Bell's Theorem: Proving Its Vitality in Local Realistic Models

[DrChinese]

If you follow some of my posts, you probably already know that I am a big advocate of Bell's Theorem. I thought I would share a little exercise that shows another aspect of why it is important. Deposited today in the preprint archive was the following article:

Waves, Particles, and Quantized Transitions: A New Realistic Model of the Microworld, by Alan M. Kadin

He introduces a local realistic model, complete with a bunch of formulae and other support. So naturally, the first thing I do is look at the section where Bell is addressed. After all, no one will read it if that is not dealt with. So I find this:

"Since the two particles can be far apart at the time the first measurement is made, this would seem to violate (at least the spirit of) special relativity. Alternatively, if no such instantaneous collapse occurs, then each of the two particles must remember their initial preparation in a way that incorporates the final result, via some sort of “hidden variables”. But a general analysis of these types of correlated measurements by Bell has led to a set of inequalities that constrain the existence of “local hidden variables”. A number of experiments have been done, practically all using correlated photons and polarization measurements, and these tend to confirm the standard quantum predictions, as opposed to an alternative explanation based on local hidden variables. These results have been generally interpreted to rule out any alternative to standard quantum mechanics, although some questions about possible “loopholes” in the results continue to be discussed.

"The present picture questions the real existence of the entangled product states that are used in the conventional explanation of these EPR-type experiments, and instead proposes that each quantum wave represents a localized real-space rotating vector field consistent with local realism. Furthermore, in terms of the optical experiments, the present picture suggests that single photons are necessarily circularly polarized with spin h, in contrast to linearly polarized single photons with zero spin, which are essential to the interpretation of many of these measurements. From this point of view, an electromagnetic wave that passes through a linear polarizer must be a superposition of at least 2 counter-rotating CP photons. It would be interesting to re-analyze the results of these experiments with this picture in mind, to see if this could account for the measured results in a way that does not require non-locality."

What?? "Interesting"!? Sir, it is not interesting, it's required! Send this puppy straight to the bit bucket 'cause this dog won't fly. Fortunately, most "would be" authors of local realistic theories pause before they send papers like this out because they cannot address Bell properly. And that is another reason why Bell is so important. It provides a line in the sand that is supposed to filter out work like this. But every so often, one comes through anyway. Then all you do is look for the section on Bell...



-DrC

 

[xts]

I don't agree. We don't need Bell at all!
Pauli or Heisenberg - they are pretty sufficient to help us. Or just common sense (more than 2 counter rotating directions?)
The guy misses much simpler things that Bell's Theorem:

wave that passes through a linear polarizer must be a superposition of at least 2 counter-rotating CP photons. It would be interesting to re-analyze the results of these experiments with this picture in mind

He doesn't understand, that every phenomenon looks the same regardless what base we prefer to use in our analysis.

 

[DrChinese]

I don't agree. We don't need Bell at all!

Don't say it! Life wouldn't be worth living anymore.

Obviously this paper has lots of problems, but the section on Bell (or lack thereof) puts things into perspective for me very quickly.

 

[xts]

OK. We need and respect Bell for other reasons (e.g. for nobilitation of quantum engineer profession) but I insist he is not necessary to filter out maniacs.

 

[csmcmillion]

From the Physics Virtual Bookshelf at U of Toronto:

'In 1975 Stapp called Bell's Theorem "the most profound discovery of science." Note that he says science, not physics. I agree with him.'

David M. Harrison, Department of Physics, University of Toronto

http://www.upscale.utoronto.ca/PVB/Harrison/BellsTheorem/BellsTheorem.html

 

[Dickfore]

If you follow some of my posts, you probably already know that I am a big advocate of Bell's Theorem.

How can one advocate or oppose a mathematical theorem?!

 

[ThomasT]

How can one advocate or oppose a mathematical theorem?!

Bell's theorem has come to refer to not just the mathematical inequalities but what their violation implies, which is that local realistic models of quantum entanglement are ruled out. I think that DrC is referring to that broader meaning, ie., what might be inferred from the maths in light of experimental results. If I'm mistaken wrt that, then I apologize.

 

[DrChinese]

Bell's theorem has come to refer to not just the mathematical inequalities but what their violation implies, which is that local realistic models of quantum entanglement are ruled out. I think that DrC is referring to that broader meaning, ie., what might be inferred from the maths in light of experimental results. If I'm mistaken wrt that, then I apologize.

Yeah, what he said.

P.S. Thx.

P.P.S. There might be some theorems which are more useful than others.

 

[Dickfore]

Ok, so you meant the "experimental verification of Bell's inequalities" or "theoretical prediction of a new theory regarding Bell's inequalities", didn't you?

 

[ppnl]

Ok, so you meant the "experimental verification of Bell's inequalities" or "theoretical prediction of a new theory regarding Bell's inequalities", didn't you?

Actually I think what is important is understanding the ontological and epistemological consequences of Bell. Having predictions is nice and experimental confirmation of predictions is what science is. But it is the consequences that leave you gobsmacked.

 

[Dickfore]

Actually I think what is important is understanding the ontological and epistemological consequences of Bell. Having predictions is nice and experimental confirmation of predictions is what science is. But it is the consequences that leave you gobsmacked.

I would not delve into philosophical questions arising from the predictions of a scientific theory. After all, philosophers had not been aware of these issues before the scientific theory predicted them.

 

[xts]

After all, philosophers had not been aware of these issues before the scientific theory predicted them.

Sure. Scientists hadn't been aware of them neither. That is what constitutes progress - both in science and in philosophy.

What should worry us is, that majority of philosophers tend to ignore scientific discoveries made even over hundred years ago (they still discuss Leibnizian concepts of time). So we should support those of them, who are worried by implications of Bell's inequality and its observed (by Aspect and his followers) violation and try to incorporate such discoveries into mainstream of philosophy.

 

[Dickfore]

Sure. Scientists hadn't been aware of them neither. That is what constitutes progress - both in science and in philosophy.

Nevertheless, they had arrived at them following the scientific method. This is infinitely far away for philosophers.

So we should support those of them, ...

Who's 'we'?

 

[xts]

scientific method. This is infinitely far away for philosophers.
...Who's 'we'?

Not for all philosophers, and we should support those philosophers, who are not that far away. That support is what (as I understand him) Dr.C called 'advocacy'.

we == those, who respect 'scientific method'

 

[ppnl]

Nevertheless, they had arrived at them following the scientific method. This is infinitely far away for philosophers.

Scientific method is a product of philosophy. Empiricism is a philosophical stance. The fact that most philosophers wander off into an intellectual waste land does not change this.

 

[Dickfore]

Scientific method is a product of philosophy.

Wrong.

 

[Fra]

I agree with ppnl that scientific method belongs to the philosophy.

The writings I have read that actually describes and defines the scientific method as we know it, and tries to justify it as "rational", are nothing but philosophical papers.

The most common confusion even by some educated people is that some people tend to think that philosophy is just incoherent ramblings or poetry, which isn't the case.

The very core of for example Poppers reasoning as outlined in his classic book "The logic of scientific discovery", starts around a classic philosophical problem of induction, and this is what he wants to avoid and seek an as close to deductive description of "science" as possible.

The original quest for the "scientific method" was the quest for a RATIONAL method for acquiring and establishing objective knowledge. This is as opposed to old times "educated opinions" of priests and other supposedly "knowledgable people". People was seeking a rational and objective way to search for knowledge. This rationality is what is called science, but the abstraction of the method is nevertheless embedded in philosophy.

I think the idea that science is "obvious" and part of deductive logic is a common illusion. Just read poppers struggle on howto avoid induction in describing science and judge if he was successful or not.

/Fredrik

 

[Dickfore]

It might be that the idea for the scientific method belongs to philosophy, but the scientific method is not used by philosophers, but by scientists. The empiricism you're quoting was a contemporary to Newton. Do you know how much has science and mathematics progressed since then?

 

[Fra]

All I wanted to add is something which I think is actually important in particular in any discussion about the foundations of physics is that there is sometimes a tendency to dismissing away important philosophical difficulties when it comes to justifying certain common structural realism that I would say most (not all) physicists subscribe to. This is the structural realism that is implicit in the "belief" that the laws of nature are fixed and timeless and that science task is to simply "unravel" them.

All I'm suggesting is that this is often apparent, you can often tell from how a paper is written how the author thinks about these things. And my personal opinion is that a lot of physicists are having a somewhat "simplistic" attitude towards the very justification of the scientific method - yet they depend on it.

(Still this is only weakly connect to the OT so I'll try to fade out my contribution here)

/Fredrik

 

[SpectraCat]

As with most things, there have always been those who just ignored what the "experts" were saying and did what they thought were right. These were actually the first scientists, who hewed to the scientific method before any philosophers had even considered it. Take Archimedes .. he was a scientist by the modern definition, who used experiment and observation to learn about the world, however at the time, the Aristotelians were saying that all knowledge comes from pure thought, and experiments were for dummies. Roger Bacon was another example of a scientist who pre-dates modern conceptions of the scientific method. My point here is that the scientific method *is* self-evident, and stems from the following train of thought:

Person 1: "I wonder how <dimension> that <property of some object> is?"
Person 2: "Let's see if we can measure it."
Person 1: "If you measure it now, how can you be sure it's value won't be different tomorrow."
Person 2: "Hmm, good point. I don't expect it to change with time, but we can always measure it again to make sure we get the same value."

The ideas expressed in that simple dialog (particularly the last one) are so "obvious" that people used and relied on them (and still do) all the time without even thinking about it or realizing what they were doing. The Egyptians built the pyramids, ancient man invented the wheel and cultivated crops, Romans built bridges that still stand today ... all by relying on the scientific method without explicitly doing science.

So, while I understand the core of Fra's point that our *understanding* of the scientific method is based on philosophical insight, the core idea and approach seem to me to be an innate part of human nature.

 

[Fra]

I guess I could start to argue a little bit but in the everyday sense I agree with all Spectracat says.

My point becomes obvious not in practicing science in general, but rather in specific circumstances where we consider the foundations of physics, and physicla law. In particular when we face the apparent fact that the KNOWLEDGE or information ANY system can HOLD about another system, is constrained by several funny things. Such as information bounds, and subjectivity (observer dependnecen) of the INFERENCE systems used.

These are some quite subtle points, which are admittedly irrelevant for the superficial discussion, but since my own interest lies in the foundations of physics, unification of interactions there is a "domain" where this point becomes acute (or at least so I claim, we all may disagree).

/Fredrik

 

[ppnl]

It might be that the idea for the scientific method belongs to philosophy, but the scientific method is not used by philosophers, but by scientists. The empiricism you're quoting was a contemporary to Newton. Do you know how much has science and mathematics progressed since then?

Since the study of nature was once called natural philosophy then scientists are philosophers. Most philosophers don't deal with scientific method much but then most biologists don't deal with general relativity much. It is understandable that scientists would want to deny their history as philosophers given the mess that philosophy is generally but there it is.

 

[UChr]

As with most things, there have always been those who just ignored what the "experts" were saying and did what they thought were right. These were actually the first scientists, who hewed to the scientific method before any philosophers had even considered it. Take Archimedes .. he was a scientist by the modern definition, who used experiment and observation to learn about the world, however at the time, the Aristotelians were saying that all knowledge comes from pure thought, and experiments were for dummies. Roger Bacon was another example of a scientist who pre-dates modern conceptions of the scientific method. My point here is that the scientific method *is* self-evident, and stems from the following train of thought:

Person 1: "I wonder how <dimension> that <property of some object> is?"
Person 2: "Let's see if we can measure it."
Person 1: "If you measure it now, how can you be sure it's value won't be different tomorrow."
Person 2: "Hmm, good point. I don't expect it to change with time, but we can always measure it again to make sure we get the same value."

The ideas expressed in that simple dialog (particularly the last one) are so "obvious" that people used and relied on them (and still do) all the time without even thinking about it or realizing what they were doing. The Egyptians built the pyramids, ancient man invented the wheel and cultivated crops, Romans built bridges that still stand today ... all by relying on the scientific method without explicitly doing science.

So, while I understand the core of Fra's point that our *understanding* of the scientific method is based on philosophical insight, the core idea and approach seem to me to be an innate part of human nature.

Speaking of Bell and EPR discussion: the starting point was theoretical philosophical speculation . Only much later turning to experimental results.

 

[Dickfore]

Speaking of Bell and EPR discussion: the starting point was theoretical philosophical speculation . Only much later turning to experimental results.

Wasn't the EPR paper published in a scientific journal?

 

[ppnl]

Wasn't the EPR paper published in a scientific journal?

Yes but Einsteins objection to QM was essentially philosophical in nature. He could not accept the loss of determinism. You cannot do science without addressing complex epistemological and ontological questions. Look at string theory and the objections to it for example.

Separating science from philosophy is like separating the sound from the music. Without the sound there is no music. Without the music the sound is just noise.

 

[SpectraCat]

Yes but Einsteins objection to QM was essentially philosophical in nature. He could not accept the loss of determinism. You cannot do science without addressing complex epistemological and ontological questions. Look at string theory and the objections to it for example.

Separating science from philosophy is like separating the sound from the music. Without the sound there is no music. Without the music the sound is just noise.

While I understand your point, and tend to agree with it for my own personal purposes, there are entire branches of science where progress is made on a daily basis without any direct (or even indirect) consideration of philosophical issues. As I said above, I agree that our understanding of the scientific method relies on philosophy. This becomes particularly important at the frontiers of science, because in such areas the distinction between data and interpretation can become quite blurry. However the application of the scientific method, which has been going on for millenia in one form or another, does not.

 

[ppnl]

While I understand your point, and tend to agree with it for my own personal purposes, there are entire branches of science where progress is made on a daily basis without any direct (or even indirect) consideration of philosophical issues.

Only because the major philosophical issues in these branches have been settled long ago. For example few people doubt the existence of atoms today. But Ernst Mack, who influenced Einsteins development of relativity, didn't believe in atoms. I think there was a school of doubters clear up to WWII. Implicitly then when we accept atoms we are rejecting Mach's phenomenalism. Qm may force us to reexamine that.

We have a similar problem today with string theory that may not be settled for a hundred years.

And that is what is important about Bell. It forces us to examine the epistemological and ontological consequences of our theory.

 

[Physics Monkey]

I like this question. I will just briefly state why I don't think Bell (= Bell inequalities, etc.) is that important.

1. I accept that Bell is a useful filter for theories.
2. I accept that Bell plays some role in "foundations" (related to 1)

The reason why I don't think Bell is terribly important is because I don't see it leading to anything else. It feels like the end rather than the beginning for me. Perhaps this is simply my ignorance. If so, I would be happy to be corrected.

I am a practicing quantum many-body theorist which means I think about all the great mysteries associated with entanglement, many interacting quantum dof, quantum computers, quantum dynamics, and all that good stuff. I have never used Bell for anything in my field, and I don't know anyone in the same general line of work who has. The people I know who work with Bell seem mostly to test the inequality in ever more elaborate settings. This is why I see Bell as an end rather than a beginning. For my money, there are a lot of ideas in physics (not to mention science in general) that are more profound and productive than Bell. This is not to say that Bell isn't cool, only that my criteria for importance are based in part on the ability of an idea to lead to new ideas and results.

 

[atyy]

I like this question. I will just briefly state why I don't think Bell (= Bell inequalities, etc.) is that important.

1. I accept that Bell is a useful filter for theories.
2. I accept that Bell plays some role in "foundations" (related to 1)

The reason why I don't think Bell is terribly important is because I don't see it leading to anything else. It feels like the end rather than the beginning for me. Perhaps this is simply my ignorance. If so, I would be happy to be corrected.

I am a practicing quantum many-body theorist which means I think about all the great mysteries associated with entanglement, many interacting quantum dof, quantum computers, quantum dynamics, and all that good stuff. I have never used Bell for anything in my field, and I don't know anyone in the same general line of work who has. The people I know who work with Bell seem mostly to test the inequality in ever more elaborate settings. This is why I see Bell as an end rather than a beginning. For my money, there are a lot of ideas in physics (not to mention science in general) that are more profound and productive than Bell. This is not to say that Bell isn't cool, only that my criteria for importance are based in part on the ability of an idea to lead to new ideas and results.

So you'd put the chiral anomaly above the inequality?

 

[Physics Monkey]

So you'd put the chiral anomaly above the inequality?

I would. I would especially put above the inequality the general idea of anomalies - that certain quantum theories may inevitably break a symmetry of the classical limit.

 

[atyy]

I would. I would especially put above the inequality the general idea of anomalies - that certain quantum theories may inevitably break a symmetry of the classical limit.

I wonder if it's known which work Bell preferred?

BTW, have any anomalies been awarded the Nobel Prize (not that that's necessarily the final indicator, but it's good for bar talk)?

Also, just to throw in an additional comparison, how about the Berry phase? In a sense that's in old quantum mechanics and has some of the character of "fundamentals", and so could be an end, yet historically it seems to have been a beginning too. (They really need to award a Nobel for that, for IgNobel aesthetics;)

 

[Physics Monkey]

I wonder if it's known which work Bell preferred?

BTW, have any anomalies been awarded the Nobel Prize (not that that's necessarily the final indicator, but it's good for bar talk)?

Also, just to throw in an additional comparison, how about the Berry phase? In a sense that's in old quantum mechanics and has some of the character of "fundamentals", and so could be an end, yet historically it seems to have been a beginning too. (They really need to award a Nobel for that, for IgNobel aesthetics;)

I don't know, that's an interesting question.

There has been a Dirac Prize partially for the chiral anomaly given to Adler and Jackiw (Bell had died).

I would also put Berry's phase above Bell's theorem. I have used it often, as have many others.

 

[unusualname]

I like this question. I will just briefly state why I don't think Bell (= Bell inequalities, etc.) is that important.

1. I accept that Bell is a useful filter for theories.
2. I accept that Bell plays some role in "foundations" (related to 1)

The reason why I don't think Bell is terribly important is because I don't see it leading to anything else. It feels like the end rather than the beginning for me. Perhaps this is simply my ignorance. If so, I would be happy to be corrected.

I am a practicing quantum many-body theorist which means I think about all the great mysteries associated with entanglement, many interacting quantum dof, quantum computers, quantum dynamics, and all that good stuff. I have never used Bell for anything in my field, and I don't know anyone in the same general line of work who has. The people I know who work with Bell seem mostly to test the inequality in ever more elaborate settings. This is why I see Bell as an end rather than a beginning. For my money, there are a lot of ideas in physics (not to mention science in general) that are more profound and productive than Bell. This is not to say that Bell isn't cool, only that my criteria for importance are based in part on the ability of an idea to lead to new ideas and results.

I believe Bell was due to get the Nobel Prize in Physics after the work of Aspect, Zeilinger (maybe later?) and others confirmed his result, but he died unexpectedly and Nobels are not awarded posthumously.

Bell settled the EPR argument, and showed local hidden variables were not nature, so quite a big deal really.

 

[atyy]

I don't know, that's an interesting question.

There has been a Dirac Prize partially for the chiral anomaly given to Adler and Jackiw (Bell had died).

I would also put Berry's phase above Bell's theorem. I have used it often, as have many others.

Jackiw, Bell's collaborator, has, with Shimony, written a very interesting article about Bell's entire work, beginning from his early years. At first, I was going to read it mischievously as "depth"=inequality and "breadth"=anomaly, but the two strands seem to have run in parallel. http://arxiv.org/abs/physics/0105046

 

[Physics Monkey]

I believe Bell was due to get the Nobel Prize in Physics after the work of Aspect, Zeilinger (maybe later?) and others confirmed his result, but he died unexpectedly and Nobels are not awarded posthumously.

Perhaps. Or perhaps he would have gotten it for anomalies instead. This is (partially) what the Dirac medal was given to Jackiw and Adler for after Bell died.

Bell settled the EPR argument, and showed local hidden variables were not nature, so quite a big deal really.

Well, as I already explained, I believe such statements imply a degree of objectivity that is debatable. Don't get me wrong, Bell's theorem is great, but in my view it has more to do with what quantum mechanics is not than with what quantum mechanics is. I am more interested in the latter and hence place greater subjective value on ideas that I feel advance that goal. And I continue to see the theorem as an end rather than a beginning.