Spin difference between entangled and non-entangled

[miosim]

This model fails at other angles, but it works for the 5 easy angles: 0, 90, 180, 270, 360.

stevendaryl,

Your explanation helped me better understand the corresponding sections of the "BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST" by Aspect. I still not fully understand the math leading to the "red line" but now I understand a concept.

Just looking in this paper at QM model (6) and hidden variable model (16) one can tell that (6) may be link with Malus law

while (16) couldn't.

Question: Does the hidden variable model (16) contradicts with Malus law.Thanks

 

[Alien8]

The red line is not the only possibility for a local realistic theory. It's just that it is the prediction for a very specific locally realistic model that agrees with QM at the points $\theta = 0^o, 90^o, 180^o, 270^o, 360^o$.

Those are perfect correlation and perfect anti-correlation angles. How can any local theory predict 100% matching or 100% mismatching pairs?

 

[DrChinese]

Question: Does the hidden variable model (16) contradicts with Malus law.

Yes, (16) contradicts Malus (which applies to a single photon stream rather than entangled pairs) in the sense that the single photon analogy would also be a straight line relationship.

 

[DrChinese]

Those are perfect correlation and perfect anti-correlation angles. How can any local theory predict 100% matching or 100% mismatching pairs?

Sure. All you need is a lot of hidden variables. Something like:

Hidden polarization at 00 degrees= -
Hidden polarization at 01 degrees= +
Hidden polarization at 02 degrees= +
Hidden polarization at 03 degrees= +
...
Hidden polarization at 30 degrees= +
Hidden polarization at 31 degrees= -
Hidden polarization at 32 degrees= +
Hidden polarization at 33 degrees= -
...
Hidden polarization at 60 degrees= -
Hidden polarization at 61 degrees= +
Hidden polarization at 62 degrees= -
Hidden polarization at 63 degrees= -
...
etc.

You would get perfect correlations with the above. There is no requirement that it is some simple formula. It could be a bunch of values that average to some formula.

 

[miosim]

Question: Does the hidden variable model (16) contradicts with Malus law.

DrChinese,
I am retrieving my question because I realized how wrong it is. Indeed, the "the red line" is for spin particles and not for polarized photons.

Reading the wiki link http://en.wikipedia.org/wiki/Local_hidden_variable_theory provided on your page I found the following graph:

Fig. 2: The realist prediction (solid curve) for quantum correlation in an optical Bell test. The quantum-mechanical prediction is the dotted curveIn this article the relation between Malus Law and predictions are mentioned multiple times (see below), but I still can't grasp their exact relationship.

1). In optical experiments using polarisation, for instance, the natural assumption is that it is a cosine-squared function, corresponding to adherence to Malus' Law."

2). If we make realistic (wave-based) assumptions regarding the behaviour of light on encountering polarisers and photodetectors, we find that we are not compelled to accept that the probability of detection will reflect Malus' Law exactly

3). By varying our assumptions, it seems possible that the realist prediction could approach the quantum-mechanical one within the limits of
experimental error (Marshall, 1983), though clearly a compromise must be reached. We have to match both the behaviour of the individual light beam on passage through a polariser and the observed coincidence curves. The former would be expected to follow Malus' Law fairly closely, though experimental evidence here is not so easy to obtain. We are interested in the behaviour of very weak light and the law may be slightly different from that of stronger light.

My question is:
What is exact (theoretical) relation between QM predictions, realistic predictions and Malus law.

Thanks

 

[DrChinese]

DrChinese,
I am retrieving my question because I realized how wrong it is. Indeed, the "the red line" is for spin particles and not for polarized photons.

Reading the wiki link http://en.wikipedia.org/wiki/Local_hidden_variable_theory provided on your page I found the following graph:

Fig. 2: The realist prediction (solid curve) for quantum correlation in an optical Bell test. The quantum-mechanical prediction is the dotted curveIn this article the relation between Malus Law and predictions are mentioned multiple times (see below), but I still can't grasp their exact relationship.

...

My question is:
What is exact (theoretical) relation between QM predictions, realistic predictions and Malus law.

Thanks

What would happen if you measured pairs of photons that were NOT entangled but had the same, random polarizations? You would get the graph above (solid line) which is also a "realistic" scenario/hypothesis. That differs noticeably from the results you get from entangled pairs (dashed line). So you can reject the hypothesis.

 

[Alien8]

DrChinese,

Fig. 2: The realist prediction (solid curve) for quantum correlation in an optical Bell test. The quantum-mechanical prediction is the dotted curve

In this article the relation between Malus Law and predictions are mentioned multiple times (see below), but I still can't grasp their exact relationship.

My question is:
What is exact (theoretical) relation between QM predictions, realistic predictions and Malus law.

Solid curve is the prediction based on Malus' law. It's 1/2 from QM prediction. To get that I think you work out independent probabilities where Pa(+) = Pb(+) and Pab(+ and +) = Pa(+)Pb(+).

3). By varying our assumptions, it seems possible that the realist prediction could approach the quantum-mechanical one within the limits of
experimental error (Marshall, 1983), though clearly a compromise must be reached. We have to match both the behaviour of the individual light beam on passage through a polariser and the observed coincidence curves. The former would be expected to follow Malus' Law fairly closely, though experimental evidence here is not so easy to obtain. We are interested in the behaviour of very weak light and the law may be slightly different from that of stronger light.

I think to check Malus' law all we need is to look at Alice and Bob's readings individually. Total number of "+" should be about the same as "-" no matter what angle settings is at either Alice or Bob's analyzer. I don't see why would that not be easy to verify, but I also don't see that would change anything because it says nothing about how the two readings are supposed to match against each other. In local theory there is no any connection between the two events so the rest is in the hands of probability theory, and because the two events are supposed to be independent we use the equation for independent probabilities: P(A and B) = P(A)P(B), which leads to that solid cure. Or something like that, I'm not quite sure how to work out the integral.

 

[miosim]

In local theory there is no any connection between the two events so the rest is in the hands of probability theory, and because the two events are supposed to be independent we use the equation for independent probabilities: P(A and B) = P(A)P(B), which leads to that solid cure.

It starts making sense to me. I need to study this statistical approach in more details. I expect that this statistical approach doesn't treat a pair of particle as classical objects. These particles still should exhibit "weird" quantum behavior cased by some "weird" hidden variables.

I should take a brake until I better understand the statistical approach.

Thank you for the help

 

[DrChinese]

I think to check Malus' law all we need is to look at Alice and Bob's readings individually. Total number of "+" should be about the same as "-" no matter what angle settings is at either Alice or Bob's analyzer. I don't see why would that not be easy to verify, but I also don't see that would change anything because it says nothing about how the two readings are supposed to match against each other. In local theory there is no any connection between the two events so the rest is in the hands of probability theory, and because the two events are supposed to be independent we use the equation for independent probabilities: P(A and B) = P(A)P(B), ...

You are correct. The sentence you highlighted in the wiki article and the sentence that follows, these should not appear in the article and reflect a bias by the writer (who is a local realist). I can tell from the reference to Marshall (1983). Local realists love to add stuff into the wiki pages and it is a lot of work to keep it out. I occasionally police the Bell page for that. :)

 

[moriheru]

$\psi(x) = \sum\limits_{n} \phi_{n}(x)$.

Not very helpfull but anyway...one usually replaces the summs with integrals or sums stepse of lim a-->0

 

[stevendaryl]

Solid curve is the prediction based on Malus' law. It's 1/2 from QM prediction. To get that I think you work out independent probabilities where Pa(+) = Pb(+) and Pab(+ and +) = Pa(+)Pb(+).
I think to check Malus' law all we need is to look at Alice and Bob's readings individually. Total number of "+" should be about the same as "-" no matter what angle settings is at either Alice or Bob's analyzer. I don't see why would that not be easy to verify, but I also don't see that would change anything because it says nothing about how the two readings are supposed to match against each other. In local theory there is no any connection between the two events so the rest is in the hands of probability theory, and because the two events are supposed to be independent we use the equation for independent probabilities: P(A and B) = P(A)P(B), which leads to that solid cure. Or something like that, I'm not quite sure how to work out the integral.

No, a local theory doesn't imply independence of the results, and it does not imply $P(A and B) = P(A)P(B)$. The reason why not is that even though $A$ can't influence $B$, and $B$ can't influence $A$, there might be a third cause that influences both. That's what the "local hidden variables" idea is all about: whether the correlations can be explained by assuming that there is a cause (the hidden variable) that influences both measurements.

A locally realistic model based on Malus' law is this: assume that in the twin-photon version of EPR, two photons are created with the same random polarization angle $\phi$. If Alice's filter is at angle $\alpha$ then she detects a photon with probability $cos^2(\alpha - \phi)$. Similarly, if Bob's filter is at angle $\beta$, then he detects a photon with probability $cos^2(\alpha - \phi)$. The correlation $E(\alpha, \beta)$ would then be:

$E(\alpha, \beta) = P_{++} + P_{--} - P_{+-} - P_{-+}$

where $P_{++}$ is the probability both Alice and Bob detect a photon, $P_{+-}$ is the probability Alice detects one and Bob doesn't, etc.

For this model,
$P_{++} = \frac{1}{\pi} \int d\phi cos^2(\alpha - \phi) cos^2(\beta - \phi) = \frac{1}{8} + \frac{1}{4}cos^2(\alpha - \beta)$
$P_{+-} = \frac{1}{\pi} \int d\phi cos^2(\alpha - \phi) sin^2(\beta - \phi) = \frac{1}{8} + \frac{1}{4}sin^2(\alpha - \beta)$
$P_{-+} = \frac{1}{\pi} \int d\phi sin^2(\alpha - \phi) cos^2(\beta - \phi) = \frac{1}{8} + \frac{1}{4}sin^2(\alpha - \beta)$
$P_{--} = \frac{1}{\pi} \int d\phi sin^2(\alpha - \phi) sin^2(\beta - \phi) = \frac{1}{8} + \frac{1}{4}cos^2(\alpha - \beta)$

So
$E(\alpha, \beta) = \frac{1}{2}(cos^2(\alpha - \beta) - sin^2(\alpha - \beta)) = \frac{1}{2} cos(2 (\alpha - \beta))$

That's exactly 1/2 of the QM prediction.

 

[Alien8]

Thanks for that. I'll take your answer to the other thread about CHSH derivation which is about photons and polarizers rather than magnetic moments and magnets this thread is about.

 

[miosim]

In local theory there is no any connection between the two events so the rest is in the hands of probability theory, and because the two events are supposed to be independent we use the equation for independent probabilities: P(A and B) = P(A)P(B), which leads to that solid cure.

As I understand, Einstein accepts the the prediction of quantum mechanics; he just disagree about causes.
So why the predicted probabilities in the Bell's theorem for the local realism and for QM are different? It seams that per Einstein they should be the same.

 

[stevendaryl]

Thanks for that. I'll take your answer to the other thread about CHSH derivation which is about photons and polarizers rather than magnetic moments and magnets this thread is about.

Some of the graphs posted are about the spin-1/2 experiment, and some are about the photon case. The graph in your message #77 is about photons, not electrons. The graph in #66 is about electrons.

The arguments are basically the same in either case, but the details are different, such as the fact that perfect anti-correlation is at 90 degrees for the photon case, but at 180 degrees for the electron case.

 

[miosim]

A locally realistic model based on Malus' law

If a locally realistic model is based on Malus' law, does it means that QM model is in conflict with the Malus' law because it has a different than realistic model predicted probability?

 

[stevendaryl]

If a locally realistic model is based on Malus' law, does it means that QM model is in conflict with the Malus' law because it has a different than realistic model predicted probability?

No, not really. Malus' law is about how the intensity of polarized light is attenuated by a polarizing filter. It doesn't say anything about photons. QM agrees with Malus' law in those cases where the number of photons is very large.

Malus' law says nothing about individual photons, or the probability that two different photons pass through two different filters. What I was saying is that you could come up with a law for photons inspired by Malus' law that would apply probabilistically to individual photons, but such a law doesn't agree with experiment.

Since Malus' law doesn't say anything about individual photons, no experiment involving individual photons can really contradict Malus' law.

 

[miosim]

Malus' law says nothing about individual photons, or the probability that two different photons pass through two different filters.

Is the Malus' law about intensity of polarized light attenuated by a polarizing filter could be derived from the QM of individual photons?

 

[stevendaryl]

Is the Malus' law about intensity of polarized light attenuated by a polarizing filter could be derived from the QM of individual photons?

Yes. QM predicts that if a photon passes through one filter, then it will pass through a second filter with probability $cos^2(\theta)$, where $\theta$ is the angle between the two filters. So if intensity is proportional to the number of photons that pass through, then this makes the same prediction as Malus' law.

 

[miosim]

Yes. QM predicts that if a photon passes through one filter, then it will pass through a second filter with probability cos 2 (θ) cos^2(\theta), where θ \theta is the angle between the two filters. So if intensity is proportional to the number of photons that pass through, then this makes the same prediction as Malus' law.

A locally realistic model based on Malus' law is this: assume that in the twin-photon version of EPR, two photons are created with the same random polarization angle ϕ \phi ...

Would be fair to say that the differences between realistic and QM models in the Bell's theorem is that realistic model is equivalent to the photon that already interacted with a polarizer while for the QM model photon didn't have any interaction yet?

 

[DrChinese]

So why the predicted probabilities in the Bell's theorem for the local realism and for QM are different? It seams that per Einstein they should be the same.

Einstein died before Bell published. He never knew, and would have been forced to re-assess his position had he known.

 

[DrChinese]

Would be fair to say that the differences between realistic and QM models in the Bell's theorem is that realistic model is equivalent to the photon that already interacted with a polarizer while for the QM model photon didn't have any interaction yet?

No. Realistic models assume there are values for observables at all times. For QM, observables take a value at the time of observation and depending on the nature of the observation.

It is difficult to give more specifics on realistic models because a) they don't match experiment; and b) you can make up as many wrong ones as you like.

 

[miosim]

Einstein died before Bell published. He never knew, and would have been forced to re-assess his position had he known.

Unfortunately he didn't have opportunity to respond to Bell's theorem.

 

[miosim]

It is difficult to give more specifics on realistic models because a) they don't match experiment ...

If the incorrect model was chosen it should not be a surprise that it doesn't match experiment.
I would like to have a better understanding of how the realistic models was derived, probably from the EPR paper and I believe this derivation was sufficiently scrutinized. Do you have any references for this topics?

Thanks

 

[miosim]

DrChinese,
I found online the article about Bell’s theorem that talk about issues I concern with.

http://www.scholarpedia.org/article/Bell's_theorem#factorizability

What is your opinion about this article? Does it represent the mainstream view on Bell’s theorem or it tilts toward the “realism” in QM (opposite to Copenhagen interpretation) so I should take it as one point of view only?

 

[stevendaryl]

If the incorrect model was chosen it should not be a surprise that it doesn't match experiment.
I would like to have a better understanding of how the realistic models was derived, probably from the EPR paper and I believe this derivation was sufficiently scrutinized. Do you have any references for this topics?

Thanks

Well, in this thread, we've discussed two different local hidden variables models, and neither one matches the predictions of QM. Two examples doesn't prove anything, which is why it is so important that Bell proved a theorem showing that there are no locally realistic models at all that reproduce the predictions of quantum mechanics.

 

[DrChinese]

DrChinese,
I found online the article about Bell’s theorem that talk about issues I concern with.

http://www.scholarpedia.org/article/Bell's_theorem#factorizability

What is your opinion about this article? Does it represent the mainstream view on Bell’s theorem or it tilts toward the “realism” in QM (opposite to Copenhagen interpretation) so I should take it as one point of view only?

I don't consider this a useful article. It re-writes history and emphasis to be consistent with Norsen's well-known views on the matter. The authors are Bohmians and it is written from an unabashed perspective to push that intepretation.

It's sad really, because the science of Bohmian Mechanics does not need a distorted historical derivation to give it relevance. Bell himself was an advocate, probably their best advocate in the long run.

 

[atyy]

I don't consider this a useful article. It re-writes history and emphasis to be consistent with Norsen's well-known views on the matter. The authors are Bohmians and it is written from an unabashed perspective to push that intepretation.

It's sad really, because the science of Bohmian Mechanics does not need a distorted historical derivation to give it relevance. Bell himself was an advocate, probably their best advocate in the long run.

Why do you consider the article inaccurate?

 

[DrChinese]

Why do you consider the article inaccurate?

I didn't use the word "inaccurate", preferring to indicate it is not useful to any understanding of the subject. I wouldn't read it to learn about QM, history of EPR/Bell, or even BM. An example: "The new strategy also sheds some light on the meaning of locality." Locality is all that this article indicates is at the root of Bell, which is a denial of the role of realism.

That is consistent for Norsen (I am quite sure he wrote most of the historical part as I am well familiar with his writing style). In his mind, violation of a Bell Inequality equates to a proof of non-locality. That view is generally rejected by the community in favor of one in which realism may alternately (or additionally) be rejected. You will find few in the scientific community who advocate a realistic view of QM regardless of the locality issue.

But hey, read away and judge for yourself! :)

 

[atyy]

Does it represent the mainstream view on Bell’s theorem or it tilts toward the “realism” in QM (opposite to Copenhagen interpretation) so I should take it as one point of view only?

One should not take Copenhagen to be necessarily anti-realist. Copenhagen assumes a commonsense realism by virtue of the Heisenberg cut. It is agnostic about the realism of the wave function, and takes an operational or instrumental approach to the wave function as a useful tool for calculating the probabilities of events. Most versions of Copenhagen assume enough reality to agree that quantum mechanics predicts the violation of Bell inequalities by systems at spacelike separation. There are versions of Copenhagen such as Quantum Bayesianism which try to avoid this, but these are not the only flavours of Copenhagen. Historically, some versions of Copenhagen have denied the existence of hidden variables, because of von Neumann's purported proof against the existence of hidden variables, which was not widely known to be flawed before Bell. Modern versions of Copenhagen do not necessarily deny the possibility of hidden variables.

 

[atyy]

I didn't use the word "inaccurate", preferring to indicate it is not useful to any understanding of the subject. I wouldn't read it to learn about QM, history of EPR/Bell, or even BM. An example: "The new strategy also sheds some light on the meaning of locality." Locality is all that this article indicates is at the root of Bell, which is a denial of the role of realism.

That is consistent for Norsen (I am quite sure he wrote most of the historical part as I am well familiar with his writing style). In his mind, violation of a Bell Inequality equates to a proof of non-locality. That view is generally rejected by the community in favor of one in which realism may alternately (or additionally) be rejected. You will find few in the scientific community who advocate a realistic view of QM regardless of the locality issue.

But hey, read away and judge for yourself! :)

I see. But perhaps the definition of "realism" is debated? I suspect Norsen would consider Many-Worlds to be realistic, whereas I think you would not?

 

[DrChinese]

I see. But perhaps the definition of "realism" is debated? I suspect Norsen would consider Many-Worlds to be realistic, whereas I think you would not?

Not sure about that (MWI). But it would not be fair to say the definition of "realism" is debated so much as it is distorted. Norsen's position is quite clear in his paper "Against 'Realism'":

http://arxiv.org/abs/quant-ph/0607057

His non-mainstream position is obvious from the extract:

"Carefully surveying several possible meanings, we argue that all of them are flawed in one way or another as attempts to point out a second premise (in addition to locality) on which the Bell inequalities rest... We thus suggest that the phrase `local realism' should be banned from future discussions of these issues, and urge physicists to revisit the foundational questions behind Bell's Theorem."

He and I have discussed this ad infinitum, in fact our discussions may have spurred him to write that paper. :) Norsen is regarded as brilliant in the area, but has been harshly reviewed by Shimony and others. I would be happy to refute him any day of the week, as it is not that hard.

 

[wle]

Locality is all that this article indicates is at the root of Bell, which is a denial of the role of realism.

Well what is the role of "realism"? I know that the default catchphrase many authors use is that Bell's theorem rules out "local realism", but I've never seen a good explanation of what "realism" actually means in this context or why it's a necessary part of the argument. If it just means measurement outcomes in an experiment being predetermined, then that's not necessary as an assumption in order to derive Bell inequalities (Bell himself was quite explicit about this in later essays, starting at least as early as the mid 1970s).

That is consistent for Norsen (I am quite sure he wrote most of the historical part as I am well familiar with his writing style). In his mind, violation of a Bell Inequality equates to a proof of non-locality. That view is generally rejected by the community in favor of one in which realism may alternately (or additionally) be rejected. You will find few in the scientific community who advocate a realistic view of QM regardless of the locality issue.

I'm not aware of such a consensus, at least among people who actually do research on the topic. There's certainly some disagreement on the terminology and the finer points of what Bell's theorem is about, but as far as I'm aware, Norsen's expositions on Bell's theorem are known about and at at least reasonably well regarded in the community. I'm certainly not aware of any overwhelming consensus that "realism", "determinism", "counterfactual definiteness", etc., is a necessary or important ingredient in Bell's theorem. For instance, the terminology that I'm most familiar with is that the correlations that satisfy Bell inequalities are just called the "local set" or the "local polytope".

 

[DrChinese]

Well what is the role of "realism"? I know that the default catchphrase many authors use is that Bell's theorem rules out "local realism", but I've never seen a good explanation of what "realism" actually means in this context or why it's a necessary part of the argument.

How many quotes from folks like Aspect and Zeilinger would it take to convince you that "local realism" is what is ruled out by Bell? EPR is all about realism (defined as simultaneous elements of reality there, as well as by Bell). Locality is an afterthought to EPR, as they assumed there would be no spooky action at a distance. As to why it is necessary to the Bell argument, simply look after Bell's (14) and you will see realism introduced as an assumption (let c be a unit vector...).

Honestly, I was asked my opinion and gave it. After hours of discussing this with Travis, I am not likely to change my opinion any more than he is likely to change his. If we want to continue this discussion, we should do it outside of this thread as I think we have strayed off target.

 

[wle]

How many quotes from folks like Aspect and Zeilinger would it take to convince you that "local realism" is what is ruled out by Bell? EPR is all about realism (defined as simultaneous elements of reality there, as well as by Bell). Locality is an afterthought to EPR, as they assumed there would be no spooky action at a distance. As to why it is necessary to the Bell argument, simply look after Bell's (14) and you will see realism introduced as an assumption (let c be a unit vector...).

Honestly, I was asked my opinion and gave it. After hours of discussing this with Travis, I am not likely to change my opinion any more than he is likely to change his. If we want to continue this discussion, we should do it outside of this thread as I think we have strayed off target.

This isn't about me personally convincing you or vice versa. If you want to hold the opinion that Bell's theorem rules out something called "local realism", that's one thing and it can be debated. It's certainly how a lot of physicists and textbooks would describe Bell's theorem. But if you're going to insist that this is how 99% of theorists working in the field today would explain Bell's theorem and Norsen represents a 1% anti-mainstream fringe stance, then that's not my impression based on my exposure to what's going on in the field. For instance, there was a review article published on the topic earlier this year [1] (which, incidentally, I'd recommend to anyone looking for a modern overview of the field) that hardly mentions realism at all.

[1] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, "Bell nonlocality", Rev. Mod. Phys. 86, 419 (2014), arXiv:1303.2849 [quant-ph].

 

[DrChinese]

[1] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, "Bell nonlocality", Rev. Mod. Phys. 86, 419 (2014), arXiv:1303.2849 [quant-ph].

You are correct that "realism" is not mentioned. This definitely follows Norsen's reasoning. I am surprised to see Cavalcanti in the list of authors, as he had recently written about "local realism" in the same vein as I. So you may be correct that the tide has changed.