! How can a "formalism" suffer from a "loophole"? I think that this question gives another indication that you fail to understand the meaning of this loophole issue.

Bell's inequality is a mathematical formulation also. And it does suffer from many loopholes. Your question tell's me you believe loopholes are problems in the experiments rather than Bell's inequalities. How come then that in every paper trying to address a loophole, they always derive new inequalities which account for the loophole cases? See the original paper about coincidence-time loophole which confirms this. The loophole is in Bell's inequality not the experiment and Quantum mechanics also makes assumptions about coincident events.

 

[kobak]

I will answer a bit later, but a quick question right away: are you going to answer my considerations about double-slit? Sorry for bothering if you were going to anyway. It's just that I don't want this topic to get lost.

And then from the technical side, there's also this \lambda issue.

 

[mn4j]

I will answer a bit later, but a quick question right away: are you going to answer my considerations about double-slit? Sorry for bothering if you were going to anyway. It's just that I don't want this topic to get lost.

And then from the technical side, there's also this \lambda issue.

I was in a hurry earlier so here is my response to your double-slit experiment. In de Raedt's model of the double slit experiment, the fact the detector learns is not crucial for the model. All that matters is that somewhere along the path of the photons, you have entities that learn. So just to be clear, it could be the slits that learn. He clearly explains this in one of the papers, I'm not sure which one but I can find it. I already mentioned in this thread, maybe you did not see it, that a good way to test this would be to use a different set of apparatus for each event. So again, I agree with de Raedt. If you use a different set of apparatus for each event you will not obtain the same results. You will not see a diffraction pattern if you combine the results later. Moving the detector alone while you have other DLM's in the path of the photons will not rule out de Raedt's model that DLM's are responsible for the result. The only way to rule out any learning is to use a completely different set of apparatus for each event.

The other test will be to use a single set of apparatus, but emit the photons one at a time at such long intervals between each other that the detector and slits are allowed to reach stationary state before the next event arrives. I bet you that there will be no interference pattern, even if everything is left in exactly the same position.

I am not sure what lambda issue you were referring to. If you are referring to this:

Here's one particular example (maybe it's not the most important one. I don't remember any more, but I just have this written down anyway). Seevinck and Larsson say that in de Raedt's model \gamma is less then \gamma_0 which would be necessary to violate the inequality modified to take a loophole into account (and this equality is still violated by QM). de Raedt triumphally replies that they made a mistake in derivation, and then presents his own version of this derivation, which results in \gamma -> 0. Zero is clearly still less than \gamma_0, but he never comments on it.

This is a mischaracterization of the response. Are you sure you read it? The short summary of the Seevinck and Larsson critique is that de Raedt's model can not reproduce the coincidences of many real experiments. De Raedt goes on to show in his reply how his model reproduces the coincidences. Nowhere in his reply did he derive \gamma \rightarrow 0. If you disagree, provide the page and equation number.

Here is what de Raedt says about this issue on page 3 of their short response which for some reason you claim it is too long (5 pages cf 3 pages for the critique):

By trying to put our work in the context of ”hidden
variable theories”, Seevinck and Larsson also made mis-
takes in elementary algebra. Seevinck and Larsson assume
that the probability of coincidences is given by the denom-
inator of Eq. (6) in Ref. [2] (see Appendix A of Ref. [1]),
from which they derive an expression for the probability of
coincidences \gamma (see Eq. (8) in Ref. [1]). However, Seevinck
and Larsson apparently overlooked the fact that in going
from Eq. (3) to Eq. (6) (see Ref. [2]), we take the limit
W/T0 = τ /T0 → 0 and let the number of events N in
both the numerator and denominator go to infinity.Al-
though the ratio remains finite,...

Emphasis added.

Also note that a majority of the Seevinck and Larsson comment is a strawman because they are mostly responding to claims De Raedt never made.

 

[kobak]

Hi mn4j, I'm going to reply you later (there are actually several things I'd like to think about before I answer), but there's a technical moment that I'd like to clarify right away.

Consider the following harmonic oscillator equation.
<br /> y(t) = A sin(\omega t + \theta)<br />
in your favourite plotting package, generate a range of t values. Any range you choose. Using two random number generators, pick two sets of triplets (A, \omega, \theta)
use one set to calculate the corresponding y(t)_1 and the other set to calculate the corresponding y(t)_2 with the previously generate t values.
Plot y(t)_1 vs y(t)_2 and confirm that indeed there is a correlation between the two, no matter what values of (A, \omega, \theta) you used for each, however randomly you generated them.

I don't need to wait until I come to the lab tomorrow and can use Matlab to see that what you are saying is just wrong (if I understood you correctly, which I'm not sure). Here's an example: take both amplitudes to be 1, both frequencies to be 1 as well, and phases to be 0 and \pi/2. Then we'll have: X = sin(t), Y = cos(t). The plot of this function in the XY plane is a circle, and the correlation between X and Y in this case is obviously 0.

It's also obvious how to get a perfect correlation of 1, just take X=Y=sin(t). By fiddling with the parameters it's possible to get any correlation coefficient between -1 and 1.

Since it's completely obvious, I'm not sure whether I understood you correctly. Could you clarify it please?

 

[mn4j]

I don't need to wait until I come to the lab tomorrow and can use Matlab to see that what you are saying is just wrong (if I understood you correctly, which I'm not sure). Here's an example: take both amplitudes to be 1, both frequencies to be 1 as well, and phases to be 0 and \pi/2. Then we'll have: X = sin(t), Y = cos(t). The plot of this function in the XY plane is a circle, and the correlation between X and Y in this case is obviously 0.

It's also obvious how to get a perfect correlation of 1, just take X=Y=sin(t). By fiddling with the parameters it's possible to get any correlation coefficient between -1 and 1.

Since it's completely obvious, I'm not sure whether I understood you correctly. Could you clarify it please?

I don't think you understand correlation correctly. The correlation coefficient is not a sufficient descriptor of correlation, that is why I say you should plot it and look at it. If you do not get a random distribution of points, it is correlated. The correlation coefficient is only useful when you are studying linear relationships, or you already know what function to use to convert your data such that any relationship if present will be linear.

 

[kobak]

I don't think you understand correlation correctly. The correlation coefficient is not a sufficient descriptor of correlation, that is why I say you should plot it and look at it. If you do not get a random distribution of points, it is correlated. The correlation coefficient is only useful when you are studying linear relationships, or you already know what function to use to convert your data such that any relationship if present will be linear.

I'm sorry that I'm again not continuing our main discussion (I've been rather busy during these days), but instead answering just this minor point. I would appreciate if we could use the standard terminology, otherwise it's hard to understand each other.

Correct me if I'm wrong, but when people in science say "correlation" it means linear correlation. For example, the wikipedia article on correlation (http://en.wikipedia.org/wiki/Correlation) begins with saying: "In probability theory and statistics, correlation (often measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. That is in contrast with the usage of the term in colloquial speech, denoting any relationship, not necessarily linear". It's clear that in my example X=cos(t) and Y=sin(t) are clearly _related_ because X^2+Y^2=1. But the correlation between them in the usual scientific meaning of "correlation" is 0. And with sufficiently complex nonlinear transformations anything can be transformed such, that it would be correlated with anything else.

I also note that in quantum singlet correlations (like in EPR) correlation is defined to be as the number of equal spin measurements minus the number of non-equal spin measurement over the total number of measurements. I.e. it's the normal linear correlation: results are fully correlated if they lie on a diagonal (where one axis meaning spin found at A, and the other -- spin found at B): both pluses, or both minuses.

All that probably doesn't undermine your main point at all, because our main issue is about statistical dependence. And it's possible that two values are statistically dependent, though correlation coefficient between them is 0. Like the already mentioned cos(t) and sin(t). In case you believe my understanding here is flawed, I would appreciate any corrections.

 

[mn4j]

I'm sorry that I'm again not continuing our main discussion (I've been rather busy during these days), but instead answering just this minor point. I would appreciate if we could use the standard terminology, otherwise it's hard to understand each other.

Correct me if I'm wrong, but when people in science say "correlation" it means linear correlation. For example, the wikipedia article on correlation (http://en.wikipedia.org/wiki/Correlation) begins with saying: "In probability theory and statistics, correlation (often measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. That is in contrast with the usage of the term in colloquial speech, denoting any relationship, not necessarily linear". It's clear that in my example X=cos(t) and Y=sin(t) are clearly _related_ because X^2+Y^2=1. But the correlation between them in the usual scientific meaning of "correlation" is 0. And with sufficiently complex nonlinear transformations anything can be transformed such, that it would be correlated with anything else.

I also note that in quantum singlet correlations (like in EPR) correlation is defined to be as the number of equal spin measurements minus the number of non-equal spin measurement over the total number of measurements. I.e. it's the normal linear correlation: results are fully correlated if they lie on a diagonal (where one axis meaning spin found at A, and the other -- spin found at B): both pluses, or both minuses.

Hello Kobak,
A correlation is said to exist between two 'variables' if their values change together in a manner different from what would be expected on the basis of chance. In other words, a relationship exists between both variables (cf. co-relation). Like I mentioned before The correlation coefficient is a statistic used ONLY for measuring linear relationships. A more general statistic of correlation is the NCIE or 'non-linear correlation information entropy'.

The standard terminology is to use "correlation coefficient" and NOT "correlation" when you mean correlation coefficient. It doesn't make much sense to say the correlation is zero. But it makes sense to say the correlation coefficient is zero, which again does not mean a correlation is absent.

All that probably doesn't undermine your main point at all, because our main issue is about statistical dependence. And it's possible that two values are statistically dependent, though correlation coefficient between them is 0. Like the already mentioned cos(t) and sin(t).

You are right, my main point does not depend on whether we agree on the definition of correlation.