Can grandpa understand the Bell's Theorem?

[edguy99]

...It seems like in that thread you are talking about a model where certain particles have properties that make them "defective" for particular measurement settings, if so I commented briefly on such models at the end of [post=3270631]this post[/post]:

I would not call them defective, but they do have the property that they cannot be measured in certain directions. Specifically, if you are talking about a bloch sphere as shown http://en.wikipedia.org/wiki/Rabi_problem" . The article talks about the "pseudo-spin vector" (ie, the axis of the spinning vector that is rotating around the axis of measurement). Notice, to quote the article, they are "throwing out terms with high angular velocity". Specifically, they are talking about trying to measure a spinning particle at 90 degrees to its spin and the inability of a bloch sphere to react to that measurement.

Videos of spinning bloch spheres subjected to a magnetic measuring field can be seen http://www.animatedphysics.com/videos/larmorfrequency.htm" . Notice the amount of precession going on in the lower right hand video where you have a higher angle of precession and imagine this same particle tilted a full 90 degrees. The green pseudo-spin vector would have to be perpendicular to the spin and you can imagine lots of particles that could not handle this.

 

[Jonathan Scott]

The 0/45/90 degree examples are not meaningful because simple models can approach these predictions.

I find this statement slightly confusing, perhaps requiring more context. For photon polarization, the angles 0/45/90 degrees mean that if one end is a pure state the other end is too, so a classical explanation is trivial. However, for observing the spin of a fermion (where observation angles are doubled), 0/45/90 are a useful set of relative angles for illustrating Bell's theorem, in the same way that 0/22.5/45 are for photons, provided that the last angle is achieved by turning both ends by the middle angle.

 

[JesseM]

I would not call them defective, but they do have the property that they cannot be measured in certain directions.

That's all that Fine meant by "defective" (I was just mirroring his terminology)--if you try to measure them at a given angle you won't get a + or - result that can be included in your data set. Anyway, like I said this isn't relevant to the purely theoretical question of whether Bell's theorem is correct, since the theorem deals with the incompatibility between local realism and the theoretical predictions of QM which don't include any such notion of particles that are impossible to measure at certain angles. And for the experimental question, this possibility is part of the "detector efficiency loophole" which can be closed by using a version of a Bell inequality that takes into account limits on detector efficiency.

 

[DrChinese]

...I don't really understand the details of where they get the straight line...

To tell the truth, I don't think I've actually seen an formal analysis of this (not that it is needed for anything). Intuitively, I just think of that as being a solution in which the slope is constant and nonzero. That constant slope being needed to handle the case like this (where actually the -22.5 degrees and 22.5 degrees values could be anything):

f(-22.5,0) = f(0,22.5)
f(-22.5,0) + f(0,22.5) = f(-22.5, 22.5)

So I guess that means I haven't added anything useful.

 

[DrChinese]

I find this statement slightly confusing, perhaps requiring more context. For photon polarization, the angles 0/45/90 degrees mean that if one end is a pure state the other end is too, so a classical explanation is trivial. However, for observing the spin of a fermion (where observation angles are doubled), 0/45/90 are a useful set of relative angles for illustrating Bell's theorem, in the same way that 0/22.5/45 are for photons, provided that the last angle is achieved by turning both ends by the middle angle.

That's correct. I always use photon examples. Yours works too.

 

[DrChinese]

I would not call them defective, but they do have the property that they cannot be measured in certain directions.

Don't you see that this is easily testable with entangled pairs?

Or are you saying that BOTH of a pair are "invisible"? In which case nothing is explained vis a vis Bell.

 

[Jonathan Scott]

...and as you said, that would be "equivalent to the QM special case where the emitted particles are prepared with polarization aligned with [one of] the initial observation devices."

Almost equivalent, but not quite... if the polarizations were aligned, the two would always agree the same way. Both would always be vertical, for instance. If the polarizations are not aligned, then you'd have both always agreeing, but horizontal half the time and vertical the other half the time.

Your interpretation is what I meant; I should have made it clearer that by "aligned" I meant oriented in such a way that the initial polarization was in a pure state relative to the observation direction.

 

[JDoolin]

On further thought, I realized that if the experiment worked to my expectation, then even when the two crystals are perfectly aligned, you would not get perfect agreement. I think this is what you are referring to that I boldfaced above. If the source creates photon pairs of a random polarization with "uniform distribution" then most of the time the photon would not be aligned with either polarizer. For instance if the polarization was 0, or 90 degrees, there would be a 100% agreement, but if the polarization was 45 degrees off, there would only be a 50% agreement. I made up a spreadsheet to take the avereage agreement of all angles from 0 to 357 every 3 degree increment, and found that at best, you can expect a 75% agreement rate. (There's probably a more elegant method of doing this with calculus).

By this method, I also got these values:
Perfectly aligned crystals: 75% agreement
22.5 degrees off: 68% agreement
45 degrees off: 50% agreement


But if I understand correctly, the actual experiment yields:
Perfectly aligned crystals: 100% agreement
22.5 degrees off: 85% agreement
45 degrees off: 50% agreement

...and as you said, that would be "equivalent to the QM special case where the emitted particles are prepared with polarization aligned with [one of] the initial observation devices."

Almost equivalent, but not quite... if the polarizations were aligned, the two would always agree the same way. Both would always be vertical, for instance. If the polarizations are not aligned, then you'd have both always agreeing, but horizontal half the time and vertical the other half the time.

Your interpretation is what I meant; I should have made it clearer that by "aligned" I meant oriented in such a way that the initial polarization was in a pure state relative to the observation direction.

Okay... just to make sure, because I don't have the results of any experiment. I want to verify that the results of the experiment yield 100%, 85%, 50%... Not 75%, 68%, 50%.

If you do yield 100%, 85%, 50% then it makes me think "you MUST have a polarized source." But you could check that by turning both crystals together. If the results change, then you probably have a polarized source.

If the results don't change, but you still have (aligned) 100%, (22.5 degrees) 85%, and (45 degrees) 50%, then you've got an unpolarized source, but its somehow being forced into the same polarization at both ends. At this point, I'd say you've already got "spooky action at a distance," and you don't need to go into Bell's Theorem to recognize it.

 

[Jonathan Scott]

Okay... just to make sure, because I don't have the results of any experiment. I want to verify that the results of the experiment yield 100%, 85%, 50%... Not 75%, 68%, 50%.

Yes, the 100%, 85%, 50% values are the probabilities of the two-state results matching according to QM theory and experiment. The results of a run are usually expressed as correlations, equal to probability(same) minus probability(different), giving roughly 1, 0.7, 0.

I think that the obvious classical model which uses Malus' law independently for each photon with a random initial polarization of the pair gives exactly half the correlation of QM, like the QM result diluted by a similar amount of "noise". In that case, the expected match rates would indeed be around 75%, 68%, 50%, giving correlations of 0.5, 0.36, 0.

One of the objections to some early experiments in this area was that statistical adjustments to eliminate "noise" would also hide the distinction between QM and classical predictions, but improved experiments eliminated this problem.

 

[DrChinese]

Yes, the 100%, 85%, 50% values are the probabilities of the two-state results matching according to QM theory and experiment. The results of a run are usually expressed as correlations, equal to probability(same) minus probability(different), giving roughly 1, 0.7, 0.

I think that the obvious classical model which uses Malus' law independently for each photon with a random initial polarization of the pair gives exactly half the correlation of QM, like the QM result diluted by a similar amount of "noise". In that case, the expected match rates would indeed be around 75%, 68%, 50%, giving correlations of 0.5, 0.36, 0.

One of the objections to some early experiments in this area was that statistical adjustments to eliminate "noise" would also hide the distinction between QM and classical predictions, but improved experiments eliminated this problem.

A. The Product State statistics follow the formula (for matches):

.25+ (cos^2(theta)/2)

which yields the other series you mention. In a local realistic model that follows Malus, that is what you would expect to see. Thus the match rate ranges from .25 to .75.

B. Obviously, that is far away from the QM prediction of cos^2(theta), which ranges from 0 to 1. There aren't any local realistic models that follow this prediction, of course. You can also have the local realistic model which DOES range from 0 to 1 on a straight line. Of course, that then does NOT follow Malus.

 

[JDoolin]

A. The Product State statistics follow the formula (for matches):

.25+ (cos^2(theta)/2)

which yields the other series you mention. In a local realistic model that follows Malus, that is what you would expect to see. Thus the match rate ranges from .25 to .75.

B. Obviously, that is far away from the QM prediction of cos^2(theta), which ranges from 0 to 1. There aren't any local realistic models that follow this prediction, of course. You can also have the local realistic model which DOES range from 0 to 1 on a straight line. Of course, that then does NOT follow Malus.

Yes. If you happen to try using the spreadsheet I put in post 200, you can put in this formula:
=0.25+COS(D3)^2/2
It matches the figure in cell F2, regardless of what angle you put in cell C3. But, as I mentioned before, there's probably a much more elegant way to do it with calculus, and in any case, it fails to reproduce the result of the experiment.

From making the assumption that the photons have a "local realistic" polarization variable, my most immediate interpretation of the experiment, is that somehow each pair of photons align themselves with one or the other of the crystals.

And that suggests that somehow the photon "knows in advance" which way the polarizer is going to be oriented "when" it gets to it.

 

[edguy99]

Don't you see that this is easily testable with entangled pairs?

Or are you saying that BOTH of a pair are "invisible"? In which case nothing is explained vis a vis Bell.

Yes, since the polarization match means: failure to get through one detector implies its partner will not get through either. I can try and reword a bit to clarify:

A particle modeled with the properties of a bloch sphere as shown http://en.wikipedia.org/wiki/Bloch_sphere" . This is represented below by the red area on Bob and Alice measuring devices. This picture shows that Bob and Alice measure the same up/down for particles that reach the detector, no matter the orientation of their measuring devices as long as they both measure at the same angle:

If Alice tilts here measing device by 90 degrees relative to Bob, Bob and Alice will measure the predicted 50% matches and 50% different. When Alice tilts her measuring device by 45 degrees she gets the 85% match and 15% difference with Bob that QM predicts and experiments confirm:

 

[DrChinese]

A particle modeled with the properties of a bloch sphere as shown http://en.wikipedia.org/wiki/Bloch_sphere" . ...

OK, let stop here before proceeding.

What does this have to do with anything? Entangled photons do not have any such "area" that "cannot be measured" as far as anyone knows. I seriously doubt there is anything like this with pairs of entangled 1/2 spin particles either, but really who cares? Virtually all Bell tests are with photons or other particles where this is not meaningful.

My point being that it would be nice if you were presenting an example that doesn't try to exploit some anomaly that is not general to entangled particles. Because if it is not general, it is going to be experimentally refuted by other tests.

 

[edguy99]

... Virtually all Bell tests are with photons or other particles where this is not meaningful.

I feel it is meaningful for photons. Consider the representation of a photon polarization show http://en.wikipedia.org/wiki/Polarization_(waves)" . These are taken directly from the surface of a spinning bloch sphere over time.

 

[DrChinese]

I feel it is meaningful for photons. Consider the representation of a photon polarization show http://en.wikipedia.org/wiki/Polarization_(waves)" . These are taken directly from the surface of a spinning bloch sphere over time.

OK, for whatever purpose you want to model this, sure. But you can't just say "there is a mysterious effect that causes some photon pairs to be invisible" and then say this effect should be accounted for. If they are invisible, we can't ever see them and it is as if they don't exist. So you should account for them that way.

If you are creating a model, you can give it any properties/rules you want. But then I get to bounce that against actual experiments! (P.S. There are NO experiments indicating that photons have any such property as having some angle where they are less visible. And there are plenty of ways to demonstrate that using entangled particle pairs.)

 

[edguy99]

OK, for whatever purpose you want to model this, sure. But you can't just say "there is a mysterious effect that causes some photon pairs to be invisible" and then say this effect should be accounted for. If they are invisible, we can't ever see them and it is as if they don't exist. So you should account for them that way.

If you are creating a model, you can give it any properties/rules you want. But then I get to bounce that against actual experiments! (P.S. There are NO experiments indicating that photons have any such property as having some angle where they are less visible. And there are plenty of ways to demonstrate that using entangled particle pairs.)

One thing that would destroy this model is if you could really measure 50% of the photons with a linear polarizer. I know that many calculations are done on HN50 polarizers, but the best "real" polarizing sheets that I could find on the internet were HN38. Is there a reason "ideal" HN50 polarizers don't exist?

 

[DrChinese]

One thing that would destroy this model is if you could really measure 50% of the photons with a linear polarizer. I know that many calculations are done on HN50 polarizers, but the best "real" polarizing sheets that I could find on the internet were HN38. Is there a reason "ideal" HN50 polarizers don't exist?

Not sure what you are getting at. Most experiments are done with beam splitters. There is some trade off between transmission efficiency and the quality of the output beam, but I would say that at least 95% of the light gets through irrespective of the input angle. So you are fishing around where any hypothetical effect would be glaringly obvious.

 

[JDoolin]

One thing that would destroy this model is if you could really measure 50% of the photons with a linear polarizer. I know that many calculations are done on HN50 polarizers, but the best "real" polarizing sheets that I could find on the internet were HN38. Is there a reason "ideal" HN50 polarizers don't exist?

But my understanding was that the bi-refringent crystals they used gave you very close to a 100% detection rate. Also, I can't find, at least on the internet, anything saying what HN32, HN38s or HN42 mean.

 

[edguy99]

But my understanding was that the bi-refringent crystals they used gave you very close to a 100% detection rate. Also, I can't find, at least on the internet, anything saying what HN32, HN38s or HN42 mean.

Its not the issure of the crystal but the detection. The example cited http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" shows a very clear diagram setup at Figure 1. The polarizers in question are labeled PA Polarizer A and PB Polarizer B.

As I understand the meaning of HN50 is you start with linear polarized light coming at you that could be polarized in any direction. The HN50 designation means that 1/2 the light will get through. If you imagine a clock, then "up" would be any photon polarized between 9 through noon to 3 oclock. "down" would be any photon polarized between 3 through 6 to 9 oclock. The fact that no HN50 polarizers exist, suggests that a HN32 polarizer may well only be detecting "up" light in the angles 10 oclock to 2 oclock and the other polarizer is detecting from 4 oclock to 8 oclock.

It is clear from the link, that they are only counting "detected" photons that have passed these polarizers and it seems clear from the properties of polarizers that there must be a fair number of "undetected" photons kicking around.

 

[DrChinese]

The fact that no HN50 polarizers exist, suggests that a HN32 polarizer may well only be detecting "up" light in the angles 10 oclock to 2 oclock and the other polarizer is detecting from 4 oclock to 8 oclock.

It is clear from the link, that they are only counting "detected" photons that have passed these polarizers and it seems clear from the properties of polarizers that there must be a fair number of "undetected" photons kicking around.

This is ridiculous! Are you not aware that this would be obvious with even the most simple of experiments? All you have to do is rotate a polarized source across 90 degrees and you would notice that the intensity varies differently than the cos^2 function. That doesn't happen.

I keep trying to point out to you WHY your idea makes no sense and yet you persist. It is experimentally, demonstrably WRONG and 200 years of experiments (since Malus) show the same thing. There is NO SUCH EFFECT, and you may as well admit it and move on to the next phase of your understanding.

 

[edguy99]

This is ridiculous! Are you not aware that this would be obvious with even the most simple of experiments? All you have to do is rotate a polarized source across 90 degrees and you would notice that the intensity varies differently than the cos^2 function. That doesn't happen.

I keep trying to point out to you WHY your idea makes no sense and yet you persist. It is experimentally, demonstrably WRONG and 200 years of experiments (since Malus) show the same thing. There is NO SUCH EFFECT, and you may as well admit it and move on to the next phase of your understanding.

This appears to be a different experiment from the one you cited me before. I would be happy to respond if you would give more details to the experiment you have in mind, perhaps in a new post as it is a new topic (and perhaps a link so our wording can be consistent).

 

[DrChinese]

This appears to be a different experiment from the one you cited me before. I would be happy to respond if you would give more details to the experiment you have in mind, perhaps in a new post as it is a new topic (and perhaps a link so our wording can be consistent).

Can you imagine taking a polarized light source and running it through a polarizer? If you measure the intensity of the light as you rotate it across 90 degrees, you obtain Malus' Law. You can verify this yourself for $669 if you don't accept the hundreds of thousands of experiments already performed indicating the same result over the past 200 years:

http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=53874&Detail=1

There is NO such thing as the effect you describe where light "disappears" at certain settings OTHER THAN following Malus' cos^2 rule. And guess what? Entangled photons go through a polarizer the same as unentangled photons. Same exact setup. And by the way, it works the same for both polarization entangled photons and non-polarization entangled photons. Same result every time.

 

[edguy99]

Can you imagine taking a polarized light source and running it through a polarizer? If you measure the intensity of the light as you rotate it across 90 degrees, you obtain Malus' Law. You can verify this yourself for $669 if you don't accept the hundreds of thousands of experiments already performed indicating the same result over the past 200 years:

http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=53874&Detail=1

There is NO such thing as the effect you describe where light "disappears" at certain settings OTHER THAN following Malus' cos^2 rule. And guess what? Entangled photons go through a polarizer the same as unentangled photons. Same exact setup. And by the way, it works the same for both polarization entangled photons and non-polarization entangled photons. Same result every time.

Thank you for the link. The reason this is a different experiment is that in this case, you are passing the same photon through a compination of first one, then a second polarizer. When doing the calculations, do you assume a hn50 polarizer is used? I would prefer to discuss a link where it is a little clearer what calculations are being used.

 

[DrChinese]

Thank you for the link. The reason this is a different experiment is that in this case, you are passing the same photon through a compination of first one, then a second polarizer. When doing the calculations, do you assume a hn50 polarizer is used? I would prefer to discuss a link where it is a little clearer what calculations are being used.

Arrgh. It is an experiment. No assumptions are necessary. You record the results and plot them.

This may shock you, but the same thing holds when you remove one of the polarizers; as lasers, being coherent, are (mostly) polarized in a single orientation. Again, you can try this for $669.

And just to remind everyone reading of the relevance to Bell's Theorem: edguy99's "model" is intended to "explain" Bell test results showing incompatibility with local realism. And the important feature of ANY such model is that it will NOT match the predictions of QM. One of which is Malus. Note that if edguy99 was correct, Malus would be wrong.

 

[edguy99]

Arrgh. It is an experiment. No assumptions are necessary. You record the results and plot them.

This may shock you, but the same thing holds when you remove one of the polarizers; as lasers, being coherent, are (mostly) polarized in a single orientation. Again, you can try this for $669.

And just to remind everyone reading of the relevance to Bell's Theorem: edguy99's "model" is intended to "explain" Bell test results showing incompatibility with local realism. And the important feature of ANY such model is that it will NOT match the predictions of QM. One of which is Malus. Note that if edguy99 was correct, Malus would be wrong.

Sorry, you lost me. You are correct, I could buy the equipment, do the experiment, post the results of the experiment and then discuss them, but if there are posted results of this experiment, I think it would be easier.

Also, I have not suggested Malus is wrong?

 

[JDoolin]

Its not the issure of the crystal but the detection. The example cited http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" shows a very clear diagram setup at Figure 1. The polarizers in question are labeled PA Polarizer A and PB Polarizer B.

As I understand the meaning of HN50 is you start with linear polarized light coming at you that could be polarized in any direction. The HN50 designation means that 1/2 the light will get through. If you imagine a clock, then "up" would be any photon polarized between 9 through noon to 3 oclock. "down" would be any photon polarized between 3 through 6 to 9 oclock. The fact that no HN50 polarizers exist, suggests that a HN32 polarizer may well only be detecting "up" light in the angles 10 oclock to 2 oclock and the other polarizer is detecting from 4 oclock to 8 oclock.

It is clear from the link, that they are only counting "detected" photons that have passed these polarizers and it seems clear from the properties of polarizers that there must be a fair number of "undetected" photons kicking around.

The http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" shows an experimental setup which is not at all like the one that I have been made to understand. In the experiment that was described to me, the light went straight in opposite directions from the source, into the bi-refringent crystal, and then into the photo-multiplier.

The diagram in the article referenced, however, shows the beam going through a Collimating Lens, Blue Filter, Beam Aperture, A LASER POLARIZER, a QUARTZ PLATE, and a MIRROR before it goes through the crystal.

I was made to think that it was completely unpolarized light which went through the birefringent crystal. I would think that any of these extra items, especially the polarizer, the quartz plate, and the mirror ought to be taken into account.

I was also made to think that the entangled photons came out of the source in opposite directions. But the diagram seems to only split the photons after they have been painstakingly polarized.

Is this just the wrong diagram?

 

[DrChinese]

Sorry, you lost me. You are correct, I could buy the equipment, do the experiment, post the results of the experiment and then discuss them, but if there are posted results of this experiment, I think it would be easier.

Also, I have not suggested Malus is wrong?

Yes, you ARE saying that Malus is wrong. Remember all that stuff you posted about "if it is between 10 o'clock and 2 o'clock..." and all the variations on that? Well, Malus doesn't have anything like that. It is ONLY about cos^2 when it comes to the relative angle setting.

And I keep telling you that this has been checked literally hundreds of thousands of times in the past 200 years. With entangled photons, this has probably "only" been tested thousands of times. And there is NO SUCH EFFECT AS YOU SUGGEST.

It is definitely possible to construct a local realistic model. But it will not agree with QM (per Bell). And it will not match experiment. So I think you should re-examine your line of reasoning.

 

[edguy99]

Yes, you ARE saying that Malus is wrong. Remember all that stuff you posted about "if it is between 10 o'clock and 2 o'clock..." and all the variations on that? Well, Malus doesn't have anything like that. It is ONLY about cos^2 when it comes to the relative angle setting.

And I keep telling you that this has been checked literally hundreds of thousands of times in the past 200 years. With entangled photons, this has probably "only" been tested thousands of times. And there is NO SUCH EFFECT AS YOU SUGGEST.

It is definitely possible to construct a local realistic model. But it will not agree with QM (per Bell). And it will not match experiment. So I think you should re-examine your line of reasoning.

I do not agree. As I read it, the Bell reasoning assumes at least two important things:

1/ In the experiment all of the particles must be accounted for.
2/ If a particle is measured a second time, you cannot assume that the first measurement had any affect on the particle.

In my opinion: Use of anything other then a HN50 filter does not account for all of the particles and a photon in a polarizer appears to have an affect on the particle as it affects whether or not it gets through the next polarizer.

I am happy to talk about a particle that is subjected to 2 polarizers, but I would want a real example to work from.

 

[DrChinese]

The http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" shows an experimental setup which is not at all like the one that I have been made to understand. In the experiment that was described to me, the light went straight in opposite directions from the source, into the bi-refringent crystal, and then into the photo-multiplier.

The diagram in the article referenced, however, shows the beam going through a Collimating Lens, Blue Filter, Beam Aperture, A LASER POLARIZER, a QUARTZ PLATE, and a MIRROR before it goes through the crystal.

I was made to think that it was completely unpolarized light which went through the birefringent crystal. I would think that any of these extra items, especially the polarizer, the quartz plate, and the mirror ought to be taken into account.

I was also made to think that the entangled photons came out of the source in opposite directions. But the diagram seems to only split the photons after they have been painstakingly polarized.

Is this just the wrong diagram?

No, this is a great source for you. You should definitely analyze the setup so you understand what is happening. I can explain any particular elements in a general manner.

Normally, the Alice and Bob output beams from a Type I PDC setup come out only slightly off angle from each other (each 4-5 degrees from center). To send them in opposite directions requires additional apparatus such as fiber or a mirror. (Most diagrams show them going in opposite directions just for clarity of concept, and this is not literal.)

The input source is polarized on the diagonal relative to the axes of the Type I BBo crystals which produce the entangled pairs. If you think about it a bit, there are only a few things to take into account really. You can have a brighter beam or dimmer beam. You can have it oriented so it goes through one crystal more than the other, or as close to equal as possible (this is controlled by how close to the diagonal you are at). To produce polarization entanglement, you cannot know whether a pair emerged from one crystal or the other - you must not be able to tell.

Finally, keep in mind that most of the source passes straight through the PDC apparatus and is NOT split. That would be 99.9999% of the light. So that needs to be filtered out so that it is not accidentally detected.

 

[DrChinese]

I do not agree. As I read it, the Bell reasoning assumes at least two important things:

1/ In the experiment all of the particles must be accounted for.
2/ If a particle is measured a second time, you cannot assume that the first measurement had any affect on the particle.

In my opinion: Use of anything other then a HN50 filter does not account for all of the particles and a photon in a polarizer appears to have an affect on the particle as it affects whether or not it gets through the next polarizer.

If you read Bell, you will find none of this is mentioned anywhere. Bell is a mathematical proof.

Bell tests measure a prediction required by a Bell local realistic model which matches QM. There are no candidate LR models in existence that satisfy this. The De Raedt et al simulation models, for example, do NOT match the predictions of LR (including Malus).

And finally: Most Bell tests use polarizing beam splitters instead of polarizers (as I keep pointing out). You obviously do not understand the significance of this point. But, among other things, these have very high transmission rates and it is clear this has little bearing on the results. It does lead to some issues in terms of the so-called "fair sampling loophole" however that has been closed already via experiment.

 

[edguy99]

If you read Bell, you will find none of this is mentioned anywhere. Bell is a mathematical proof.

Bell tests measure a prediction required by a Bell local realistic model which matches QM. There are no candidate LR models in existence that satisfy this. The De Raedt et al simulation models, for example, do NOT match the predictions of LR (including Malus).

And finally: Most Bell tests use polarizing beam splitters instead of polarizers (as I keep pointing out). You obviously do not understand the significance of this point. But, among other things, these have very high transmission rates and it is clear this has little bearing on the results. It does lead to some issues in terms of the so-called "fair sampling loophole" however that has been closed already via experiment.

In the experiment you quoted me, the PA and PB polarizers, if they are not HN50, are losing more then 10% of the photons after they have been through the beam splitter. Unless you are claiming that 100% of the photons are getting through these filters (I will reassess my position if true)? All I am pointing out is if one detector is not seeing the photon, the other detector will not see it either as they are entangled - ie. the same polarization.

 

[SpectraCat]

Its not the issure of the crystal but the detection. The example cited http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" shows a very clear diagram setup at Figure 1. The polarizers in question are labeled PA Polarizer A and PB Polarizer B.

As I understand the meaning of HN50 is you start with linear polarized light coming at you that could be polarized in any direction. The HN50 designation means that 1/2 the light will get through. If you imagine a clock, then "up" would be any photon polarized between 9 through noon to 3 oclock. "down" would be any photon polarized between 3 through 6 to 9 oclock. The fact that no HN50 polarizers exist, suggests that a HN32 polarizer may well only be detecting "up" light in the angles 10 oclock to 2 oclock and the other polarizer is detecting from 4 oclock to 8 oclock.

If that is true, then how is it possible that two crossed polarizers can block 100% of the light?

 

[DrChinese]

In other words, just to be clear: The Dehlinger experiment happens to use polarizers instead of PBS's. This has no bearing on the results, but I mention because it may be a source of confusion. The question at hand is whether polarizers somehow filter out the very photons that would "ruin" the results. Well, that would ultimately require collusion between the settings on both sides as otherwise there IS NO effect from the polarizer that deviates from Malus. Nor from a PBS.

But we already know that the settings can be changed mid flight (Aspect, 1981) and that does not change things. So we would then be witnessing a non-local effect.

 

[Jonathan Scott]

The http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" shows an experimental setup which is not at all like the one that I have been made to understand. In the experiment that was described to me, the light went straight in opposite directions from the source, into the bi-refringent crystal, and then into the photo-multiplier.

The diagram in the article referenced, however, shows the beam going through a Collimating Lens, Blue Filter, Beam Aperture, A LASER POLARIZER, a QUARTZ PLATE, and a MIRROR before it goes through the crystal.

I was made to think that it was completely unpolarized light which went through the birefringent crystal. I would think that any of these extra items, especially the polarizer, the quartz plate, and the mirror ought to be taken into account.

I was also made to think that the entangled photons came out of the source in opposite directions. But the diagram seems to only split the photons after they have been painstakingly polarized.

Is this just the wrong diagram?

That's a nice paper which describes a practical modern version of the experiment. The pairs of entangled photons are not created until the laser photons hit the two-layered downconversion crystal assembly, so most of the bits you mention are actually parts of the "power supply" as far as the actual experiment is concerned.

The observation devices in this case are just polarizers (single-channel) so only one of the two states will actually be detected for a given setting, but relative rates can be obtained by rotating the polarizers.

 

[DrChinese]

In the experiment you quoted me, the PA and PB polarizers, if they are not HN50, are losing more then 10% of the photons after they have been through the beam splitter. Unless you are claiming that 100% of the photons are getting through these filters (I will reassess my position if true)? All I am pointing out is if one detector is not seeing the photon, the other detector will not see it either as they are entangled - ie. the same polarization.

Yes, I quite agree that there are some losses. But your premise is faulty for a number of reasons.

First: unless the losses are severely biased, this will have no effect on the results at all.

Second: if they were so biased, all you would need to do is rotate the 2 polarizers at various angles until you quantified that. Remember, what happens at Alice is independent of what happens at Bob if locality holds!

Third: the output of one Type 1 PDC crystal is a pair of entangled photons, but they are NOT polarization entangled! So it is quite easy to test the idea that there is something in the apparatus that is somehow changing things. And it turns out that the non-polarization entangled photons going through the apparatus do NOT follow the cos^2 relationship for coincidences. Instead, they follow the Product State statistics which is the .25+(cos^2/2) formula.

Finally: if some pairs are not seen at either spot because they contain a special hidden variable which makes them both ALWAYS be absorbed... how does that change anything for our counts? It is neither a match or a non-match.

 

[DrChinese]

In other words: all we care about is the intensity of the matched pairs as a function of relative angle. Further, we would want that function to hold across arbitrary rotations of the polarizers. That result violates the relationships of a local realistic model, in which what happens at one polarizer is causally independent of the other.

 

[DrChinese]

The observation devices in this case are just polarizers (single-channel) so only one of the two states will actually be detected for a given setting, but relative rates can be obtained by rotating the polarizers.

Yes, you are correct and I may have inadvertently confused edguy on this point. I added a post to explain further about this.

And you are quite right that the crystals should be seen as a source. Yet, for the local realist, even the existence of Type I entanglement should be a bit of a paradox. How can something be partially entangled? How does *adding* a crystal create polarization entanglement? After all, the local realist says the split occurred in one crystal or the other! QM says it splits in both.

 

[JDoolin]

http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf

~One thing I want to question is whether this is a typo: On page 3, in the left column, it says: "With the irises fully open and polarizers both set to vertical, more than 300 counts per second were observed." However, on page 4, there is a figure showing that the observation rate never exceeded 350 per 10 seconds, which would be about 30 per second.

 

[DrChinese]

http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf

~One thing I want to question is whether this is a typo: On page 3, in the left column, it says: "With the irises fully open and polarizers both set to vertical, more than 300 counts per second were observed." However, on page 4, there is a figure showing that the observation rate never exceeded 350 per 10 seconds, which would be about 30 per second.

Looks like that would be the case as I read it too.

 

[miosim]

It would be a valid point if Bell reproduces Einstein’s concept without any deviations. Instead Bell’s model lacks the major requirement for Einstein’s argument; do not contradict with the predicted result of QM. Bell doesn’t need Einstein to be around to adhere with this basic requirement.

But Einstein didn't know his concept of a local and objective model conflicted with QM in the first place! He thought it could be possible to come up with such a model that does not contradict QM, but he was wrong! Do you really not get this?

Einstein didn’t know that his concept could be transformed into a circus.

According to EPR argument the two correlated particles are represented by the two different and independent wave functions. When the first wave function collapses it reviled one complemented parameter (+spin) that gaves us a knowledge about another complemented parameter (-spin) of the second wave function. Because this wave functions has no description of this parameter the wave function and QM accordingly is incomplete.

Now let see the Bell’s ‘reasonable’ reproduction of this EPR model:

“…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…”
Then Bell ‘mumbles’ the following:
“…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. Certainly something must be modified in that, to reproduce the quantum phenomena. Previously, we implicitly assumed for the net force in the direction of the field gradient (which we always take to be in the same direction as the field) a form: F cos Q ….”

This is it. These are all efforts to recreate the EPR model in spirit of Einstein. Based on these ‘exhaustive’ efforts, Bell proclaimed that it isn’t possible to build such a model.
Is this hilarious? Is this a circus?

Bell (and his supporters) just forgot that the EPR particles are represented by the two independent wave functions and therefore their cos^2 behavior are identical to Bell’s QM model.

Secondly, if Bell decided to model EPR particles as classical ones, he must at least include interactions of these particles with polarizers (QM formalism has this interactions builtin) as follows: the polarizers, like optical ‘funnel’, modifies polarization of both photons in the direction of higher correlation and this way eliminating inequality with the QM prediction.

It seems to me that the Bell’s theorem is dead.

 

[JesseM]

Einstein didn’t know that his concept could be transformed into a circus.

According to EPR argument the two correlated particles are represented by the two different and independent wave functions. When the first wave function collapses it reviled one complemented parameter (+spin) that gaves us a knowledge about another complemented parameter (-spin) of the second wave function. Because this wave functions has no description of this parameter the wave function and QM accordingly is incomplete.

Now let see the Bell’s ‘reasonable’ reproduction of this EPR model:

“…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…”
Then Bell ‘mumbles’ the following:
“…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. Certainly something must be modified in that, to reproduce the quantum phenomena. Previously, we implicitly assumed for the net force in the direction of the field gradient (which we always take to be in the same direction as the field) a form: F cos Q ….”

This is it. These are all efforts to recreate the EPR model in spirit of Einstein.

Another totally-confident-yet-totally-ignorant argument from miosim (there is a psychological explanation for this sort of thing). The second "mumbled" statement has nothing to do with how Bell ultimately defines "local causality", it's just meant as a "trivial" and "ad hoc" model that he starts out with as an example, then shows it doesn't work and abandons it. His actual proof of the theorem that local causality is incompatible with QM has nothing whatsoever to do with that model. But I [post=3257023]already told you this before[/post]:

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."

Bell (and his supporters) just forgets that the EPR particles are represented by the two independent wave functions and therefore their cos^2 behavior are identical to Bell’s QM model.

They're not represented by "two independent wave functions" in QM, they're represented by a single wavefunction representing the entangled two-particle system. Bell is proving that no local theory can reproduce the QM prediction which is based on this single (nonlocal) wavefunction.

Secondly, if Bell decided to model EPR particles as classical ones, he must at least include interactions of these particles with polarizers (QM formalism has this interactions builtin) as follows: the polarizers, like optical ‘funnel’, modifies polarization of both photons in the direction of higher correlation and this way eliminating inequality with the QM prediction.

Bell's definition of local causality makes no specific assumptions about how the particles interact with the polarizers, but the definition is broad enough to include the possibility that the polarizers would modify polarization in a local way. Again, Bell's definition is exactly equivalent to my 1) and 2) (again see the links I gave at the end of [post=3278882]this post[/post]), and my two assumptions certainly don't rule out the possibility that the particles are modified by their interactions with the polarizers. If you want to engage Bell's argument, you need to try to think about these basic assumptions, not some strawman based on your lack of reading comprehension. You said you found my 1) and 2) too "technical", but I'd be happy to elaborate on any sentences or terms you found confusing if you want to make an effort to understand them, rather than just taking the intellectually lazy route of saying "too hard!" and going back to repeating the same old ignorant arguments and strawman, ignoring all refutations like a good http://redwing.hutman.net/~mreed/warriorshtm/ferouscranus.htm .

 

[edguy99]

If that is true, then how is it possible that two crossed polarizers can block 100% of the light?

You are correct. The example was built to show the 85/15 split at those angles are possible in a classical model and is easier to calculate. Consider if the edges are rounded out a bit:

A particle modeled with the properties of a bloch sphere as shown http://en.wikipedia.org/wiki/Bloch_sphere" . This is represented below by the density of the red area on Bob and Alice measuring devices overlaid with green values. The density of red represents the probability of measuring the photon if it is presented at that angle and is a property of the photon (cos^2).

This picture shows that Bob and Alice measuring a sequence of "up" paricles. It shows that for particles that reach the detector, Bob and Alice always measure the same no matter the orientation of their measuring devices, as long as they both measure at the same angle:

If Bob tilts his measuring device by 45 degrees, he notices that the number of matching particles drops to 50%. If Bob tilts his device by 90 degrees, he does not see any matching particles of course since he doesn't see any particles. Experimental results shown http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" figure 3:

Finally if Bob tilts his device 22.5 or 67.5 degrees he gets the 85% and 15% predicted by QM. Note these are the kind of results you would expect for http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" , table 1:

 

[Jonathan Scott]

Bell (and his supporters) just forgot that the EPR particles are represented by the two independent wave functions and therefore their cos^2 behavior are identical to Bell’s QM model.

Secondly, if Bell decided to model EPR particles as classical ones, he must at least include interactions of these particles with polarizers (QM formalism has this interactions builtin) as follows: the polarizers, like optical ‘funnel’, modifies polarization of both photons in the direction of higher correlation and this way eliminating inequality with the QM prediction.

It seems to me that the Bell’s theorem is dead.

You seem to be missing the point by increasing amounts on each attempt!

The cos^2 behaviour of two independent particles leads to only half of the correlation values predicted by QM and confirmed by experiment.

Bell's theorem is NOT based on ANY classical model; such models are only used as examples to illustrate the theory.

Bell's theorem simply points out that a triangle inequality applies to differences between sets of results in any local realistic theory, but QM violates that inequality.

 

[SpectraCat]

You are correct. The example was built to show the 85/15 split at those angles are possible in a classical model and is easier to calculate. Consider if the edges are rounded out a bit:

A particle modeled with the properties of a bloch sphere as shown http://en.wikipedia.org/wiki/Bloch_sphere" . This is represented below by the density of the red area on Bob and Alice measuring devices overlaid with green values. The density of red represents the probability of measuring the photon if it is presented at that angle and is a property of the photon (cos^2).

This picture shows that Bob and Alice measuring a sequence of "up" paricles. It shows that for particles that reach the detector, Bob and Alice always measure the same no matter the orientation of their measuring devices, as long as they both measure at the same angle:If Bob tilts his measuring device by 45 degrees, he notices that the number of matching particles drops to 50%. If Bob tilts his device by 90 degrees, he does not see any matching particles of course since he doesn't see any particles. Experimental results shown http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" figure 3:Finally if Bob tilts his device 22.5 or 67.5 degrees he gets the 85% and 15% predicted by QM. Note these are the kind of results you would expect for http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" , table 1:

Ok .. I am a little baffled .. that seems like just the basic Malus' law description for correlations between polarization measurements of unentangled photon pairs. What does any of that have to do with correlations between measurements on polarization-entangled photon pairs, which is what was studied in the experiment you cited?

 

[DrChinese]

You are correct. The example was built to show the 85/15 split at those angles are possible in a classical model and is easier to calculate. Consider if the edges are rounded out a bit:

A particle modeled with the properties of a bloch sphere as shown http://en.wikipedia.org/wiki/Bloch_sphere" . This is represented below by the density of the red area on Bob and Alice measuring devices overlaid with green values. The density of red represents the probability of measuring the photon if it is presented at that angle and is a property of the photon (cos^2).

...

You know: suppose a cat is a flying dog.

Virtually everything you have here is either wrong or makes no sense at all. Entangled particles of known spin (yes, these exist) do NOT behave statistically as you describe in your pictures. And the descriptions you provide don't demonstrate realism.

(Photons are spin 1, by the way.)

 

[DrChinese]

Bell's theorem simply points out that a triangle inequality applies to differences between sets of results in any local realistic theory, but QM violates that inequality.

Thanks, finally some sanity.

 

[JDoolin]

You seem to be missing the point by increasing amounts on each attempt!

The cos^2 behaviour of two independent particles leads to only half of the correlation values predicted by QM and confirmed by experiment.

Bell's theorem is NOT based on ANY classical model; such models are only used as examples to illustrate the theory.

Bell's theorem simply points out that a triangle inequality applies to differences between sets of results in any local realistic theory, but QM violates that inequality.

~I gather that Bell's theorem is "sufficient" to prove that Quantum Mechanics violates locality, or something like that... But is it really necessary? I'm arguing from some ignorance, because I can't recall Bell's theorem, but it seems like, when I did see it's derivation, some years ago, it was a matter of formal logic; having nothing to do with experiment whatsoever. At the time, I had no doubt that Bell's theorem was true. (That's the nature of a theorem.) If I recall correctly it was a fairly simple derivation that could be explained in 15 minutes or so on a chalk board. In the same lecture though, the results of a quantum mechanics experiment was described--just the results, mind you, not the experiment itself. The most difficult part was to see how it was that they were able to abstract the results of the experiment down to something to which one could apply Bell's Theorem; or why one would bother.

~The attached graph (below: labels added) from http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf seems to get at the issue. The experiment is not quite as perfect as I would like, because it uses two polarizers instead of two birefringent crystals. However, it seems to me, that what would happen if you used two birefringent crystals is instead of doing four runs, you would just have to do two, and you would get the \alpha =0^o and the \alpha =90^o plots simultaneously. Then you would get the \alpha =45^o and the \alpha =135^o plots simultaneously.

The way the experiment is set up, by changing alpha, you affect the chance of detection at the other polarizer. If the experiment were set up with crystals, you would NOT affect the chance of detection, but the chance of how it were lined up.

By itself, this is weird enough that I'd say you have some kind of action at a distance. A sort of non-local wave collapse. You don't have to bring up anything called "Bell's Theorem" unless you want to show me a formal proof of something that you've already convinced me of. In fact, I'm not really entirely surprised that there is something strange going on, because interference effects, (two-slit experiment, diffraction, etc) already exhibit a possibly related wave-collapse phenomenon.

But now we should also bring up the exciting aspect of the experiment. When I receive a photon through one receiver or another, Can I use this as some form of faster-than-light communication? Let's set it up with birefringent crystals at both ends instead of the polarizers so we receive 100% of the entangled photons instead of at most 50%.

First question is, can we guarantee that almost every photon coming in is from an entangled pair, and every entangled pair is going through both receivers. IF SO, then I would say, yes, you could look at the photon count and based on whether your photon count were 300/0 150/150 or 0/300, you could figure out what angle the other crystal was set at.

In practice, of course, arranging the power source, and two receivers thosands, millions or billions of miles apart for 100% mutual detection would be... difficult.

 

[SpectraCat]

But now we should also bring up the exciting aspect of the experiment. When I receive a photon through one receiver or another, Can I use this as some form of faster-than-light communication? Let's set it up with birefringent crystals at both ends instead of the polarizers so we receive 100% of the entangled photons instead of at most 50%.

First question is, can we guarantee that almost every photon coming in is from an entangled pair, and every entangled pair is going through both receivers. IF SO, then I would say, yes, you could look at the photon count and based on whether your photon count were 300/0 150/150 or 0/300, you could figure out what angle the other crystal was set at.

In practice, of course, arranging the power source, and two receivers thosands, millions or billions of miles apart for 100% mutual detection would be... difficult.

No, you can't use it for FTL communication. The simplest explanation as to why is that, for any given measurement at one end of the channel (call it your end), you cannot know a priori whether or not there has already been a measurement at the other end of the channel that determined the result at your end. In other words, if you set your polarizer at 45 degrees and detect a photon, does that mean a measurement at the other end of the channel was done "first" at (for example) 135 degrees, determining the result at your end? Or does it mean that your measurement was done "first", determining the result of your partners "future" measurement at the other end of the channel?

Note that "first" and "future" are in quotes because statements about the relative orders of events in reference frames with a space-like separation need to be carefully qualified, and we have not done that here.

 

[edguy99]

Ok .. I am a little baffled .. that seems like just the basic Malus' law description for correlations between polarization measurements of unentangled photon pairs. What does any of that have to do with correlations between measurements on polarization-entangled photon pairs, which is what was studied in the experiment you cited?

This is "just the basic Malus' law description" with one important difference. When Bob is at 22 degrees, he only has an 85% chance of measuring a vertical photon hence the drop in "coordinated hits" between Bob and Alice (he simply sees it or not). The photons are not somehow reduced in intensity by aligning their electrical vector to the measuring field.

The hidden variable theory proposed in http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf" just below figure 4 results in the straight line as shown in figure 4. Assuming that Bob (beta in the experiment) has an 85% chance of measuring a photon when at 22 degrees preserves the curved line in figure 4 and the coordinated hits measured by Bob and Alice, ie. if Bob does not measure the photon, you don't have a coordinated hit and Alices measurements of coordinated hits must have also dropped "instantly" even though she did not do anything.

 

[edguy99]

You know: suppose a cat is a flying dog.

Virtually everything you have here is either wrong or makes no sense at all. Entangled particles of known spin (yes, these exist) do NOT behave statistically as you describe in your pictures. And the descriptions you provide don't demonstrate realism.

(Photons are spin 1, by the way.)

Hey, where did you get a picture of my dog? The photons in the experiment start out linear polarized in a specific direction so are generally talked about as up or down in this type of experiment, hence the reference.