Can grandpa understand the Bell's Theorem?

[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.

 

[harrylin]

Bell's proof was a theoretical one, therefore it is purely mathematical and just as unlikely to be disproven [..].

You did not comment on Nelson's counter proof of Bell's proof; for the application in the real world there is always an aspect of definition and interpretation involved.

Harald

 

[harrylin]

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.

Nelson's paper has everything to do with Bell's theorem as you would have seen if you had clicked on the link. It starts as follows:

"Stochastic mechanics is a theory of quantum phenomena described in terms of classical random processes. An immediate objection is that such a theory is impossible due to Bell’s inequalities and their violation in experiment. Let us begin by confronting this problem."

It may be useful to start a thread on Nelson and "passive locality".

Harald

 

[JesseM]

You did not comment on Nelson's counter proof of Bell's proof; for the application in the real world there is always an aspect of definition and interpretation involved.

Harald

The paper doesn't seem to be freely available online so I can't judge it for myself, nor do I necessarily trust your claim that the paper is intended to refute Bell's theorem. (have you actually read the full paper, or did you just make a quick judgment about what you think it says based on looking at the first page?) https://www.physicsforums.com/showthread.php?t=171545 discussing this and some other related papers, post #5 claims:

In the language of Nelson:
> Theorem: Bell has shown, that active locality AND passive locality can not explain quantum mechanics.

That is, a theory which violates Bells inequality must violate active or
passive locality or both of them. The violation of active locality
would mean a spooky interaction at a distance. The violation of passive
locality would mean simply a correlation that existed since the past.

Nelsons work is mainly a mathematical analysis of Bells sloppy speaking
and does only strenghten the language of Bell with mathematical rigour.

In fact, Nelson discussed it extensively with Bell himself at this time!

His work:
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1749-6632.1986.tb12456.x

Is only not well known for one reason:

Nelson failed to modify his stochastic mechanics, that it would be a
passivly nonlocal theory. Instead he found out that his theory was
actively nonlocal.

Also, while I don't claim to understand what they're talking about, I came across this paper which says on p. 9:

However, while it is often claimed that Nelson’s theory is empirically equivalent
to quantum theory, unfortunately, as shown by Wallstrom [39], the two
theories are in fact not equivalent, because Nelson’s function S does not have
the specific multivalued structure required for the phase of a single-valued (and
continuous) complex field $$\psi$$. The Schr¨odinger equation is indeed derived, but
only for the exceptional set of wave functions with no nodes, for which the circulation
of ∇_iS around all closed curves vanishes. Since almost all wave functions
have nodal points (where $$\psi$$ = 0), quantum theory cannot be derived from Nelson’s
theory, or from any model that leads to Nelson’s theory. (Note that there
is no such problem in pilot-wave theory, where is regarded as a basic entity.)

And here is a paper by Nelson himself where he writes on the very last page:

Here we have an empirical difference between
the predictions of quantum mechanics and stochastic
mechanics. Measurements of the position
of the first particle at time t and of the second particle
at time 0 do not interfere with each other, and
the two theories predict totally different statistics.
Does anyone doubt that quantum mechanics is
right and stochastic mechanics is wrong?

 

[harrylin]

The paper doesn't seem to be freely available online so I can't judge it for myself, nor do I necessarily trust your claim that the paper is intended to refute Bell's theorem. (have you actually read the full paper, or did you just make a quick judgment about what you think it says based on looking at the first page?) [..]

Thanks for the quick feedback - regretfully I won't be able to give feedback for a few days. Yesterday I downloaded the paper, read it quickly and asked people here to explain it to me; it tackles the definitions of Bell's theorem. On purpose I did not use the word "refute"; Nelson uses the word "confront". Bell's theorem is a claim about interpretations of physics, not just mathematics. I asked people here to please explain "passive locality".

I found myself this thread, discussing a recent publication on modified stochastic mechanics:

http://www.natscience.com/Uwe/Forum.aspx/physics-research/4020/my-article-on-Bell-s-theorem-in-Ann-Phys

As this is probably important for understanding Bell's theorem, I think we should start a thread on this.

Harald

 

[DrChinese]

...As this is probably important for understanding Bell's theorem, I think we should start a thread on this.

Harald

You are free to do what you want. But if we started a thread for every paper that claims to refute Bell, we would be adding about 5 per month. Such critiques are soundly rejected because they end up modifying the Bell/EPR definitions beyond the point where they are meaningful. So basically, no one cares. There are NO generally accepted refutations of the main Bell conclusion. Despite claims to the contrary.

There is work being done to try to find ways to get around Bell using SM and various algebra. Peter Morgan's work comes to mind, which involves Lie algebra. There are tremendously complex issues involved, none of which really belong in discussions here. Peter publishes in this area regularly, and is also a member here. The point is that as you soften one element of Bell slightly, you open up opportunities/issues elsewhere. That may help us to better probe things. But it doesn't change Bell per se.

 

[DrChinese]

I also want to add that many of the Bell "refuters" are hopelessly lost in the past in the sense that there have been many experiments in the past 10 years which dramatically change the landscape. For example, entanglement of particles which have never shared a common past is a very powerful counterexample to ANY traditional local theory.

http://arxiv.org/abs/quant-ph/0201134

Thus in the modern post-Bell/Aspect world, the requirements have been raised substantially for any LR theory.

 

[Gordon Watson]

..
A thought-experiment shows grandpa can understand Bell's theorem.

A grandpa came to visit last Saturday, so I showed him this thread. His reply follows:

<<<SNIP>

Further to Saturday's discussion of that web-thread on Bell's theorem, https://www.physicsforums.com/showthread.php?t=488690, here's my reply:


How grandpa understands Bell's theorem in the context of Aspect's experiment.

Aspect Abstract = http://arxiv.org/abs/quant-ph/0402001
Aspect PDF = http://arxiv.org/pdf/quant-ph/0402001

Notes re notation:

1. V (below) stands for the Greek "nu" in Aspect's article.

2. Where Aspect [page 8, eqn (15)] uses P₊(a), I use P(a+|V₁', a); etc.

3. Where Aspect [page 4, eqn (5)] uses P₊₊(a, b), I use P(ab++|V₁, a; V₂, b); etc.

4. Since all probabilities are conditional, I have included the conditions for clarity. Such clarifications do not change Aspect's experimental results in any way.


Grandpa's thought-experiment:

0. For starters, Gordon, let yourself be "Alice-in-Wonderland" for a day.

1. In his article above, Aspect generically identifies the photons in an entangled pair as V₁ and V₂; Aspect's Fig. 1, page 3.

2. Take just one of Aspect's singlet-entangled photon-pairs, and identify these two photons as V₁' and V₂'.

3. Test V₁' with a linear polarizer oriented a; Aspect's Fig. 1, page 3.

4. Say outcome is a+. This indicates that, after the photon-polarizer interaction, V₁' is polarized in the a direction.

5. Now, Alice; please, very carefully: Retrieve V₁', restore it to its pristine condition, and retest it at a again.

6. The result is a+ again. And so on; each re-test of the retrieved-and-restored V₁' at orientation a yields a+ with certainty.

6a. Note this very important point: There is NO implication here (whatsoever) that pristine V₁' -- or, which is the same, "retrieved-and-restored" V₁' -- was polarized a+ prior to its first (or prior to any subsequent re-test) polarizer-photon interaction. It was not! It is not.

6b. For a similar view, see Bell: Speakable and Unspeakable in Quantum Mechanics, 1987, 2004, page 82, though in a different setting: "... and each particle, considered separately, is unpolarized here ... ." [Bell's emphasis.]

7. Now, Alice; with added confidence in your retrieve-and-restore technique: Test and re-test retrieved-and-restored V₁', at orientation b, many times.

8. Outcome: P(b+|V₁', b) = cos^2 (a, b). P(b–|V₁', b) = sin^2 (a, b).

[NB: What if you had been working with a different photon-pair; say V₁" and V₂". And (say) V₁" at orientation a had given the result a–? No problem. That a– notation says that the post-test polarization of V₁" is orthogonal to orientation a. Then the multi-test outcomes of that photon (V₁") at orientation b would be:

P(b+|V₁", b) = sin^2 (a, b). P(b–|V₁", b) = cos^2 (a, b).]

9. Outcome-consequence that we will now use: Since V₂' is correlated with V₁' via the conservation of total angular momentum at their creation, the behavior of pristine V₂' under test is the same as the behavior of pristine V₁' (which is the same as "recovered-and-restored" V₁' under test by you, as Alice).

10. So there is no mystery that we obtain the following results for Aspect's experiments (now over many trials, on many entangled pairs, with no photon now recovered). That is, with the photons generically identified by Aspect as V₁ and V₂, we have (just as Aspect says; but now introducing the conventional Alice and Bob of EPR-Bohm fame):

Alice (single detections, polarizer oriented a): P(a+|V₁, a) = P(a–|V₁, a) = 1/2.

Bob (single detections, polarizer oriented b): P(b+|V₂, b) = P(b–|V₂, b) = 1/2.

11. Joint expectation, Aspect's correlation coefficient (page 5):

E(a, b) = P(a+, b+|V₁, a; V₁, b) – P(a+, b–|V₁, a; V₂, b) – P(a–, b+|V₁, a; V₂, b) + P(a–, b–|V₁, a; V₂, b)

= [cos^2 (a, b)]/2 – [sin^2 (a, b)]/2 – [sin^2 (a, b)]/2 + [cos^2 (a, b)]/2

= cos^2 (a, b) – sin^2 (a, b) = cos 2(a, b)] = QM result; see Aspect page 4, eqn (6).

12. QED. In this way I understand Bell's theorem in accord with my own (and Einstein's) locally causal world-view. In my opinion, Bell's theorem arises from a very narrow interpretation of the EPR definition of an element of reality. In my opinion -- viewed narrowly in the context of EPR's term "corresponding" -- the EPR definition is a classical concept; so Bell's theorem applies to classical systems.

(I think that it was you that told me that Einstein never used this "EPR-expression" in his own writings?)

Now we know that we can never get to QM from classical concepts: that move is blocked by the finite value of Planck's constant, etc. On the other hand, we can always get to classical concepts from QM. Thus, above, each real-local-causal element of quantum reality (my element of physical reality; the orientation of the total spin of each particle) is perturbed by the interaction of each carrier-particle (here, each Aspect photon) with the polarizer.

Aspect's experiment confirms the above derived correlations. Such correlations arise from the conservation of total spin when each pair of photons is created. This has nothing to do with non-locality, FTL, or similar ideas.

Rather, recognizing that we live in a quantum world, and using quantum thinking, we by-pass Bell's classical block on understanding. In this way we better understand the local-causal-realistic marvels associated with quantum-entanglement.

...............

Explanatory note re a common question:

Why did you measure the "recovered-and-restored" V₁' at b.

1: Because (seeking to ensure that no non-local "influence" can be brought into the discussion), you seek to understand how one photon responds to varied tests. This must be done via a thought-experiment, since any real test perturbs the photon and effectively destroys it. (The above thought experiment is not much different to that one done by Einstein, where he traveled with a photon.) When you understand the V₁' response to b, you then also understand how its twin V₂' responds at b; via their pristine spherically-symmetric singlet-state correlation. So, after those repeated tests, testing "recovered-and-restored" V₁' at b, you now understand how the pristine correlation of Aspect's V₁ and V₂ delivers the QM outcome statistics: locally, causally and realistically.

2: Because you need to circumvent the following "possibility": Suppose you test V₂' at b, AND suppose your critics insisted that "non-locality", "FTL", "collapse of wave-function", etc., were (somehow) physical and real. Then your critics could say that the measurement on V₁' had influenced V₂' "non-locally ++". So the above thought-experiment eliminates all such loop-hole claims from the "non-local + "FTL" + ..." community.

3: Because you can then understand Bell's theorem in accord with my own (and Einstein's) locally causal and realistic world-view.

4: Because, most importantly, the above locally-causal-and-realistic thought-experiment eliminates the need for any other explanatory mechanism re entangled-particle dynamics and outcomes.

5. Because Aspect's experiment is then the physically-possible, the real experiment that confirms the validity of your thought-experiment. QED.


Hoping this all makes sense re this Grandpa's understanding of Bell's theorem, please get in touch re any matter that's not clear, etc.

Yours, etc.,

>>

 

[JesseM]

9. Outcome-consequence that we will now use: Since V₂' is correlated with V₁' via the conservation of total angular momentum at their creation, the behavior of pristine V₂' under test is the same as the behavior of pristine V₁' (which is the same as "recovered-and-restored" V₁' under test by you, as Alice).

First of all, according to QM this is simply wrong, if you do two successive measurements with angles a and b on photon V1', the result of the second measurement with angle b is not expected to automatically be the same as a single measurement of V2' with angle b. Even if we leave that aside and just think about "locally causal" models in general without worrying whether they agree with QM in every respect, it would still be impossible to have a locally causal model with the following properties:

1. If you measure V1' successively at angle a and then b, then if the first result was a+ the probability of getting b+ or b- for the second is P(b+|V₁', b) = cos^2 (a-b) and P(b–|V₁', b) = sin^2 (a-b), while if the first result was a- the probability of getting b+ or b- for the second is P(b+|V₁', b) = sin^2 (a-b) and P(b–|V₁', b) = cos^2 (a-b).

2. If you measure V2' only once, then if you measured V2' at a it would be guaranteed to give the same result as the first measurement of V1', and if you measured V2' at b it would be guaranteed to give the same result as the second measurement of V1'.

3. The measurements of V1' and V2' are carried out at a spacelike separation

The reasoning for why this is impossible is exactly the same as the reasoning behind the normal version of Bell's theorem, again the critical thing to realize is that in order to have perfect correlations in a locally causal theory, it would have to be true that photon V1' had predetermined results for any possible choice of a and b even before it reached the polarizers, and photon V2' had identical predetermined results. Do you agree with this point? I'm not sure because you never answered my last question in the [post=3239888]other thread[/post] when I asked you about it, and have also avoided the subject when I asked you on earlier occasions. This issue is central to Bell's whole argument, if you're not interested in actually thinking about Bell's proof but just want to trumpet the fact that you believe you've disproved him by finding a locally causal theory that reproduces QM predictions, without actually giving enough of a detailed model to demonstrate that the equations you write for correlations are even possible under local causality, you shouldn't be doing so on this forum.

 

[Gordon Watson]

First of all, according to QM this is simply wrong, if you do two successive measurements with angles a and b on photon V1', the result of the second measurement with angle b is not expected to automatically be the same as a single measurement of V2' with angle b. Even if we leave that aside and just think about "locally causal" models in general without worrying whether they agree with QM in every respect, it would still be impossible to have a locally causal model with the following properties:

1. If you measure V1' successively at angle a and then b, then if the first result was a+ the probability of getting b+ or b- for the second is P(b+|V₁', b) = cos^2 (a-b) and P(b–|V₁', b) = sin^2 (a-b), while if the first result was a- the probability of getting b+ or b- for the second is P(b+|V₁', b) = sin^2 (a-b) and P(b–|V₁', b) = cos^2 (a-b).

2. If you measure V2' only once, then if you measured V2' at a it would be guaranteed to give the same result as the first measurement of V1', and if you measured V2' at b it would be guaranteed to give the same result as the second measurement of V1'.

3. The measurements of V1' and V2' are carried out at a spacelike separation

The reasoning for why this is impossible is exactly the same as the reasoning behind the normal version of Bell's theorem, again the critical thing to realize is that in order to have perfect correlations in a locally causal theory, it would have to be true that photon V1' had predetermined results for any possible choice of a and b even before it reached the polarizers, and photon V2' had identical predetermined results. Do you agree with this point? I'm not sure because you never answered my last question in the [post=3239888]other thread[/post] when I asked you about it, and have also avoided the subject when I asked you on earlier occasions. This issue is central to Bell's whole argument, if you're not interested in actually thinking about Bell's proof but just want to trumpet the fact that you believe you've disproved him by finding a locally causal theory that reproduces QM predictions, without actually giving enough of a detailed model to demonstrate that the equations you write for correlations are even possible under local causality, you shouldn't be doing so on this forum.

..

Jesse, I'll get back to you re all of this.

BUT please note: In Grandpa's thought experiment the situation that you refer to does not arise. At least as I understand the situation:-

There are no successive measurements on a single photon (as generally understood by these terms) because the photon, after one test, is retrieved and RESTORED to its pristine state.

So, in terms of any photon in Grandpa's thought-experiment, it is always a first test on a pristine photon (not a succession of tests). For example, Grandpa could have said (as another thought-experiment): Just select another photon that yields a+ when tested at orientation a. [This could be done, in a thought-experiment which admitted no non-locality, FTL, etc., by testing a string of V₂ photons at orientation a (at Bob's end). When the outcome a+ is there observed, you then subject its pristine twin V₁ to test at b (at Alice's end).

This second thought-experiment would equally go through. AND deliver the same mathematical relations.

That's the essence of the thought-experiment, as I see it. But I'll check further.

PS-1: Do you not see that these thought-experiment scenarios differ (markedly) from your (and the common) expression for "successive real tests on real photons"?

PS-2: As for Grandpa's thought-experiment delivering the same results at the same settings in Aspect's experiment:-

P(a+, a+|V₁, a; V₂, a) = P(aa++|V₁, a; V₂, a) = cos^2 (a, a) = 1.

GW

 

[JesseM]

There are no successive measurements on a single photon (as generally understood by these terms) because the photon, after one test, is retrieved and RESTORED to its pristine state.

There is no "restoring" procedure in QM.

For example, Grandpa could have said (as another thought-experiment): Just select another photon that yields a+ when tested at orientation a. [This could be done, in a thought-experiment which admitted no non-locality, FTL, etc., by testing a string of V₂ photons at orientation a (at Bob's end). When the outcome a+ is there observed, you then subject its pristine twin V₁ to test at b (at Alice's end).

How is this different from just doing a normal Bell test and looking only at the subset of trials where a+ was observed at the V2 location, throwing out all the other trials where that didn't happen? Either way, if you have a 100% chance of b+ for V1 whenever you get a+ for V2 when the same angle is chosen (a = b), then (if the measurements are made at a spacelike separation, and the experimenters choose the angle at random) under local realism implies predetermined results for all possible angles. Which leads to the rest of Bell's argument, and proves that local realism is incompatible with the relation cos^2(a-b)

PS-1: Do you not see that these thought-experiment scenarios differ (markedly) from your (and the common) expression for "successive real tests on real photons"?

No, I don't see any marked difference, Bell's argument would seem to apply either way, unless you are claiming the measurements on V1 and V2 are not made at a spacelike separation.

PS-2: As for Grandpa's thought-experiment delivering the same results at the same settings in Aspect's experiment:-

P(a+, a+|V₁, a; V₂, a) = P(aa++|V₁, a; V₂, a) = cos^2 (a, a) = 1.

Yes, but you're just asserting that the cos^2 relationship for getting the same result is possible, when in fact it is impossible under local realism if the measurements are at a spacelike separation. You need to actually address the basics of Bell's argument, not just make empty assertions.

 

[Gordon Watson]

I wrote:

9. Outcome-consequence that we will now use: Since V₂' is correlated with V₁' via the conservation of total angular momentum at their creation, the behavior of pristine V₂' under test is the same as the behavior of pristine V₁' (which is the same as "recovered-and-restored" V₁' under test by you, as Alice).

In reply, you wrote:

First of all, according to QM this is simply wrong, ...

So you are saying that Grandpa's Thought Experiment (GTE) is contradicted by Quantum Theory (QT); and presumably Aspect's experiment? Since I accept both GTE and QT, I'd welcome a more detailed explanation (with special reference to QT) of why you take this view. To be very clear: IMHO, GTE and QT are as one -- allowing of course for the fact that (evidently) QT has never before contemplated GTE. (But see below re the importance of thought-experiments.)

Please also note that your continuation [... next, below] is invalid and misleading. GTE does not do "successive measurements" as that phrase is commonly understood. I prefer to use the word "test", not "measurement"; and here's what we find:


GTE has this sequence: Test, retrieve, restore to pristine condition, re-test.

Your implication has this sequence: Test, test.


So if your reference is to your sequence and QT, we will probably agree.

But the question you need to answer is this: Can you show me where, precisely, GTE and QT disagree?

... if you do two successive measurements with angles a and b on photon V1', ...

Well, of course, if you do something different with QM tests, you generally do get something different re QM outcomes. But, as noted above, GTE does NOT do as you suggest.

... the result of the second measurement with angle b is not expected to automatically be the same as a single measurement of V2' with angle b.

Of course, under your sequence of "successive tests" [Test, test], we agree.

But you must here address the GTE sequence [Test, retrieve, restore to pristine condition, re-test]. In which case the outcomes are identical. This identity is confirmed by QT and by Aspect's experiment (the latter being a practical outworking, a proxy, a surrogate for GTE).

Even if we leave that aside and just think about "locally causal" models in general without worrying whether they agree with QM in every respect, it would still be impossible to have a locally causal model with the following properties:

1. If you measure V1' successively at angle a and then b, then if the first result was a+ the probability of getting b+ or b- for the second is P(b+|V₁', b) = cos^2 (a-b) and P(b–|V₁', b) = sin^2 (a-b), while if the first result was a- the probability of getting b+ or b- for the second is P(b+|V₁', b) = sin^2 (a-b) and P(b–|V₁', b) = cos^2 (a-b).

2. If you measure V2' [sic] only once, then if you measured V2' at a it would be guaranteed to give the same result as the first measurement of V1', and if you measured V2' at b it would be guaranteed to give the same result as the second measurement of V1'.

3. The measurements of V1' and V2' are carried out at a spacelike separation

This part of your response continues with reference to "successive" tests" -- see also (presumed) typo marked [sic]. However: If you rephrase the above, consistent with the GTE sequence and QT, the correct conclusion is the diametric opposite to yours.

The reasoning for why this is impossible is exactly the same as the reasoning behind the normal version of Bell's theorem, ...

But GTE is a quantum-based experiment, involving quantum events. As eaglelake said in that earlier post:

<SNIP>
Essentially, Bell’s theorem describes a classical experiment, not a quantum one. ... ... In that sense, Bell’s theorem is about classical physics. It is about an experiment that has several possible outcomes, which are mutually exclusive. ... ... we do not simultaneously perform the experiments for the other components and “unperformed experiments have no results.” Thus, we have no values from the unperformed experiments to be used in our calculations! If we insist on using the inferred values from unperformed experiments we often get contradictions and paradoxes. That is what happens in Bell’s theorem. Several results are used to obtain his inequality. But the experiment he describes can yield only one of those values. The other results are from unperformed experiments, and are, therefore meaningless in quantum mechanics, but Bell uses them as we would in a classical calculation. Consequently, quantum events violate Bell’s inequality while classical experiments satisfy it.

GTE involves quantum events, and quantum events violate Bell’s inequality while classical experiments satisfy it. That, as I see it, is the whole point of GTE: GTE involves quantum events and GTE suggests an underlying local realism. [Which views are not taken to be those of eaglelake.]

... again the critical thing to realize is that in order to have perfect correlations in a locally causal theory, it would have to be true that photon V1' had predetermined results for any possible choice of a and b even before it reached the polarizers, and photon V2' had identical predetermined results. Do you agree with this point?

Do I agree that the results are determined? Yes. And I accept that the results of unperformed tests can be statistically predicted.

But since I take the view (promulgated by Peres), that unperformed experiments have no results, what could it POSSIBLY mean for a photon to "have" an infinity of "predetermined results"? For that infinity arises from the fact that a and b are just two arbitrary orientations from the infinity of orientations in 2-space.

As you know: I take a very different, QM-based, view. The paired-photons in GTE (and hence each Aspect pair), are correlated by the conservation of total angular momentum. If we consider the orientation of such (in 3-space), there are an infinity of such. So I take the view that no two pairs have the same orientation: so every pair is different.

Further, that orientation in 3-space is the local realistic hidden-variable; no two pairs the same, and our tests not revealing any of them! So what could it mean, in QT terms, for each photon to "have" an infinity of "predetermined results"? It seems to me that is how you would describe the diameters of a classical sphere?

Note that, if every Aspect-photon in the world were tested at orientation a, there are just two (2) equivalence classes under such a test: The class that yields the a+ result, and the class that yields the a– result. Similarly for Bob's test at orientation b. So we find in GTE, no requirement for "predetermined results of unperformed experiments". Rather, a requirement (as specified) to understand how the four (4) equivalence classes relate under determinism.

I'm not sure because you never answered my last question in the [post=3239888]other thread[/post] when I asked you about it, and have also avoided the subject when I asked you on earlier occasions. This issue is central to Bell's whole argument, if you're not interested in actually thinking about Bell's proof but just want to trumpet the fact that you believe you've disproved him by finding a locally causal theory that reproduces QM predictions, without actually giving enough of a detailed model to demonstrate that the equations you write for correlations are even possible under local causality, you shouldn't be doing so on this forum.

Well: I'm here to learn. And I try to learn from what is invariably true, or close thereto. And from my mistakes, and those of others. Since I've done much thinking about BT, and since the issue central to "Bell's whole argument" is a classical one, and since I live in a quantum world - I seek to understand that which is central to that quantum world ... and "Einstein's arguments". To that end, my PF-signature alerts students to that interest of mine. And in that context, my probings, fumblings, mumblings, etc., re my point of view lead to questions for discussion, correction, etc.

I'd therefore hope that there would not be a pattern here, of getting close to the nitty-gritty of an issue and finding the thread locked. So that still leaves us discussing GTE in its terms; a fairly detailed model, as I see it, with a specific question to you:

Where does GTE breach QT, having in mind that Aspect's experiment is a valid surrogate for GTE?

In that regard, I wrote:

..
BUT please note: In Grandpa's thought experiment the situation that you refer to does not arise. At least as I understand the situation:- There are no successive measurements on a single photon (as generally understood by these terms) because the photon, after one test, is retrieved and RESTORED to its pristine state.

So, in terms of any photon in Grandpa's thought-experiment, it is always a first test on a pristine photon (not a succession of tests).

The GTE sequence is: Test, retrieve, restore to pristine condition, re-test.

You replied:

There is no "restoring" procedure in QM.

Of course. And, in STR, there is no "pursuing a beam of light with velocity c" when one is aged 16. However, that story continues: "One sees that in this paradox the germ of the special relativity theory is already contained." Einstein, "Autobiographical Notes", in Schilpp (1954: p. 53).

Re GTE, we are discussing a thought-experiment that delivers results in accord with QT and Aspect's experiments.
..

 

[Gordon Watson]

There is no "restoring" procedure in QM.

See response above.

How is this different from just doing a normal Bell test and looking only at the subset of trials where a+ was observed at the V2 location, throwing out all the other trials where that didn't happen? Either way, if you have a 100% chance of b+ for V1 whenever you get a+ for V2 when the same angle is chosen (a = b), then (if the measurements are made at a spacelike separation, and the experimenters choose the angle at random) under local realism implies predetermined results for all possible angles. Which leads to the rest of Bell's argument, and proves that local realism is incompatible with the relation cos^2(a-b)

My emphasis.

It seems to me that your "local realism" is of the classical kind - akin to Mermin's "instruction sets". That the predetermined test-results are pre-existing, and not the product of each photon-polarizer interaction.

Here's a typical example of that genre: Kuttner & Rosenblum (The Physics Teacher, 48, 2010, p. 125) write: "Bell's theorem in a nutshell: Suppose that unobserved objects in our world have physically real properties that are NOT created by their observation."

GTE proceeds from a different supposition: We know that we cannot get to QM from classical concepts: that move is blocked by the finite value of Planck's constant, etc. On the other hand, we can always get to classical concepts from QM. In GTE, each real-local-causal element of quantum reality (an element of physical reality; the orientation of the total spin of each particle) is perturbed by the interaction of each carrier-particle with the polarizer.

Aspect's experiment confirms the GTE correlations. Such correlations arise from the conservation of total spin when each pair of photons is created. So, recognizing that we live in a quantum world, and using quantum thinking, we by-pass Bell's classical block on understanding. In this way we better understand the local-causal-realistic marvels associated with quantum-entanglement.

So GTE employs a real element of physical reality (total-spin orientation) and shows how it manifests: in full accord with QT and Aspect's experiment.

No, I don't see any marked difference, Bell's argument would seem to apply either way, unless you are claiming the measurements on V1 and V2 are not made at a spacelike separation.

This has been addressed before: The Alice and Bob tests are space-like separated.

Yes, but you're just asserting that the cos^2 relationship for getting the same result is possible, when in fact it is impossible under local realism if the measurements are at a spacelike separation. You need to actually address the basics of Bell's argument, not just make empty assertions.

The cos^2 relation emerges from GTE. Not much different to the emergence of the cos^2 relation in QT? As for the basics of Bell's argument: see Kuttner & Rosenblum above. In my view, this is the naive (narrow) interpretation of "EPR elements of physical reality". GTE rejects this view and those EPR elements.
..

 

[JesseM]

So you are saying that Grandpa's Thought Experiment (GTE) is contradicted by Quantum Theory (QT); and presumably Aspect's experiment? Since I accept both GTE and QT, I'd welcome a more detailed explanation (with special reference to QT) of why you take this view.

Since my response was specifically about what would happen if you did multiple measurements on V1' via your notion of "recovering and restoring", I think it was clear that I was talking specifically about this notion when I said the thought-experiment is contradicted by QM. In QM there is no way to "recover and restore" an already-measured photon V1' in such a way that a subsequent measurement on V1' would show the same correlations with its entangled twin V2' as the first measurement. But I already explained this in my response, so I'm not really sure what you're confused about.

Please also note that your continuation [... next, below] is invalid and misleading. GTE does not do "successive measurements" as that phrase is commonly understood. I prefer to use the word "test", not "measurement"; and here's what we find:GTE has this sequence: Test, retrieve, restore to pristine condition, re-test.

I would say "test ... re-test" is commonly understood as "successive measurements", regardless of what happens in between ("successive" just means the two happen in a sequence, it doesn't say anything about what happens in between). Again, QM simply doesn't allow any intermediate procedure between successive measurements that would "restore to pristine condition" and cause the same correlations between V1' and V2' to occur on the "re-test" as on the first "test". This would be a clear violation of the uncertainty principle, as you could "test" V1' for its spin on one axis a, then "restore to pristine condition" and "re-test" for spin on a different axis b (spin on different axes have uncertainty relations just like position and momentum), and then via the "test" and "re-test" you could predict with 100% certainty what the result of a measurement of V2' would reveal on either a or b, so there'd be no sense in which knowledge of one gives uncertainty in the other.

[But you must here address the GTE sequence [Test, retrieve, restore to pristine condition, re-test]. In which case the outcomes are identical. This identity is confirmed by QT and by Aspect's experiment (the latter being a practical outworking, a proxy, a surrogate for GTE).

You think there is any notion of "restoring to pristine condition" in the Aspect's experiment? If so you're completely misunderstanding something, this isn't possible at all in QM with one member of an entangled pair.

Even if we leave that aside and just think about "locally causal" models in general without worrying whether they agree with QM in every respect, it would still be impossible to have a locally causal model with the following properties:

1. If you measure V1' successively at angle a and then b, then if the first result was a+ the probability of getting b+ or b- for the second is P(b+|V₁', b) = cos^2 (a-b) and P(b–|V₁', b) = sin^2 (a-b), while if the first result was a- the probability of getting b+ or b- for the second is P(b+|V₁', b) = sin^2 (a-b) and P(b–|V₁', b) = cos^2 (a-b).

2. If you measure V2' [sic] only once, then if you measured V2' at a it would be guaranteed to give the same result as the first measurement of V1', and if you measured V2' at b it would be guaranteed to give the same result as the second measurement of V1'.

3. The measurements of V1' and V2' are carried out at a spacelike separation

This part of your response continues with reference to "successive" tests" -- see also (presumed) typo marked [sic].

There was no typo where you put "[sic]" above, I meant V2', not V1'. Again the idea you seem to be expressing is that if we do a measurement #1 on V1', the "recover and restore" V1', then do a second measurement on V1' (which I call "successive" since I don't think that word implies anything about what happens in between), then you think the second measurement on V1' will show the same correlations with the first measurement on V2' as the first measurement on V1' would have. For example, you would say that if our second measurement on V1' was on angle b and gave result b+, then if our first measurement on V2' had also been at angle b, we'd be guaranteed to see b+ with V2' as well--am I misunderstanding?

But GTE is a quantum-based experiment, involving quantum events.

Unless I have misunderstood your notion of "recover-and-restore" (see above), the experiment is not possible in QM.

Do I agree that the results are determined? Yes. And I accept that the results of unperformed tests can be statistically predicted.

But since I take the view (promulgated by Peres), that unperformed experiments have no results, what could it POSSIBLY mean for a photon to "have" an infinity of "predetermined results"?

Peres is not a local realist! A local realist must necessarily say that the local variables associated with the particle immediately prior to encountering the measuring device (polarizer, Stern-Gerlach) must have already predetermined what results it would give to any possible setting it might encounter at the measuring-device. This is necessary in order to explain how the two particles are guaranteed with probability 1 to always give the same results if they encounter devices with the same setting, despite the fact that neither particle can causally influence one another. After all, if the particles' responses to any possible setting were not predetermined by the value of local variables prior to measurement, that would imply some random element in what result each one would give when it encountered the measuring-device, so there would always be a nonzero probability the two members of the pair would give different results.

If you don't understand this very basic aspect of Bell's reasoning, then after all this time you really haven't understood the first thing about the theorem you are trying so hard to overturn. As I said in my last post on the other thread:

it must nevertheless be true that the results for each detector setting are predetermined by the hidden variables of the two particles after they have been emitted but prior to the moment when Alice and Bob make a choice of detector settings (at least this must be true in any Bell experiment where Alice and Bob are guaranteed to get opposite--or identical--results each time they choose the same setting). If you don't understand why this must be the case, we should probably go back to my basic definition of local realism offered in [post=3196744]post #94[/post] from the other thread (also see my response to your question about the meaning of my phrase "irreducibly nonlocal" in [post=3213709]post #135[/post])

We could also discuss the paper where I think Bell gives the clearest argument for why local realism (what he calls "local causality") implies predetermined results, using an argument about the past light cones of each measurement, see [post=3248153]this post[/post] where I link to and discuss his paper La nouvelle cuisine. But I would rather not derail this thread to discuss your misconceptions about Bell's theorem and I already asked you not to spread out the same arguments over multiple threads, so for further discussion of the "local realism implies predetermined results" idea, please respond on the other thread.

As you know: I take a very different, QM-based, view. The paired-photons in GTE (and hence each Aspect pair), are correlated by the conservation of total angular momentum. If we consider the orientation of such (in 3-space), there are an infinity of such. So I take the view that no two pairs have the same orientation: so every pair is different.

QM does not say that each pair has a well-defined angular momentum vector prior to measurement, but OK, in a local realist theory you're free to make such an assumption.

Further, that orientation in 3-space is the local realistic hidden-variable; no two pairs the same, and our tests not revealing any of them! So what could it mean, in QT terms, for each photon to "have" an infinity of "predetermined results"?

It would just mean that the orientation of the angular momentum vector is sufficient to determine whether the particle gives + or - in response to each possible detector setting.

To put it another way, suppose we imagine a godlike being who just knows the value of all hidden variables associated with the particles (under your suggestion, an angular momentum vector) without having to interact physically with anything. Suppose this being also knows the complete equations of the fundamental laws of physics, and can calculate perfectly the answer to any sufficiently well-defined problems involving these laws. In this case, if the being sees a particular particle rushing towards a detector with a known angular momentum vector, then if she doesn't yet know what angle the detector is going to be set at (perhaps because this decision has not yet been made, and is going to be made in a truly random fashion), but she does know it's going to be set to one of three possible angles a, b, and c, then with her knowledge of the angular momentum vector and the basic laws of physics she can at least predict with 100% certainty whether the particle will give + or - if angle a is chosen, and likewise for b and c. Whichever one actually ends up chosen, her prediction for that angle is guaranteed to be correct based on her knowledge of the angular momentum vector and the basic laws of physics, even though she didn't know in advance which of the three was going to be chosen. In this case, her three predictions about the result at each angle would be the "predetermined results" for each angle, results which are "predetermined" by the value of the particle's hidden variables (its angular momentum vector) and the basic laws of physics governing how the particle interacts with the detector.

Again, if you don't see the need for such predetermined results even in a local realist theory where the particles can't communicate, feel free to quote the above and respond to it on the other thread, I don't want to derail this one.

The GTE sequence is: Test, retrieve, restore to pristine condition, re-test.

You replied:

There is no "restoring" procedure in QM.

Of course. And, in STR, there is no "pursuing a beam of light with velocity c" when one is aged 16. However, that story continues: "One sees that in this paradox the germ of the special relativity theory is already contained." Einstein, "Autobiographical Notes", in Schilpp (1954: p. 53).

But Einstein did not claim that this thought-experiment should have any well-defined answer in his finished theory of relativity, it was just something he thought about when young that made him realize a problem with some earlier non-relativistic views of electromagnetism (see this page for an excellent discussion of the meaning of the role of this thought-experiment in his thinking). If you agree that "of course" there is no possible restoring procedure in QM, why do you keep asking me why the thought-experiment is incompatible with QM? Einstein would not have disagreed that the thought-experiment of a normal observer (one made of massive particles, and who had a clock that could measure time) traveling along with a light beam was incompatible with relativity! Neither SR nor GR can give you an answer to what the outcome of this thought-experiment would be, because they both judge the basic premise to be impossible. Similarly QM can say nothing about what would happen under your thought-experiment because the premises are incompatible with QM, the thought-experiment is only meaningful if you want to explore some non-QM theory (like my suggestion of a hidden variables theory which is meant to give the same result as QM if only a single measurement is made on each particle, but which differs from QM in allowing your "recover and restore" procedure).

 

[DrChinese]

Do I agree that the results are determined? Yes. And I accept that the results of unperformed tests can be statistically predicted.

But since I take the view (promulgated by Peres), that unperformed experiments have no results, ...

This is absurd (and that is being kind). You say the results are (pre)determined, which is a realistic stance, and then reject that by saying that what you can't measure isn't real. Well, which is it?

Further, you say that the results of unperformed tests CAN be statistically predicted. Well, perhaps you care to back this up by showing us your predictions for a dataset of photons, at settings 0/120/240. Put up!

(JesseM, sometimes I wonder... know what I mean?)

 

[Gordon Watson]

..
Jesse, many thanks for the nice reply above. I'll be happily addressing all the points that you raise; but maybe you could save me from addressing some unimportant side-issues re BT. SO: In the interim, could you comment on the following, please. I think it might short-cut and by-pass the need to discuss many irrelevancies:

AS I understand BT: Bell based his argument on two primary assumptions. Let me call them (hopefully with your approval and agreement) "Einstein-locality" and "EPR-realism".

In my world-view, the view that is behind all my PF posts, I accept "Einstein-locality" but I totally reject "EPR-realism" in quantum situations.

I have done so from my first reading of EPR; it is a stand-out silliness, imho; and it was well-known to the founding-fathers of QT that a test perturbed the tested system. (In private discussions, one close to those fathers scathingly agreed that it was often wrongly-overlooked or misunderstood later on.) So I believe that I am in good company with this rejection of "EPR-realism".

To take just one example of that company: From my readings, I believe that Einstein also rejected "EPR-realism". He was cranky with Podolsky's editing of EPR. And while there's much discussion about what made him cranky, all that I can say is that I too would be cranky about the naive realism associated with "EPR-realism". Moreover, I can find no reference to it anywhere in Einstein's writings.

So if Bell is a refutation of "EPR-realism", well I'm on his side. And your side. So the question then arises: Is Bell limited to a refutation of "EPR-realism" or of "realism" in general?

Imho, BT is not a rejection of "realism" in general because many leading commentators and professors use the naive "EPR-realism" in their discussions; note: they make no mention of the more general one. They make no mention of that early, more-general and properly realistic QM view. Examples (from hundreds): Throughout Mermin we find "instruction sets" -- "EPR-realism" if I ever saw it. In Zeilinger et al. (roughly, as I recall) we find "EPR-realism" expressed something like this: "Bell's realism assumption assumes that the outcome of a test on a pristine particle reflects properties that the particle had prior to and independent of the test," -- again, "EPR-realism" if I ever saw it.

Can I make it any clearer: It is this NR (naive-realism, or "EPR-realism") that I object to, and reject. And surely we do not need to discuss BT to reject it! For it seems to me to be a carry-over from classical theory -- and, imho, we cannot understand quantum-reality if we allow ourselves to be bound by classical or naive-realism or "EPR-realism".

Comments and critique, please. And thanks again.

GW

 

[Gordon Watson]

This is absurd (and that is being kind). You say the results are (pre)determined, which is a realistic stance, and then reject that by saying that what you can't measure isn't real. Well, which is it?

Further, you say that the results of unperformed tests CAN be statistically predicted. Well, perhaps you care to back this up by showing us your predictions for a dataset of photons, at settings 0/120/240. Put up!

(JesseM, sometimes I wonder... know what I mean?)

..

Dearest DrC, I do not wonder; I know!

You were recently caught out, very badly, misrepresenting my position.

And, as I understand the PF guidance, with respect to the following, you're being naughty again.

Please: Do not high-jack this thread -- with "The DrChinese Challenge" -- just open a new one.

Just put it up!

You know what I mean!

Just let me know; OK?

GW

 

[miosim]

I also want to add that many of the Bell "refuters" are hopelessly lost in the past in the sense that there have been many experiments in the past 10 years which dramatically change the landscape. For example, entanglement of particles which have never shared a common past is a very powerful counterexample to ANY traditional local theory.

As I understand all these experiments observe the cos^2 correlation. This result is predicted by the 200 year-old Malus law. Does it mean that non-locality and FTL communication could be derived from the Malus law? If it is, why do we need Bell’s theorem?

***

I just finished reading BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST by Alain Aspect. This paper convinced me that in Bell’s theorem, the EPR correlation is presented as the classical deterministic corpuscular model of the photons. It is hard to believe that this model is proclaimed as a “reasonable” Supplementary Parameters Theory in the “spirit of Einstein’s ideas.” This deterministic corpuscular EPR model is completely foreign to QM and also doesn’t have any wave like properties. Of course this “reasonable dummy” mechanical model was found to be incompatible with QM.
Aspect characterized this finding as a discovery. I found this discovery laughable.

I also don’t understand how Bell and Aspect could believe that this model is in the “spirit of Einstein’s ideas.” In his paper, Aspect admitted that for Einstein “fields rather than particles are at the bottom of everything.” Bell in his article mentioned that “determinism is not a presupposition for Einstein in his analysis, regardless of a widespread and erroneous conviction that for Einstein determinism was always the sacred principle.”

However Bell didn't see any problem with this “dummy” EPR model and after knocking it down Bell proclaimed that that the search for alternative realistic models is hopeless and that the local realistic model that would explain the cos^2 correlation does not exist. This opinion was widely accepted within the scientific community.

I am not sure about the scientific approach to non-existence and impossibility, but among us grandpas and grandmas, we don’t believe in proof of non-existence UNLESS in the ABSOLUTELY defined area of knowledge. For example I may prove to myself the non-existence of a dime in my empty pocket, but only after thorough searching it; and even then I may have some reservations.

I don’t agree with Bell/Aspect that the search for realistic models is hopeless and can ofer one. For example, after separation, two correlated photons are represented by their own wave functions having hidden variables that determine antiparallel properties of these photons. However these photons are never perfectly correlated (this could be tested) because of a probability dictated by the respective wave functions. According to this model, if the photon is “retrieved and RESTORED to its pristine state” the second time it would have somewhat different polarization. This local realistic model isn’t helpful for the EPR argument because the absolute knowledge about the polarization of one “correlated” photon would not tell an exact polarization for another photon. However, as I understand the main reason for the EPR argument is to achieve a realistic understanding of physical reality (regardless of our ability to observe) and in this sense, I think that this simplified model is in agreement with the spirit of Einstein’s ideas.

While admitting the limitation of the EPR argument (exploited by Bell’s theorem) I can’t accept the alternative views in terms of "don't ask, don't tell policies” and can’t accept the absurdities of QM interpretation even though they are accepted as the norm within mainstream science.
I am planning (but not reday yet) to start the thread to discuss my views on this topic and already have a name for this thread: “Can a grandpa understand the QM?”
I am not sure if the rules of this forum tolerate the dilettante who is questioning the foundation of QM and may need to find another one.

 

[JesseM]

As I understand all these experiments observe the cos^2 correlation. This result is predicted by the 200 year-old Malus law.

No, it most certainly is not predicted by Malus' law which is not about multiple photons (or light beams) measured by separate polarizers, but rather about a single light beam going through two polarizers in succession (or a single pre-polarized beam going through a single polarizer) as I already explained in post #111 and you ignored:

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.

I just finished reading BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST by Alain Aspect. This paper convinced me that in Bell’s theorem, the EPR correlation is presented as the classical deterministic corpuscular model of the photons.

Big surprise, you've been "convinced" of the ignorant opinion you've kept repeating from the very beginning, even though others have already told you, over and over again, that this is complete nonsense (Bell's argument does not assume anything specific about the nature of particles, including whether they behave deterministically, it only uses the basic premises of local realism which I outlined [post=3245651]here[/post]). You continually ignore all the explanations and questions people put to you (like my repeated question about whether you understand why local realism implies that there are predetermined results for each measurement axis), so it kind of seems like you think you already know everything important about Bell's theorem and have no interest in actually learning anything about it from your dialogue here. If that's the case, the forum rules say this is a place to learn about mainstream physics, which may include open-minded questioning but doesn't include continual assertions that it's all wrong without accepting any possibility your understanding may be mistaken. If you continue to blithely repeat completely ignorant statements without listening to explanations of why they're wrong or answering questions, I'm just going to report further posts like this to the moderators because I don't think they belong on this forum.

 

[JesseM]

..
Jesse, many thanks for the nice reply above. I'll be happily addressing all the points that you raise; but maybe you could save me from addressing some unimportant side-issues re BT. SO: In the interim, could you comment on the following, please. I think it might short-cut and by-pass the need to discuss many irrelevancies:

AS I understand BT: Bell based his argument on two primary assumptions. Let me call them (hopefully with your approval and agreement) "Einstein-locality" and "EPR-realism".

I don't know what you mean by EPR-realism, please explain. If it implies that measurements simply reveal preexisting values of properties like spin (as opposed to the possibility that the measurement process alters the value, and so the measured value is not the same one the particle had immediately before measurement), then no, Bell certainly did not include that as one of his "primary assumptions". Remember that in my last post on the other thread I linked to an earlier post explaining my understanding of the basic premises of local realism (or what Bell called "local causality"):

we should probably go back to my basic definition of local realism offered in [post=3196744]post #94[/post] from the other thread (also see my response to your question about the meaning of my phrase "irreducibly nonlocal" in [post=3213709]post #135[/post])

...please look these links over and explain (on the other thread) whether your term "EPR-realism" is meant to go beyond the assumptions I give (in which case I would disagree that Bell assumed "EPR realism"), or whether Einstein-locality + EPR-realism are equivalent to those assumptions.

 

[DrChinese]

... For example, after separation, two correlated photons are represented by their own wave functions having hidden variables that determine antiparallel properties of these photons. However these photons are never perfectly correlated (this could be tested) because of a probability dictated by the respective wave functions. ...

As I have said any number of times, this hypothesis has been tested and rejected. The tests show perfect correlation to over 100 SD (depending on which version you look at) and rejects the idea that Product state statistics result. (Please note that all tests of perfect correlations are part and parcel of a standard Bell test.)

miosim, you have shown over and over that you have no desire to understand Bell's Theorem. After over 100 posts, I don't believe you have learned anything new. Your desire is clearly to disprove it (or find a reason to reject ot). In this regard, I can be of no service. Have a nice day, I am bowing out of this one.