Can grandpa understand the Bell's Theorem?

[miosim]

You've missed the point. As we've said several times Bell's theorem does not relate to any specific classical model, although you can use particular classical models to illustrate it. Bell's theorem proves that the results of QM cannot be reproduced by ANY local realistic model.

It the provided links below, please pinpoint (the best would be to copy and past) the formula or logical deduction that reflects the “local realism” as a physical property/characteristic/value etc., and that enters Bell's theorem as initial condition.

“BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST”
by Alain Aspect
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf

BERTLMANN'S SOCKS AND THE NATURE OF REALITY by J. Bell
http://hal.archives-ouvertes.fr/docs/00/22/06/88/PDF/ajp-jphyscol198142C202.pdf

 

[JesseM]

However, in my phenomenological model the entangled photons aren't perfectly correlated when no longer interact.

Then how do you explain the fact that, according to QM, if they are both measured with a polarizer at the same angle they are guaranteed to give the same results with probability 1? Do you imagine them "communicating" non-locally to coordinate their behaviors?

 

[miosim]

Then how do you explain the fact that, according to QM, if they are both measured with a polarizer at the same angle they are guaranteed to give the same results with probability 1? Do you imagine them "communicating" non-locally to coordinate their behaviors?

As I understand, with the polarizers at the same angle, there is no issue with EPR model to have the same 100% correlation as QM model, but without need of non-locality.

BERTLMANN'S SOCKS AND THE NATURE OF REALITY by J. Bell , page C2-49
http://hal.archives-ouvertes.fr/docs...198142C202.pdf

“… Thus the ad hoc model does what is required of it (i.e., reproduces
quantum mechanical results) only at (a - b) = 0, (a - b) = s/2 and
(a - b) = n, but not at intermediate angles...”

 

[JesseM]

As I understand, with the polarizers at the same angle, there is no issue with EPR model to have the same 100% correlation as QM model, but without need of non-locality.

That's true, but the whole reason there is "no issue" is that you are free to imagine that each particle just had identical predetermined results for each possible angle, so that no matter what angle was selected they would both give the same results. I'm asking how you would explain it in your model, since you said the photons "aren't perfectly correlated when no longer interact", which I took to mean they don't have a perfectly correlated set of predetermined results.

 

[Jonathan Scott]

It the provided links below, please pinpoint (the best would be to copy and past) the formula or logical deduction that reflects the “local realism” as a physical property/characteristic/value etc., and that enters Bell's theorem as initial condition.

“BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST”
by Alain Aspect
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf

BERTLMANN'S SOCKS AND THE NATURE OF REALITY by J. Bell
http://hal.archives-ouvertes.fr/docs/00/22/06/88/PDF/ajp-jphyscol198142C202.pdf

I'm not interested in rereading those papers (even though they were both very interesting first time).

"Local" is easy, in that in practice it effectively means not involving faster-than-light signals.

"Realism" is a bit more complicated, as we assume it every day and it's difficult to work out exactly what we are assuming. It's mostly to do with being able to assume that we could have done a different measurement on the same system and got some other result. One way of describing it is called "counterfactual definiteness (CFD)", which you can Google for more information.

 

[Jonathan Scott]

I should point out that if you've learned ordinary Newtonian physics and Special Relativity, then at first glance locality and realism both appear to be "obvious", and it's quite tricky to accept that QM could find a way round them.

The way to understand Bell's theorem is to learn it first in terms of that "obvious" model, then try to understand what would need to break to provide a way round it, which is far more difficult, especially when it comes to realism.

If you come up with any model involving waves, particles or whatever which are subject to the usual rules of locality and realism, Bell's theorem says it is simply impossible for it to reproduce the results of QM, regardless of the details.

Note that Bell's theorem does NOT rule out the possibility that QM has some underlying deterministic mechanism, but it does say that any such mechanism must either violate locality or realism (or possibly both).

 

[Philip000]

I also am a grandfather, and I’ve read of Bell’s theorem as follows.
A calcite crystal is set at a position similar to 12 o’clock and the spin polarity of photons directed at it gives a fixed set of readings.
The same crystal is turned to 1 o’clock and gives a different set of readings.

In a reversed world, and one that is handed, the same readings are taken of paired photons, and these agree with the set of readings taken in the non-reversed world.

Both the reversed and non reversed worlds are described as local realities or places where classical observations and measurements are made.

Bell’s theorem, as I have read of it, goes on to say that if the reading at 1 o’clock in both worlds show the same difference from readings taken at 12 o’clock in both worlds, then the differences added together represent an addition of local realities as defined by classical measurement.

It goes on to say that Bell’s inequality shows that this is not so, and that experimental results have shown that differences between the 1 o’clock measurements in both worlds are greater than that which is arrived at by adding both local measurements.

If the reversed and non reversed world’s 1 o’clock positions show 25% differences from the 12 o’clock position, then the total difference between the measurements taken in both worlds should be 25% + 25% = 50%.
However, test results show that the differences between the two 1 o’clock positions is actually 75%, hence Bell’s inequality.

Personally, I have a problem with this, because the 1 o’clock position in the reversed world represents the 11 o’clock position in the non reversed world, and if you try to compare the readings of a calcite taken at 11 o’clock with those taken at 1 o’clock in either world, you will find that there is a 75% difference.

This has nothing to do with the addition of localities, it is just a fact that as you turn a calcite crystal, so the set of results it gives change in line with the following.
If 12 0’clock is taken as the control set:
1 o’clock is 25% different from it,
2 o’clock is 75% different from it,
3 o’clock is 100% different from it.

The same would be true if any other clock position was taken as the control point, and the read out of differences to the control point is always different by the same percentages as the angles represented by moving away from it are altered, to finally arrive at a 90 degree angle from the control point, which is a totally different reading from that taken at the control point.

As I see it, if Bell’s addition of the reversed and non reversed worlds is taken as the 25% differences from a control point that is the same in both worlds, and if viewing the results of the differences between 1 o’clock positions in each world effectively becomes the difference between 11 o’clock and 1 o’clock in either of these worlds, then the sum of 25% + 25% = 50% is unrelated to the facts.

Unrelated is not unequal, it is just a totally different calculation, and if the explanation of Bell’s theorem I have been reading explains it properly, then as I see his inequality, this theorem is not based on the available classical facts, but on trying to say that 2 apples should equal a pear, when they obviously don’t.

Please understand that I am not a physicist, and that mathematical formulas leave me with a headache, however, from a simple commonsense point of view, and taken from the explanation I have read, it seems to me that the error in Bell’s theorem is not that of locality or classical measurement, but simply a problem that comes from not defining the control points of his measurements and the later experiments adequately.

Local reality, as a classical measurement, is always defined by a control point, and if you move the control point without noticing that you have done so, the result is an error of measurement and not an expression of quantum deep space or a yet to be defined non-local reality.

If my interpretation of Bells theorem is correct, then I claim grandfather rights over it, if it isn’t, then I claim a grandfather’s right to voice it based on the facts available to me.

 

[miosim]

That's true, but the whole reason there is "no issue" is that you are free to imagine that each particle just had identical predetermined results for each possible angle, so that no matter what angle was selected they would both give the same results. I'm asking how you would explain it in your model, since you said the photons "aren't perfectly correlated when no longer interact", which I took to mean they don't have a perfectly correlated set of predetermined results.

It is correct. In my model the polarization of correlated photons isn’t perfectly matched and I expect the difference is within uncertainty principle.
Therefore the correlation function of these photons is less than 100%.

I also expect that in my model correlated photons have different (within uncertainty principle) wavelength. I think that this can be tested by forcing correlated photons to interfere with each other after they passed respective polarizers.

 

[miosim]

I'm not interested in rereading those papers (even though they were both very interesting first time).

"Local" is easy, in that in practice it effectively means not involving faster-than-light signals.

"Realism" is a bit more complicated, as we assume it every day and it's difficult to work out exactly what we are assuming. It's mostly to do with being able to assume that we could have done a different measurement on the same system and got some other result. One way of describing it is called "counterfactual definiteness (CFD)", which you can Google for more information.

To understand the Bell’s theorem (as any other theorem) the initial condition need to be better understood; specifically why this theorem treats differently EPR and standard QM model. I would like to put this difference under “magnifying glass.”

It seams to me that the initial conditions for EPR model in Bell’s theorem are oversimplified to the level of Newtonian mechanics. The logic in Bell’s theorem leads to the correlation function that contradicts the classical Malus’ law. According to this law, the intensity of completely polarized light that passed polarizer is proportional to cos²θ (the same as for QM). If EPR photons aren’t in compliance with Malus’ law I need to know why. If EPR photons are in compliance with Malus’ law, it seems to me, that the Bell’s theorem should be thrown out of window.

 

[JesseM]

It is correct. In my model the polarization of correlated photons isn’t perfectly matched and I expect the difference is within uncertainty principle.
Therefore the correlation function of these photons is less than 100%.

The uncertainty principle doesn't suggest any limits to measurements of perfect correlation with the same polarizer setting, it only deals with incompatible observables like position and momentum. If you're saying the correlation function is less than 100% even under idealized experimental conditions (as opposed to it being just a practical issue), then your model disagrees with QM.

 

[miosim]

The uncertainty principle doesn't suggest any limits to measurements of perfect correlation with the same polarizer setting, it only deals with incompatible observables like position and momentum.

In my model uncertainty principle is also applicable to polarisation of photons (and probably to a range of other physical properties of subatomic particles).
However the uncertainty priniple in my model is different than Heisenberg’s unsertuntly priniple. My model accepts the existence of “hidden” variables and don’t impose the theoretical barrier studying these variables.

If you're saying the correlation function is less than 100% even under idealized experimental conditions (as opposed to it being just a practical issue), then your model disagrees with QM.

Indeed the correlation function in my model is less that 100% under idealized experimental conditions. However I expect that my model isn’t in a conflict with mathematical formalism of QM. I am not sure if the 100% correlation is derived from QM or it is just an expectation. At the same time my model is sharply contradicts with all interpretations of QM and replaces the existing head twisting QM theories with a reasonable and realistic description of physical reality.

 

[Jonathan Scott]

To understand the Bell’s theorem (as any other theorem) the initial condition need to be better understood; specifically why this theorem treats differently EPR and standard QM model. I would like to put this difference under “magnifying glass.”

It seams to me that the initial conditions for EPR model in Bell’s theorem are oversimplified to the level of Newtonian mechanics. The logic in Bell’s theorem leads to the correlation function that contradicts the classical Malus’ law. According to this law, the intensity of completely polarized light that passed polarizer is proportional to cos2θ (the same as for QM). If EPR photons aren’t in compliance with Malus’ law I need to know why. If EPR photons are in compliance with Malus’ law, it seems to me, that the Bell’s theorem should be thrown out of window.

Bell's Theorem has nothing to do with specific models. It basically says that if you measure the number of differences between set A and set B then between set A and set C then the number of differences between set B and set C cannot exceed the sum of the differences in the two separate cases, then points out that matching certain QM predictions requires violation of this inequality.

The pairs of photons in Aspect's experiments and similar comply with Malus' law, but in a non-classical way, in that if you assume one of the photons is observed in a pure state, then the results at the other end are as predicted by Malus' law, in exactly the same way as if a single photon was emitted from one device with a known polarization and observed at the other.

In contrast, classical physics would predict that the pair of photons would start off with polarization in some definite but unknown direction, and then that each of the photons would independently reproduce Malus' law relative to that original direction. This gives a much weaker correlation, which is typically of the form (1+x)/2 where x is the QM-predicted (and experimentally observed) correlation.

If you only change one observation device, it would be theoretically possible that the experiment happens to have been producing photons which are always in a pure state relative to the other device, in which case classical and QM predictions would match. If you change both observation devices separately then it is not possible for the experiment to emit photons which are in a pure state relative to one or another device all of the time unless there is some form of communication back from the observation devices to the experiment. Experiments have been done with very fast switching at both ends (with different frequencies) between different observation devices where the switches and observation devices are far enough from the experiment that even a light-speed signal could not communicate the current state, yet even in that case the experiments continued to match QM predictions.

 

[jed clampett]

The pairs of photons in Aspect's experiments and similar comply with Malus' law, but in a non-classical way, in that if you assume one of the photons is observed in a pure state, then the results at the other end are as predicted by Malus' law, in exactly the same way as if a single photon was emitted from one device with a known polarization and observed at the other.

In contrast, classical physics would predict that the pair of photons would start off with polarization in some definite but unknown direction, and then that each of the photons would independently reproduce Malus' law relative to that original direction. This gives a much weaker correlation, which is typically of the form (1+x)/2 where x is the QM-predicted (and experimentally observed) correlation.

This is pretty much the point I was making earlier when I said you get in trouble as soon as you find correlations close to 100%. You don't need to agonize over what's going on at 45 or 22.5 degrees. Jonathan Scott has expressed this more clearly than me. (Although interestingly enough, he still finds it useful to talk about what "classical physics would predict (for a) pair of photons", as compared to my use of the phrase "classical photons".)

If you only change one observation device, it would be theoretically possible that the experiment happens to have been producing photons which are always in a pure state relative to the other device, in which case classical and QM predictions would match. If you change both observation devices separately then it is not possible for the experiment to emit photons which are in a pure state relative to one or another device all of the time...

The predictions could match only if the source happened to be producing polarized pairs with the same orientation as the arbitrarily placed detectors. There is no physical reason this should happen in practice. Again, you can rule it out by rotating the source with respect to the detectors. If the correlation is 100% at all angles, you can't explain it by saying the photons simply started out with the same polarization.

 

[DrChinese]

...Indeed the correlation function in my model is less that 100% under idealized experimental conditions. However I expect that my model isn’t in a conflict with mathematical formalism of QM. I am not sure if the 100% correlation is derived from QM or it is just an expectation. At the same time my model is sharply contradicts with all interpretations of QM and replaces the existing head twisting QM theories with a reasonable and realistic description of physical reality...

Wow, in your world what is 1+1? I mean, you say it is local realistic but don't bother to show any evidence. You are making some pretty wild claims, when you obviously lack the basic understanding of the issues involved. Does it ever occur to you that your model is completely worthless and provides absolutely no useful predictions? I think you have a serious misunderstanding of theoretical and experimental science, and how they relate to each other.

You have strayed far from the point where you are asking questions. Now you are making more and more statements as if they are factual. Sorry, sir, they are not! Personal theories are not welcome here when presented in this manner. Cite evidence to support your ideas. Or ask a question that can be answered by someone with suitable knowledge. But the "head twisting" QM you mention has been around longer than you have and generations of physicists have used it with good effect. (Unless you were born before 1927.)

You might try doing your research BEFORE making the claim. It shocks me to see people wanting the credit before they doing the requisite work. Well, that might work around your friends but it doesn't work that way in science. (Oh, and please present that research elsewhere as it violates forum rules.)

P.S. The 100% correlation IS derived from theoretical predictions of QM and they have been experimentally verified to over a hundred standard deviations. Do you know what a standard deviation is? Or is that just another "head twisting" concept?

 

[DrChinese]

I really think this thread was misnamed. It should be named: "Posts from a grandpa who doesn't really want to learn anything about Bell, and would rather tell us his 'common sense' views on the subject."

To all the Grandpas (and grandmas and dads and moms and sons and daughters) out there: Try taking a little time to understand the argument BEFORE you reject it! If you don't understand the mathematical basis, that's fine, hey I don't understand a lot about biochemistry myself. But I think I know not to embarrass myself by pulling opinions out of the blue and posting them publicly.

Meanwhile, the Bell argument is pretty simple to follow if you will just sit down and work through it. The math is NOT hard at all! And the Bell logic works with pretty much any assumptions of local realism you would care to define. But you will need to put forth such a definition (or accept the standard ones, such as Einstein's).

a) QM: generally accepted and supported by tens of thousands of experiments with no significant modification to theory in the past 80 years.
b) QM+LR: generally rejected, per Bell, approaching 50 years.
c) If you want to keep LR, you will need to change QM somehow, in which case it will no longer match experiments! So it will be useless!
d) Or you can change LR so it is no longer LR per Bell. In which case no one really cares.

 

[miosim]

DrChinese ,

In the post #43 you urged me to attempt to construct a realistic model to see that this isn’t possible according to Bell’s theorem.
I probably should politely decline this proposition knowing that this may derail the topics of this thread. Sorry for that.
I promise to do not refer my model any more in this thread because my goal here isn’t presenting my controversial views but to gain a better understanding of the Bell’s theorem.

a) QM: generally accepted and supported by tens of thousands of experiments with no significant modification to theory in the past 80 years.
b) QM+LR: generally rejected, per Bell, approaching 50 years.

1). The Aristotle’s views were dominated for almost a 2000 of years.
2). The classical Newtonian mechanics was dominated for centuries and until the end of 19th century it was believed that the description of the physical world was practically completed.
I think that 1) and 2) cancel a) and b).

c). http://plato.stanford.edu/entries/qm-bohm/#com
“…In 1932 John von Neumann, one of the greatest mathematicians of the twentieth century, claimed to have mathematically proven that Einstein's dream, of a deterministic completion or reinterpretation of quantum theory, was mathematically impossible. This claim of von Neumann was almost universally accepted among physicists and philosophers of science….
But in 1952 an impossible happened… It was in papers by David Bohm that explicitly showed that Neumann was wrong (my wording). … Bohmian mechanics is, quite clearly, a counterexample to the claims of von Neumann, so something has to be wrong with von Neumann's argument. In fact, according to John Bell von Neumann's assumptions (about the relationships among the values of quantum observables that must be satisfied in a hidden-variables theory) are so unreasonable that the "the proof of von Neumann is not merely false but foolish!" Nonetheless, some physicists continue to rely on von Neumann's proof…”

Taking in account the history that led to Bell’s theorem and existing controversy (like FTL interactions) I can’t lightly accept the explanations that don’t have a sense to me regardless that they reflect the mainstream views. I want to understand it by my self.

Specifically, I would like to understand how “locality” , determinism” or any other characteristic related to EPR arguments enter the Bell’s theorem that eventually were rejected as impossible.
Using the provided links below, can anybody pinpoint (the best would be copy and past from inks below) the formula or logical deduction related to LR, determinism etc., that as the physical properties/characteristics enter Bell's theorem as initial condition.

BERTLMANN'S SOCKS AND THE NATURE OF REALITY by J. Bell
http://hal.archives-ouvertes.fr/docs...198142C202.pdf

In the Alain Aspect’s article “BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST”
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf



P.S.
a) I know what STD is. I have an engineering degree, but my background in QM and associated math are very shallow.

b) I apologize for the late respond. I am on a road this week, but should be able to respond in the evening.

 

[JesseM]

DrChinese ,

In the post #43 you urged me to attempt to construct a realistic model to see that this isn’t possible according to Bell’s theorem.
I probably should politely decline this proposition knowing that this may derail the topics of this thread. Sorry for that.

Do you understand that Bell's theorem isn't making any claims about what the correct theory in the real world is, it's just about the incompatibility of the theory of QM with local realism? So even if experiments turned out not to match the theory of QM, and experiments could be explained by a local realist model, this would have nothing to do with refuting Bell's theorem. DrChinese's challenge was specifically to try to construct a local realist model that agrees with all the predictions of QM, including the 100% correlation for entangled photons when the same polarizer angle is used.

Specifically, I would like to understand how “locality” , determinism” or any other characteristic related to EPR arguments enter the Bell’s theorem that eventually were rejected as impossible.
Using the provided links below, can anybody pinpoint (the best would be copy and past from inks below) the formula or logical deduction related to LR, determinism etc., that as the physical properties/characteristics enter Bell's theorem as initial condition.

BERTLMANN'S SOCKS AND THE NATURE OF REALITY by J. Bell
http://hal.archives-ouvertes.fr/docs...198142C202.pdf

In the Alain Aspect’s article “BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST”
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf

Your first link doesn't work, you must have copied and pasted the url from a post that included a "..." in the middle to shorten it, rather than copying it directly from the address bar on your browser. Anyway, personally I think the best paper of Bell's for understanding the physical issues is his paper "La nouvelle cuisine", most of which can be read on google books starting here (it can also be found in his book Speakable and Unspeakable in Quantum Mechanics), and which I summarized some major points of in [post=3248153]this post[/post]. The good thing about this paper is that it explicitly defines locality in terms of the idea that local facts in one region of spacetime should depend only on facts about the past light cone of that region (hopefully you know enough about relativity to be familiar with the idea of light cones?) As I mentioned in the post, the critical step where the locality assumption is invoked in the equations is on this page when he goes from equation 6.9.2 to equation 6.9.3.

edit: looks like the Bertlmann's Socks paper can be found here. In this case the equation where locality is invoked, analogous to equation 6.9.3 in "La nouvelle cuisine", is equation (11) on p. 15 of the pdf (and eq. 10 on the same page deals with an analogous situation involving heart attacks statistics in two cities). Similarly Aspect invokes locality to justify the idea that there are "supplementary parameters" (hidden variables) which predetermine the result for any given setting, that's how he gets equations (10) on p. 7. You never answered my question which I asked a few times earlier, do you or do you not understand why local realism demands that if there are 100% correlations whenever the same detector settings are chosen, and the choice of settings is random, that must imply that local parameters specific to each particle predetermined their results for each possible setting, even before the experimenters made their choice of settings?

 

[DrChinese]

DrChinese ,

[A] I promise to do not refer my model any more in this thread because my goal here isn’t presenting my controversial views but to gain a better understanding of the Bell’s theorem.


1). The Aristotle’s views were dominated for almost a 2000 of years.
2). The classical Newtonian mechanics was dominated for centuries and until the end of 19th century it was believed that the description of the physical world was practically completed.
I think that 1) and 2) cancel a) and b)...

[C] Taking in account the history that led to Bell’s theorem and existing controversy (like FTL interactions) I can’t lightly accept the explanations that don’t have a sense to me regardless that they reflect the mainstream views. I want to understand it by my self.

Specifically, I would like to understand how “locality” , determinism” or any other characteristic related to EPR arguments enter the Bell’s theorem that eventually were rejected as impossible.

[A] Thank you.


This has nothing to do with Bell. At. All. Using this logic, you simply reject anything you don't understand or don't like.

BTW, it was recently discovered that the average temperature of the human body was closer to 98.5 degrees F than 98.6. Think that has any significance to this discussion?


[C] There is no controversy about Bell to speak of. (Except maybe amongst lay readers.) I am not saying there are NO scientific professionals who deny it, but certainly no more than deny the Big Bang, evolution or relativity. (There are a few out there in these groups who are otherwise respected, believe it or not.) But this is about as settled an area as there is.

Again, as you learn more about Bell you will come to understand that there are literally hundreds if not thousands of different inequalities that lead to the same result (incompatibility of QM and LR using all kinds of definitions of Locality and Realism). There are many different theoretical predictions for the existence of entanglement, almost all of which should not exist in a Local Realistic world. Their very existence is a counterexample to LR. This is the main reason that no one questions Bell anymore.

As JesseM says, Bell is not asserting QM is correct. It merely says that IF you use the EPR definitions of "elements of reality" and "locality" - which are additional requirements to an LR model NOT present in QM - THEN you cannot reproduce the QM predictions. As I have said many times, you can demonstrate this for yourself if you try the angles I mentioned. Hopefully by now you see this.

I completely agree that you have a right to understand this for yourself and I continue to encourage you to do so. Believe me, I fought many of these same ideas when I first learned about Bell - I am no sheep*! It can take patience. But I am comfortable enough to listen to the evidence of professionals and kick it around a bit before I speak out.

In all honesty: having spoken to many over the years here at PhysicsForums, you need to get a better understanding of the strengths of the Bell reasoning before you begin mounting attacks. Wishing and doubting are not enough. In my opinion, even Einstein would have accepted this had he lived to see Bell. Because Bell is the "child" of EPR.

*Although I have been accused of being a shill for the scientific establishment in the past, this could not be further from the truth.

 

[harrylin]

[..]
This has nothing to do with Bell. At. All. Using this logic, you simply reject anything you don't understand or don't like.

His reply related to what you wrote, which indeed was not on topic; it's wise to check the original before making baseless accusations.

Such a blooper has also happened to me. Probably it's better to usually include two levels of citations in discussions but there is no automatic way to do that, or is there? I don't know what "Multiquote" is supposed to do, only that it doesn't do that...

 

[miosim]

JesseM,

I tried to follow the papers and references to your previous posts you suggested, but I need more time to read them carefully.
I think that we should proceed more systematically and focus on the original papers first (one at the time) before discussing your previous posts which are reflections on the original publications. At this point I am reday (read finally) to discuss the “BERTLMANN'S SOCKS AND THE NATURE OF REALITY” by J. Bell.
(this link should work now). http://hal.archives-ouvertes.fr/docs/00/22/06/88/PDF/ajp-jphyscol198142C202.pdf
Next I would discuss the “BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST” by Alain Aspect’s http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf
because it is closely related to the previous one. Then we can proceed with any paper you suggested and I would need some time to read them first. Then we can check any previous posts you suggest.

First let me respond to your question.

Do you understand that Bell's theorem isn't making any claims about what the correct theory in the real world is, it's just about the incompatibility of the theory of QM with local realism?
So even if experiments turned out not to match the theory of QM, and experiments could be explained by a local realist model, this would have nothing to do with refuting Bell's theorem. DrChinese's challenge was specifically to try to construct a local realist model that agrees with all the predictions of QM, including the 100% correlation for entangled photons when the same polarizer angle is used.

I disagree with this assessment.
First, I want to clarify that “random settings” is referred to the angle between polarizers (set in parallel) and axes, but not to the angle between polarizers.
Second, the original Bell's theorem indeed don’t make explicit claims about what the correct theory is. However the incompatibility with math of QM means the incompatibility with Malus law (identical with a math of QM ) and experiments this law is based on. Therefore any model that is incompatible with result predicted by Malus law is doomed. It is why the Bell’s theorem implicitly claims the correctness of QM theory.

The Bell's theorem compares the math of the QM with the math of naïve classical ad-hoc model that suppose to reflects the EPR model/argument.
Page c2-48
“Let us illustrate the possibility of what Einstein had in mind in the context of the particular quantum mechanical predictions
already cited for the EPRB gedanken experiment. These predictions make it hard to believe in the completeness of quantum formalism. But of course outside that formalism they make no difficulty whatever for the notion of local causality. To show this explicitly we exhibit a trivial ad hoc space-time picture of what might go on. It is a modification of the naive classical picture already described…”

I think that Einstein would slap Bells’ hands for such distortion of EPR argument that is a 100% QM system (governed by wave function) plus hidden parameters as a way to explain QM behavior. Instead, Bell stripped QM properties from EPR model reducing into Newtonian mechanic. It is why Bell (and the rest) found appropriate explaining the Bell’s theorem in terms of balls, sucks and other tangible objects – because in Bell's interpretation the “EPR” model is not the QM system any more.
From this point on it is obvious that this “corpuscular” Newtonian model of photons wouldn’t be compatible with math of QM supported by experimental results of Malus law.
Fig.3 in http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf clearly illustrates this.

It is why the entire Bell’s inequality is based on false premise of comparing QM and Newtonian models.

As soon as Bell established this inequality he jumped to not substantiated conclusions as follow (see page C2-52):
“… Let us summarize once again the logic that leads to the impasse.
The EPRB correlations are such that the result of the experiment on one
side immediately foretells that on the other, whenever the analyzers
happen to be parallel. If we do not accept the intervention on one side
as a causal influence on the other, we seem obliged to admit that the
results on both sides are determined in advance anyway, independently
of the intervention on the other side, by signals from the source and
by the local magnet setting. But this has implications for non-parallel
settings which conflict with those of quantum mechanics. So we cannot
dismiss intervention on one side as a causal influence on the other.”

I found disturbingly unintelligent the conclusion that the “… intervention on one side as a causal influence on the other as inevitable…”
The EPR model offers clear and simple explanation of this phenomenon: both individual correlated photons behave according to QM wave function and therefore EPR photons are 100% in agreement with QM prediction for any non-parallel settings of polarizers.

I have to go now.

 

[JesseM]

Do you understand that Bell's theorem isn't making any claims about what the correct theory in the real world is, it's just about the incompatibility of the theory of QM with local realism?
So even if experiments turned out not to match the theory of QM, and experiments could be explained by a local realist model, this would have nothing to do with refuting Bell's theorem. DrChinese's challenge was specifically to try to construct a local realist model that agrees with all the predictions of QM, including the 100% correlation for entangled photons when the same polarizer angle is used.

I disagree with this assessment.

Well then, you just don't know what you're talking about, my statement above is a completely obvious and basic description of what the theorem is claiming, it's utterly uncontroversial and no physicist would disagree with it. If you're not willing to listen to what people who actually understand the theorem say about it, then there doesn't seem much point in continuing this discussion, but if you're willing to accept that you may be mistaken in your understanding of what the theorem is saying, perhaps we can identify the source of your misconceptions.

First, I want to clarify that “random settings” is referred to the angle between polarizers (set in parallel) and axes, but not to the angle between polarizers.

The two polarizers are not set in parallel on every trial, rather their angles relative to the coordinate axis are randomly varied independently. The idea is that the experimenters agree in advance that on each trial they will randomly set their own polarizer to one of three possible angles relative to the coordinate axis, so only on 1/3 of all trials we should expect them to both have chosen the same angle relative to the coordinate axis (i.e. only on 1/3 of trials will the two polarizers be parallel). QM predicts that in this subset of trials we should expect a 100% correlation, so Bell started with that assumption, and then looked at what happened when you combined this assumption with the assumption of local realism. What he found was that (100% correlation when same angle is chosen) + (local realism) implies (Bell inequalities are respected). But QM predicts the Bell inequalities will not be respected, thus showing that the predictions of QM are incompatible with local realism. As I said before this is a purely theoretical claim, it doesn't depend on whether either QM or local realism (or neither) is true in the real world, it just proves that it's logically impossible they could both be true simultaneously.

If any of this differs from your previous understanding of what Bell's theorem is proving, please point out the first statement above that doesn't match what you thought Bell was doing, and I can show you that you're wrong by quoting some appropriate section of the Bertlmann's socks paper (or any other you like).

Second, the original Bell's theorem indeed don’t make explicit claims about what the correct theory is, but the incompatibility with math of QM means the incompatibility with Malus law (identical with a math of QM )

No, you misunderstand Malus' law here, it's a law in classical electromagnetism which only predicts what happens when the same electromagnetic wave is passed through two polarizers at different angles in succession (or when a single pre-polarized wave with known polarization angle passes through a single polarizer), whereas in Bell's theorem QM is being used two make a prediction about how two entangled particles behave when each is sent through a different polarizer. So while the equation is the same, the physical meaning of the equation is rather different in the two cases.

The Bell's theorem compares the math of the QM with the math of naïve classical ad-hoc model that suppose to reflects the EPR model/argument.
Page c2-48
“Let us illustrate the possibility of what Einstein had in mind in the context of the particular quantum mechanical predictions
already cited for the EPRB gedanken experiment. These predictions
make it hard to believe in the completeness of quantum formalism. But
of course outside that formalism they make no difficulty whatever for
the notion of local causality. To show this explicitly we exhibit a trivial
ad hoc space-time picture of what might go on. It is a modification
of the naive classical picture already described…”

Yes, he starts by assuming a specific "naive classical model" with a modified force law given by equation (2), but if you read further in the paper he later makes the argument more general and considers what would have to be true in all possible models respecting the "local causality" (same as local realism) he mentions above. Note he immediately shows on p. C2-49 that this naive model fails to match up with QM "at intermediate angles", and then goes on to say:

"Of course this trivial model was just the first one we thought of, and it worked up to a point. Could we not be a little more clever, and device a model which reproduces the quantum formulae completely? No. It cannot be done, so long as action at a distance is excluded."

So he's saying all locally causal models which exclude action-at-a-distance will fail to match up with QM, not just the "trivial model" he brought up briefly on p. c2-48. To explain why this is true, he first starts with the analogy of Bertlmann's socks, which is intended to illustrate how one can derive an inequality based on the idea that if pairs of entangled particles (or pairs of socks) always given identical results when subjected to the same test, that must be because each member of the pair had a set of properties (assigned to them by the source when they were created at a common location) that gave them the same set of predetermined results for each possible test. In a "locally causal" universe this is the only way to explain how you always see perfect correlations whenever experimenters choose the same test, as he explains on c2-52:

"Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet set."

I think that Einstein would slap Bells’ hands for such distortion of EPR argument that is a 100% QM system (governed by wave function) plus hidden parameters as a way to explain QM behavior. Instead, Bell stripped QM properties from EPR model reducing into Newtonian mechanic.

Nope, as explained above you're just misunderstanding the difference between his initial "trivial model" which was just meant as an example, and the subsequent more general argument. The more general argument does not assume anything specific about the model beyond the idea that it's locally causal, i.e. there can be no causal influences which travel faster than the speed of light.

 

[DrChinese]

His reply related to what you wrote, which indeed was not on topic; it's wise to check the original before making baseless accusations.

Well: it wasn't baseless (Aristotle & Newton, really?) because, as I have said many times, examples of "scientific error" would undermine ALL science equally. And I would hardly call these towers of science "erroneous". I would love to be as erroneous as they.

Not really sure why folks bring up scientific error as a counterexample to Bell, I see that argument fairly often. I guess when you believe in something so thoroughly disproven, that may be your only angle.

So here's the deal: If you are looking for hidden variables, don't bother looking for them in the past light cone; they aren't there! They are either in the present (non-local) or in the future (time symmetric). Or they don't exist at all.

 

[DrChinese]

The EPR model offers clear and simple explanation of this phenomenon: both individual correlated photons behave according to QM wave function and therefore EPR photons are 100% in agreement with QM prediction for any non-parallel settings of polarizers.

Wow, you have cleverly turned the clock back to 1935. Have you not understood anything which has been discussed in this thread in the previous 110 posts? JesseM and I have patiently tried to help you understand Bell. And you keep pretending it doesn't exist. Bell came AFTER EPR.

Note to self: One definition of "insanity"=repeating actions while expecting different outcomes...

 

[miosim]

Well: Not really sure why folks bring up scientific error as a counterexample to Bell, I see that argument fairly often. I guess when you believe in something so thoroughly disproven, that may be your only angle.

My reference to Aristotle & Newton is not about errors but a reminder that a scientific argument shouldn’t be based on the reference to authority or mainstream views, because they are not cut in a stone.

 

[miosim]

Wow, you have cleverly turned the clock back to 1935. Have you not understood anything which has been discussed in this thread in the previous 110 posts? JesseM and I have patiently tried to help you understand Bell. And you keep pretending it doesn't exist. Bell came AFTER EPR.

Note to self: One definition of "insanity"=repeating actions while expecting different outcomes...

DrChinese,

I would appreciate more substantial comments about my post #111

 

[DrChinese]

My reference to Aristotle & Newton is not about errors but a reminder that a scientific argument shouldn’t be based on the reference to authority or mainstream views, because they are not cut in a stone.

And wrong again you are!

The stated policy at PhysicsForums is to advance generally accepted science, except in certain special forum areas (of which Quantum Physics is not one). Check the guidelines. References to mainstream published work (the authority I guess you eschew) are not only encouraged, but sometimes required.

 

[DrChinese]

DrChinese,

I would appreciate more substantial comments about my post #111

As stated numerous times previously, EPR were completely unaware of the fact that their model fails both the Bell logic and experimental tests a la Aspect.

EPR thought that an LR model might eventually be found that provided QM predictions. Bell showed that impossible.

EPR thought that the HUP could be beat using entangled particle pairs. Aspect showed that to be incorrect as well.

Is that substantial enough? You are just going to wave your hand and reject this, not much I can help you with there.

 

[harrylin]

Well: it wasn't baseless (Aristotle & Newton, really?) because, as I have said many times, examples of "scientific error" would undermine ALL science equally. And I would hardly call these towers of science "erroneous". I would love to be as erroneous as they.

I would also love to be erroneous like them!

If you really think that Bell was right to the point of "authority" (even more than Newton?) how do you think that Nelson was wrong? Due to another thread I just stumbled on his paper* and I suddenly really feel like a "grandpa" because I don't understand the "passive locality" issue...

* http://onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.1986.tb12456.x/abstract

 

[DrChinese]

If you really think that Bell was right to the point of "authority" (even more than Newton?) how do you think that Nelson was wrong?

I have 2 web pages which give separate proofs of Bell's Theorem. So yes, I consider Bell both correct and authoritative.

What does Bell have to do with Nelson? (Or vice versa?) Why would I care? Nelson's paper is about locality and stochastic mechanics, which I am unlikely to see as a good pairing anyway.

 

[JesseM]

If you really think that Bell was right to the point of "authority" (even more than Newton?)

Bell's proof was a theoretical one, therefore it is purely mathematical and just as unlikely to be disproven as any other widely-accepted mathematical proof, like the proof that there is no largest prime number. Newton also came up with plenty of theoretical results about what would be true given the basic rules of Newtonian mechanics (like orbits being ellipses), not a single one of them has ever been proven wrong or ever will be, even though the rules of Newtonian mechanics have been shown to be not perfectly applicable to the real world.