Can grandpa understand the Bell's Theorem?

[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.

 

[edguy99]

...The experiment is not quite as perfect as I would like, because it uses two polarizers instead of two birefringent crystals.

This has been mentioned a couple of times now. Do you know of a good experiment using this setup (birefringent crystals) with a link that we could discuss and eliminate the polarizers?

 

[SpectraCat]

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.

That is the quantum phrasing of Malus' law .. there is no significant difference between the results or the interpretation.

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.

Detection probabilities are taken into account in the development of the equations for both the actual experiment, and the CHSH inequality used in that paper. A correlation count can only be established by comparison of the two sets of results, so the concept of an "instant drop" in the correlation count is ill defined.

 

[DrChinese]

1. 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.

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.

2. 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? ...

1. To understand why Bell is needed, let's return to the original EPR situation in which we imagine there is a more complete specification of the system possible. For example, perhaps there are hundreds of hidden elements which lead us to see the so-called perfect correlations envisioned by EPR - and you would need a lot to get these correlations. Now, you may consider this implausible, but it does show why we need Bell.

2. What is being graphed in your attached example is P(a+b), which is the coincidence rate. Nothing changes visibly on either side when looking at that side alone. So no signaling is possible.

Other than that, I pretty well agree with you.

 

[DrChinese]

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.

That also looks like my dog when I open the door and look the other way for a second.

You cannot start out with knowledge of the polarization (say as up) and expect correlations which follow the cos^2 rule.

For example: Alice set at 22.5 degrees, Bob same, the match % with polarizers will be: 73%/2 (PBS would be twice that) with Type I non-polarization entangled pairs.

On the other hand, with Type I polarization entangled pairs, the match % would be 85%/2.

My point is that your basic premise itself (how polarization is observed) can be experimentally tested directly, and found to be incorrect. This is separate from attempting to model as a Bell inequality. It fails before you get that far.

In addition, the entire point of Bell is to demonstrate that realistic solutions are not possible. You have yet to demonstrate realism. That requires providing an answer to the value of counterfactual measurements. I.e. the values for 3 settings I pick across a group of photons. If you want me to explain the rules for that, I would be happy to. Then you will see the problem more clearly with your idea.

 

[DrChinese]

This has been mentioned a couple of times now. Do you know of a good experiment using this setup (birefringent crystals) with a link that we could discuss and eliminate the polarizers?

http://arxiv.org/abs/quant-ph/9810080

Violation of Bell's inequality under strict Einstein locality conditions, Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, Anton Zeilinger

This is one of the primary references in scholarly articles. This is the top echelon of researchers.

 

[JDoolin]

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.

I wouldn't think it would matter whether it is measured first at the beta end or first at the alpha end. Cosine is an even function, so if you get Cos(a-b) or Cos(b-a) you would get the same result.

Besides which, as you mention, the two events are separated by a "space-like" interval; not a "time-like" interval, so effectively, in half of the reference frames a is before b, and in another half of the reference frames b is before a, and, of course, in some specifically defined reference frames, the two events are simultaneous.

 

[JDoolin]

1. To understand why Bell is needed, let's return to the original EPR situation in which we imagine there is a more complete specification of the system possible. For example, perhaps there are hundreds of hidden elements which lead us to see the so-called perfect correlations envisioned by EPR - and you would need a lot to get these correlations. Now, you may consider this implausible, but it does show why we need Bell.

2. What is being graphed in your attached example is P(a+b), which is the coincidence rate. Nothing changes visibly on either side when looking at that side alone. So no signaling is possible.

Other than that, I pretty well agree with you.

The way I understood the graph is it shows the N(A and B) which is the number of events where both A and B were detected at the same time.

Now you seem to be saying that the overwhelming majority of photons detected at A and B are non-coincident, so that the slight change caused by this effect would be miniscule? I could see how it might be miniscule or perhaps statistically too small to measure, but I don't understand how it could be zero.

 

[SpectraCat]

I wouldn't think it would matter whether it is measured first at the beta end or first at the alpha end. Cosine is an even function, so if you get Cos(a-b) or Cos(b-a) you would get the same result.

What you seem to be missing is that in order to transmit information over such a channel, the person receiving the transmission must know both a and b. However, in order to transmit information, the person sending the information must be free to change one of those parameters. Furthermore, cos(a-b) defines the coincidence rate (or coincidence probability) ... in order to transmit information, you would have to know about specific coincident events at both ends of the channel. That obviously requires a comparison step, and thus a lightspeed (or slower) channel.

Just think about being at one end of such a channel with a space-like separation to the other end. What can you do? You can choose the angle of your polarizer (lets say b), and record photon detection events. Let's assume that the photons arrive at a known, constant rate of 1 per second. What do you see? Each second you check your detector to see if a photon was registered, detection events count as 1's, non-detection events as 0's. How can you extract information from that channel?

[EDIT: That last question was poorly phrased ... I meant to ask, how can you know that the information you are receiving is due to manipulations performed at the other end of the channel, rather than just random noise?]

Besides which, as you mention, the two events are separated by a "space-like" interval; not a "time-like" interval, so effectively, in half of the reference frames a is before b, and in another half of the reference frames b is before a, and, of course, in some specifically defined reference frames, the two events are simultaneous.

Yup.

 

[DrChinese]

The way I understood the graph is it shows the N(A and B) which is the number of events where both A and B were detected at the same time.

You have it right. So how would you know N(A and B) unless both sides were in communication? And what method do you plan to use to get that information?

And just to be clear: the intensity on either detector never changes.

 

[DrChinese]

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.

Are you back to invisible photons? Those won't enter into any experimental statistics anywhere. Or?

 

[JDoolin]

You have it right. So how would you know N(A and B) unless both sides were in communication? And what method do you plan to use to get that information?

And just to be clear: the intensity on either detector never changes.

This might be easier to resolve if I had information on exactly what the intensity (in photons per second) is actually received by either detector. I believe I have only been given the number of coincident events at around 300 every 10 seconds, but not the total intensity.

If we could assure ZERO non-coincident photons, then you'd have a number between 0 and 100% of max. If it is 90% non-coincident photons, then you'd have a signal between 90 and 100% of max. If it is made up of 99.99% non-coincident photons, then you'd get a signal between 99.99% and 100% of the maximum, and you might as well say "the intensity on either detector never changes, because the change would be statistically insignificant.

 

[DrChinese]

This might be easier to resolve if I had information on exactly what the intensity (in photons per second) is actually received by either detector. I believe I have only been given the number of coincident events at around 300 every 10 seconds, but not the total intensity.

If we could assure ZERO non-coincident photons, then you'd have a number between 0 and 100% of max. If it is 90% non-coincident photons, then you'd have a signal between 90 and 100% of max. If it is made up of 99.99% non-coincident photons, then you'd get a signal between 99.99% and 100% of the maximum, and you might as well say "the intensity on either detector never changes, because the change would be statistically insignificant.

I will say it again: the intensity at either detector NEVER changes (beyond normal deviations). About 50% of the incident photons come through Alice's polarizer. This is true regardless of what Bob does. Or whether Bob does anything at all.

You can see the separate intensity for Alice and Bob in the experiment as N(A) and N(B). That looks to be about 85,000 per run IIRC.

 

[JDoolin]

I will say it again: the intensity at either detector NEVER changes (beyond normal deviations). About 50% of the incident photons come through Alice's polarizer. This is true regardless of what Bob does. Or whether Bob does anything at all.

You can see the separate intensity for Alice and Bob in the experiment as N(A) and N(B). That looks to be about 85,000 per run IIRC.

Is that 85,000 photon events in each 10 second run? (Edit: Out of which 300 are "coincident" events?)

 

[DrChinese]

I think so, although that seems high to me. I assume because this is an undergrad setup and the controls don't need to be too tight. If you look at the Weihs et al paper, they get a much higher rate of matches.

 

[JDoolin]

I think so, although that seems high to me. I assume because this is an undergrad setup and the controls don't need to be too tight. If you look at the Weihs et al paper, they get a much higher rate of matches.

I guess the more relevant question is what's the standard deviation. Is it
85,000 +/- 1,000, or
85,000 +/- 100, or
85,000 +/- 1 event
per 10 seconds?

If the "noise" is constant enough, then you should be able to detect a change of 300 events per second. But if the noise regularly varies from 83,000 to 87,000, then a change of 300 might not be noticed.

If you're saying the intensity is constant, but the 300 counts per 10 seconds would be statistically insignificant in the measurment of the intensity anyway, I can make sense of that. It''s just the change can't be detected over the noise.

But if the intensity were EXACTLY the same, while the coincidence events (detection of entangled particles) went DOWN, that would mean there had to be some INCREASE in the number of non-coincidence (detection of non-entangled particles) events. Where would these extra non-coincidence events come from?

 

[DrChinese]

I guess the more relevant question is what's the standard deviation. Is it
85,000 +/- 1,000, or
85,000 +/- 100, or
85,000 +/- 1 event
per 10 seconds?

If the "noise" is constant enough, then you should be able to detect a change of 300 events per second. But if the noise regularly varies from 83,000 to 87,000, then a change of 300 might not be noticed.

If you're saying the intensity is constant, but the 300 counts per 10 seconds would be statistically insignificant in the measurment of the intensity anyway, I can make sense of that. It''s just the change can't be detected over the noise.

But if the intensity were EXACTLY the same, while the coincidence events (detection of entangled particles) went DOWN, that would mean there had to be some INCREASE in the number of non-coincidence (detection of non-entangled particles) events. Where would these extra non-coincidence events come from?

It would be so much easier to forget the polarizer example and switch to the PBS example because clearly that is causing a degree of confusion. I hope you see that if there was a PBS, every photon would emerge as a + or a -. That intensity does NOT change for Alice regardless of anything Bob does. Just as importantly, the + intensity and the - intensity will be nearly equal, and that ratio will not change either.

Do you see why? In other words, you are trying to imagine an effect which does not exist. Many folks get confused about the absorption of photons by a polarizer and get lost in analyzing that. The effect to look for is the coincidence rate varying according to the cos^2 rule predicted by QM versus one of the other functions you get with a local realistic model. There is nothing that ever changes at Alice as a result of what happens at Bob EXCEPT as it appears which you count matches versus non-matches (or similar).

The reason that no one cares about photons which cannot be paired is that they don't fit the criteria of an entangled pair. We are interested only in creating pairs that fit this criteria and analyzing those. So if there were nothing but paired events - no noise - there would still be no change in intensity at Alice based on anything Bob does. And vice versa.

 

[JDoolin]

It would be so much easier to forget the polarizer example and switch to the PBS example because clearly that is causing a degree of confusion. I hope you see that if there was a PBS, every photon would emerge as a + or a -. That intensity does NOT change for Alice regardless of anything Bob does. Just as importantly, the + intensity and the - intensity will be nearly equal, and that ratio will not change either.

Do you see why? In other words, you are trying to imagine an effect which does not exist. Many folks get confused about the absorption of photons by a polarizer and get lost in analyzing that. The effect to look for is the coincidence rate varying according to the cos^2 rule predicted by QM versus one of the other functions you get with a local realistic model. There is nothing that ever changes at Alice as a result of what happens at Bob EXCEPT as it appears which you count matches versus non-matches (or similar).

The reason that no one cares about photons which cannot be paired is that they don't fit the criteria of an entangled pair. We are interested only in creating pairs that fit this criteria and analyzing those. So if there were nothing but paired events - no noise - there would still be no change in intensity at Alice based on anything Bob does. And vice versa.

No, quite likely, I'll have to start over from scratch to understand. The only assumption I'm aware of making is that the total number of photons detected must equal the number of nonentangled photons + the number of entangled photons. But there may be any number of other things I'm overlooking.

By my reasoning, if you used a birefringent crystal which passed 100% of the incoming photons to one of the two polarizations, you would STILL have a small difference between the values.

For instance using the graph from the paper I used before, and the number 85,000 you gave me earlier, if you aligned alpha with beta, you would get
84125+300=85,125 hits on the aligned axis and 84125+50=84875 hits on the non-aligned axis. A 0.3% difference.

But if you had alpha and beta at a 45 degree angle from each other, you would get 84125+175=85,000 hits through both channels; a 0% difference.


(By the way, I'm not sure what PBS stands for.)

 

[edguy99]

I think so, although that seems high to me. I assume because this is an undergrad setup and the controls don't need to be too tight. If you look at the Weihs et al paper, they get a much higher rate of matches.

I see the coincidences in the 0 to 800 range for 5 second intervals, but I don't see any measure of the N(A) or N(B) for a 5 second interval?

 

[edguy99]

... the two events are separated by a "space-like" interval; not a "time-like" interval, so effectively, in half of the reference frames a is before b, and in another half of the reference frames b is before a, and, of course, in some specifically defined reference frames, the two events are simultaneous.

Great quote.

 

[miosim]

Another totally-confident-yet-totally-ignorant argument from miosim …
… 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.

Did Bell abandon his distorted model/example of EPR? No, he diddn’t according to reference below:

http://www.scholarpedia.org/article/Bell's_theorem#S11a
“…The proof of Bell's theorem is obtained by combining the EPR argument (from locality and certain quantum predictions to pre-existing values) and Bell's inequality theorem…”

Apparently Bell didn’t abandon his model of the EPR argument and admitted that this is the best model he (or anybody else) can build:
"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."

At the same time I am a bit confused about how Bell uses EPRB arguments. “…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…”.

I don’t know if "immediately foretells" is a part of the EPRB argument. I am not sure if this is another distortion of Einstein’s views or a distortion caused by Bohm. My interpretation of Einstein’s views is based on his EPR paper (1935). Therefore if I refer to EPR, I mean this specific paper.

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.

I am not talking about the QM interpretation, but about the EPR interpretation (in the EPR paper) of particles that are represented by the two independent wave functions. http://prola.aps.org/pdf/PR/v47/i10/p777_1. Did you read the original paper?

… Again, Bell's definition is exactly equivalent to my 1) and 2) … 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.

No I don’t want to engage Bell's arguments that are based on the profoundly distorted initial conditions.

And just for your information, Bell wasn't in the least bit sympathetic to Copenhagen, he much preferred nonlocal hidden-variable theories which try to give an objective picture of what's really going on with quantum systems

By trying to provide an objective picture of what's really going on with quantum systems, Bell violated the “religious foundation” of QM built by Bohr and Heisenberg.
Bohr: "There is no quantum world. There is only an abstract quantum mechanical description. It is wrong to think that the task of physics is to find out how Nature. Physics concerns what we can say about Nature".

By violating this “foundation” Bell opened the "can with worms." He expended the scale of the wave function collapse and revealed its non-sense. This non-sense is called ‘non-local interactions’.

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.

Aspect may disagree with you. From the Bell’s Theorem : The Naive View Of An Experimentalist
“… a straightforward application of Malus law shows that a subsequent measurement performed along b on photon ν 2 will lead to P (a, b) = cos^2(a,b) …”

The author of the paper below may also disagree with you:

http://bib.irb.hr/datoteka/287013.pavicic-prd90.pdf
“…The recognition of Scully and Milomni’s theory as a theory which makes the quantum Malus law work for composite systems was clue for the poof...”
“… In other words, although being structurally different, HV on and QM predict the same experimental outcome…”

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

First, it is obviously a misleading illustration of EPR argument.
Second, as I understand, Bell’s inequalities were derived based on this specific illustration. I don't see any other model he used to compare with QM. Do you mean he compared QM with ‘locality’ in general? In this case please refer a formula to me of this "label of locality" and how it appears in Bell’s inequalities.

 

[DrChinese]

No, quite likely, I'll have to start over from scratch to understand. The only assumption I'm aware of making is that the total number of photons detected must equal the number of nonentangled photons + the number of entangled photons. But there may be any number of other things I'm overlooking.

By my reasoning, if you used a birefringent crystal which passed 100% of the incoming photons to one of the two polarizations, you would STILL have a small difference between the values.

For instance using the graph from the paper I used before, and the number 85,000 you gave me earlier, if you aligned alpha with beta, you would get
84125+300=85,125 hits on the aligned axis and 84125+50=84875 hits on the non-aligned axis. A 0.3% difference.

But if you had alpha and beta at a 45 degree angle from each other, you would get 84125+175=85,000 hits through both channels; a 0% difference.


(By the way, I'm not sure what PBS stands for.)

To come to an apples to apples basis, you would get something like this instead of what you calculated:

If you had alpha and beta at a 0 degree angle from each other, you would get 85,000 hits through both channels; a 0% difference. There would be 350 matches.

If you had alpha and beta at a 45 degree angle from each other, you would get 85,000 hits through both channels; a 0% difference. There would be 175 matches.

The only thing that varies is the number of matches. And the formula which describes it needs the relative difference - a quantum nonlocal value - as its prime variable.

 

[DrChinese]

I see the coincidences in the 0 to 800 range for 5 second intervals, but I don't see any measure of the N(A) or N(B) for a 5 second interval?

They didn't supply this value as I read it either. Since they define entangled as timetags within 6 ns, everything else is ignored. As the time window is increased, you get a lower value of S because a few unentangled* photon pairs are being considered.

*This may seem surprising, but pairs can be partially entangled. Anywhere between 0 and 100% fidelity, actually.

 

[DrChinese]

(By the way, I'm not sure what PBS stands for.)

Oops, my bad. PBS = Polarizing Beam Splitter. A PBS, like a polarizer filter, can be oriented at any angle across 360 degrees. However, it separates the incident (incoming) beam into 2 output channels, which are called H and V. Or + and -. The designation is arbitrary, as it is the angle of orientation that controls.

http://en.wikipedia.org/wiki/Beam_splitter

These remove any doubt that there is some selection process going on within the PBS itself as you get 4 permutations of coincidences, 2 of which are matches and 2 of which are mismatches.

 

[JesseM]

Did Bell abandon his distorted model/example of EPR? No, he diddn’t according to reference below:

http://www.scholarpedia.org/article/Bell's_theorem#S11a
“…The proof of Bell's theorem is obtained by combining the EPR argument (from locality and certain quantum predictions to pre-existing values) and Bell's inequality theorem…”

Apparently Bell didn’t abandon his model of the EPR argument

miosim, your reading comprehension sucks, you read stuff you obviously don't understand in the slightest and then extract a few keywords and come up with a fantasy interpretation of what you think it means that is designed to make Bell look bad. Yes, he used the EPR argument, but where the hell do you get the idea that this had anything whatsoever to do with the "trivial ad hoc space-time picture of what might go on" which he briefly introduced in the Bertlmann's socks paper (and none of his other papers) and quickly tossed aside for a more broad definition of local causality? Of course nothing in the scholarpedia article suggested anything of the sort, nor did EPR propose any sort of "trivial ad hoc space-time picture" in their paper, this is a pure fantasy that popped into your head and you immediately seized on it because it fits your ignorant preconceptions.

The "EPR argument" in this case just refers to the idea that if the values of some quantities measured at different locations are found to be perfectly correlated, then these values must have already been predetermined by local variables prior to measurement (an idea which Einstein agreed with, his two-box analogy illustrated exactly this sort of idea). As I pointed out in an [post=3275052]earlier post[/post] this follows directly from my 1) and 2) which are equivalent to the most general argument Bell makes in his "La nouvelle cuisine" paper:

In this statement, I was attempting to be as general as Bell in my definition of local realism--some of the inequalities he derived did not depend on the assumption of a perfect correlation between separated measurements, and thus in some of his papers he defined "local causality" in as broad a way as possible so that knowledge of past conditions would not predetermine the measurement results with perfect certainty. I agree, as would Bell, that if you are looking at one of the inequalities that does assume a perfect correlation between measurements with the same detector setting, in that case it must be true that the measurement outcome was predetermined prior to measurements, that there is no probabilistic element at all. This conclusion can in fact be derived from the more general assumptions about local realism, which is why it doesn't need to be a starting assumption if you want to make your proof as general as possible.

I also quoted from p. 11 of this paper which says pretty much the same thing:

There is, in particular, a tendency for a relatively superficial focus on the relatively formal aspects of Bell’s arguments, to lead commentators astray. For example, how many commentators have too-quickly breezed through the prosaic first section of Bell’s 1964 paper (p. 14-21) – where his reliance on the EPR argument “from locality to deterministic hidden variables” is made clear – and simply jumped ahead to section 2’s Equation 1 (p. 15), hence erroneously inferring (and subsequently reporting to other physicists and ultimately teaching to students) that the derivation “begins with deterministic hidden variables”? (1981, p. 157)

Again, the idea is that you start with basic local realist assumptions like my 1) and 2) (again equivalent to his assumptions in the "La nouvelle cuisine" paper, I can point out how if you are interested in actually making an effort to think about these assumptions), then it's not hard to show that in the case of perfectly correlated outcomes this implies the results of these measurements were predetermined by local variables associated with each particle before you made your measurements. That's the very general notion that the "EPR argument" refers to, not some much more specific classical model that Bell just offered in one paper as an example before disposing of it.

and admitted that this is the best model he (or anybody else) can build:
"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."

Uh, that sentence doesn't say "it's the best model", it just says that no other local model will be able to "reproduce the quantum formulae completely" either--a statement that he then goes on to prove in subsequent sections of the same paper, using arguments that have nothing to do with that original model.

Once again, you seem to jump to ridiculous interpretations of sentences that will serve your desperate need to "prove" Bell wrong, never even considering that perhaps the first interpretation that came into your head might not be the right one and that there might be other ways of reading it that don't make Bell into the cartoon idiot you want him to be. It's a basic principle of reading comprehension that you have to consider the possibility that the same sentence may be interpreted in different ways, and if your first interpretation makes the author out to be saying something completely foolish, instead of seizing on that interpretation so you can discount him, you need to take the time to consider whether there may be more "charitable" alternate interpretations (and if you can't think of any, ask defenders of the argument about it instead of jumping to conclusions). In philosophy and rhetoric, this idea goes by the name of the principle of charity. If you continue to ignore this principle, your reading comprehension will continue to suck.

At the same time I am a bit confused about how Bell uses EPRB arguments. “…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…”.

I don’t know if "immediately foretells" is a part of the EPRB argument. I am not sure if this is another distortion of Einstein’s views or a distortion caused by Bohm.

Of course it's not a distortion, Einstein's own two-box analogy, which he used to clarify what his intended meaning had been, was clearly describing exactly this sort of situation where knowing the result of one measurement (seeing whether your box has a ball in it) tells you the result of the other (if yours had a ball the other is empty and vice versa). The EPR paper also made very clear they were talking about situations where knowledge of one measurement tells you what the result of the same measurement on the other particle would be, on p. 1 they say: "A comprehensive definition of reality is, however, unnecessary for our purpose. We shall be satisfied with the following criterion, which we regard as reasonable. If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity." The entirety of the subsequent argument in the EPR paper is based on this idea.

No I don’t want to engage Bell's arguments that are based on the profoundly distorted initial conditions.

So you don't want to try to understand what Bell was actually saying and "engage" with that, you just want to go on making up fantasy strawmen that you can easily knock down? By the way "engage with" isn't code for "agree with", it just means understanding Bell's actual position and arguing based on that.

By trying to provide an objective picture of what's really going on with quantum systems, Bell violated the “religious foundation” of QM built by Bohr and Heisenberg.
Bohr: "There is no quantum world. There is only an abstract quantum mechanical description. It is wrong to think that the task of physics is to find out how Nature. Physics concerns what we can say about Nature".

Uh, QM is not a religion and Bohr is not the pope. In case you missed it, Einstein's whole purpose was to try to find an "objective picture" of this type, he was mocking the idea that the "abstract quantum mechanical description" could be complete with his two-boxes analogy:

"In front of me stand two boxes, with lids that can be opened, and into which I can look when they are open. This looking is called 'making an observation.' In addition there is a ball, which can be found in one or the other of the two boxes where an observation is made. Now I describe a state of affairs as follows: The probability is one-half that the ball is in the first box." (This is all the Schrödinger equation will tell you.) "Is this a complete description?" asks Einstein, and then gives two different answers.

"NO: A complete description is: the ball is (or is not) in the first box...

"YES: Before I open the box the ball is not in one of the two boxes. Being in a definite box only comes about when I lift the covers...

"Naturally, the second 'spiritualist' or Schrödingerian interpretation is absurd," Einstein continued tactfully, "and the man on the street would only take the first, Bornian, interpretation seriously."

But even aside from Einstein's views, saying that Bell was somehow wrong to try to find an objective picture in no way shows that Bell's theorem itself is incorrect. After all, Bell's theorem just proves that any attempt to find an objective picture obeying the principle of locality will inevitably fail to match the QM predictions. If you agree with Bohr then you may consider this result uninteresting since you never believed it would be possible to find an objective local picture in the first place, but you would have no reason to say it's actually incorrect at a technical level.

By violating this “foundation” Bell opened the "can with worms." He expended the scale of the wave function collapse and revealed its non-sense. This non-sense is called ‘non-local interactions’.

Nope, Bell's theorem makes no positive claim of the objective existence of "non-local interactions", it just proves the negative claim that any attempt to create an objective picture which features no non-local interactions will inevitably fail. This does not mean you have to adopt an objective picture that features non-local interactions, you can also just abandon the notion of any objective picture at all, as Bohr would have recommended.

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.

Aspect may disagree with you. From the Bell’s Theorem : The Naive View Of An Experimentalist
“… a straightforward application of Malus law shows that a subsequent measurement performed along b on photon ν 2 will lead to P (a, b) = cos^2(a,b) …”

In this statement (from near the bottom of p. 5 of the paper) Aspect is making the point that if you treat the measurement of photon v₁ with a polarizer at angle a as causing a "collapse" of photon v₂ into the same polarization state as v₁, then since Malus' law says that a subsequent measurement of v₁ at angle b would give a probability of (1/2)*cos^2(a,b) that v₁ passes through b, it must also be true that if v₂ is first measured with a polarizer at angle b after its state has already been "collapsed" by the measurement of v₁ at angle a (with a 1/2 probability v₁ made it through), then it must also be true that v₂ has a probability of (1/2)*cos^2(a,b) of making it through (or a probability of cos^2(a,b) that v₂ makes it through if we already know v₁ made it through). This conclusion isn't based on the classical Malus' law alone, it's based on the combination of Malus' law applied to two successive measurements of v₁, and then adding the assumption that a single measurement of v₁ causes an instantaneous "collapse" of v₂ into the same state. There would be no way to reproduce this correlation (for arbitrary choice of angles a and b) in a local classical universe where Malus' law applied but there was no instantaneous "collapse" of the 2-particle wavefunction when one particle was measured.

 

[JDoolin]

To come to an apples to apples basis, you would get something like this instead of what you calculated:

If you had alpha and beta at a 0 degree angle from each other, you would get 85,000 hits through both channels; a 0% difference. There would be 350 matches.

If you had alpha and beta at a 45 degree angle from each other, you would get 85,000 hits through both channels; a 0% difference. There would be 175 matches.

The only thing that varies is the number of matches. And the formula which describes it needs the relative difference - a quantum nonlocal value - as its prime variable.

Hmmmm. Well, that suggests to me a different interpretation. Well, it forces me to make a realization that probably seems really, really obvious to you: we know where all of the non-coincident photons are coming from!

The non-coincident photons are coming from the down-conversion crystals, just like the coincident photons are. (my earlier silliness came from thinking that the non-coincident photons were from some unknown independent source, and should stay constant.)

What probably could have been explained to me is to realize that within the down-conversion crystals, the violet light excites the atoms, and then two red photons come out. With some of the atoms, the two red photons come out simultaneously; and can be registered. But with most, you get the two red photons coming out at different times, so you can't match them to their "twin."

I still may have to think through it from scratch, but I think it's a little clearer.

 

[DrChinese]

Hmmmm. Well, that suggests to me a different interpretation. Well, it forces me to make a realization that probably seems really, really obvious to you: we know where all of the non-coincident photons are coming from!

The non-coincident photons are coming from the down-conversion crystals, just like the coincident photons are. (my earlier silliness came from thinking that the non-coincident photons were from some unknown independent source, and should stay constant.)

What probably could have been explained to me is to realize that within the down-conversion crystals, the violet light excites the atoms, and then two red photons come out. With some of the atoms, the two red photons come out simultaneously; and can be registered. But with most, you get the two red photons coming out at different times, so you can't match them to their "twin."

I still may have to think through it from scratch, but I think it's a little clearer.

Sums it up. There are any number of things that can affect entanglement. But the (effectively, per time window) simultaneous arrival means you have a pretty good pair.

I am not always aware of how familiar folks are with the various component processes. So I probably could have explained a few things better.

 

[miosim]

miosim, your reading comprehension sucks, you read stuff you obviously don't understand in the slightest and then extract a few keywords and come up with a fantasy interpretation of what you think it means that is designed to make Bell look bad. Yes, he used the EPR argument, but where the hell do you get the idea that this had anything whatsoever to do with the "trivial ad hoc space-time picture of what might go on" which he briefly introduced in the Bertlmann's socks paper (and none of his other papers) and quickly tossed aside for a more broad definition of local causality?

My fault.

Once again, you seem to jump to ridiculous interpretations of sentences that will serve your desperate need to "prove" Bell wrong, never even considering that perhaps the first interpretation that came into your head might not be the right one and that there might be other ways of reading it that don't make Bell into the cartoon idiot you want him to be. …

At the beginning, I did consider that I just misunderstood Bell, because everybody seems to agree with him. However I have an impression that Bell was under influence of conviction/belief and this is the best environment for the most foolish ideas to flourish. Science in this regards is not much different from religion.
Regarding the majority of physicists who accept Bell’s proof, I think that they are more mathematicians than physicists, meaning that for them it is more natural to think about physical processes in terms of formulas than to visualize those processes. My impression is that since emergence of QM the theoretical physics have been “hijacked” by mathematicians that transformed physics into applied mathematics.
At the same time I have my doubt also.

I don’t know if "immediately foretells" is a part of the EPRB argument. I am not sure if this is another distortion of Einstein’s views or a distortion caused by Bohm.

Of course it's not a distortion, Einstein's own two-box analogy, which he used to clarify what his intended meaning had been, was clearly describing exactly this sort of situation where knowing the result of one measurement (seeing whether your box has a ball in it) tells you the result of the other (if yours had a ball the other is empty and vice versa). The EPR paper also made very clear they were talking about situations where knowledge of one measurement tells you what the result of the same measurement on the other particle would be …

Apparently I get suspicious over the world "immediately" that is irrelevant to the EPR argument but is appropriate within Bell’s views.

 

[miosim]

“… a straightforward application of Malus law shows that a subsequent measurement performed along b on photon ν 2 will lead to P (a, b) = cos^2(a,b) …”

In this statement (from near the bottom of p. 5 of the paper) Aspect is making the point that if you treat the measurement of photon v1 with a polarizer at angle a as causing a "collapse" of photon v2 into the same polarization state as v1, …
…There would be no way to reproduce this correlation (for arbitrary choice of angles a and b) in a local classical universe where Malus' law applied but there was no instantaneous "collapse" of the 2-particle wave function when one particle was measured.

However within the EPR paper (1935) there are no “classical” particles. Instead there are two independent QM entities (described by the individual wave function) and the Quantum Malus’ law should be fully applicable to them. Why Bell ‘stripped’ EPR particles from their QM privileges?

Let’s look closely into Bell/Aspect/Your assumption that “… a single measurement of v1 causes an instantaneous "collapse" of v2 into the same state.” That means that polarizer doesn’t affect polarization of entangled photons but acts as a ON/OFF gate only.

Let’s test this assumption using Aspect’s experimental setup.
1). First let's fully align polarizers A and B and observe a maximum (say 100%) correlation.
2). Set polarizer A and B at 90 deg and observe zero correlation.
3). Let’s add one more polarizers (C) between polarizer B and the source of photon. Let’s set this polarizers at intermediate angle of 45 deg and monitor correlated photons.

1. According to EPR model we should observe about 25% of correlated photons, because EPR photons on B side will be rotated by polarizers (B and C) and the intensity/probability of these photons could be calculated according to Malus’ law.

2. However According to Bell concept, we still should have zero correlation; otherwise we have to accept that photons A and B don’t have the same polarization any more.

It seems to me that Bell theorem is in conflict not only with EPR but with Malus’ law also.

 

[JesseM]

At the beginning, I did consider that I just misunderstood Bell, because everybody seems to agree with him.

Since it's clear you still understand nothing about Bell's argument (as evidenced by the fact that you couldn't even tell his "trivial ad hoc space-time picture" apart from his actual argument), why did you decide this wasn't the case? I guess you're just a ridiculously arrogant person who thinks he doesn't need to understand a theory in detail before trusting his gut feeling that it must be wrong?

However I have an impression that Bell was under influence of conviction/belief

The irony is rich!

Apparently I get suspicious over the world "immediately" that is irrelevant to the EPR argument but is appropriate within Bell’s views.

Wait, are you saying you think the EPR argument doesn't imply that measuring one particle would "immediately" tell us what the result of an identical measurement on the other would be? You think there would be some delay in your ability to make such a prediction? If so you're wrong, EPR's argument also says you would have such immediate knowledge, just like in Einstein's two-box analogy where looking inside one box immediately tells you whether the other box has a ball in it or is empty.

However within the EPR paper (1935) there are no “classical” particles. Instead there are two independent QM entities (described by the individual wave function)

No! In QM there is no "individual wavefunction" for each one that allows them to be treated independently, instead there is a single wavefunction for the entangled 2-particle system. So when either one is measured, the wavefunction describing both of them collapses. This is precisely why no local version of Malus' law, like the one that appears in classical physics, can reproduce the correlation predicted by QM.

Why Bell ‘stripped’ EPR particles from their QM privileges?

Because he wanted to investigate whether a local theory, which posited an objective reality independent of our measurements, could reproduce QM predictions. That was also what EPR and Einstein specifically were interested in. That's kind of the whole point, it's amazing that you can spend all this time bloviating about Bell and EPR and not get this.

Let’s test this assumption using Aspect’s experimental setup.
1). First let's fully align polarizers A and B and observe a maximum (say 100%) correlation.
2). Set polarizer A and B at 90 deg and observe zero correlation.
3). Let’s add one more polarizers (C) between polarizer B and the source of photon. Let’s set this polarizers at intermediate angle of 45 deg and monitor correlated photons.

1. According to EPR model we should observe about 25% of correlated photons

What does "EPR model" even mean? EPR don't suggest a specific model, they simply suggest that when you have a perfect correlation when you make the same measurement on both particles, then both particles must have local properties that predetermine what result they will give to that measurement. For example if you know particle #1 can pass it through a polarizer at angle A (assuming that's the first polarizer it encounters), then particle #2 must also have properties that predetermine it would pass through a polarizer at angle A as well (again assuming that's the first it encounters, see the note below on how passing through multiple polarizers might change the properties). Why do you think that fact alone should tell us anything about the probability it will pass through two polarizers at different angles B and C?

2. However According to Bell concept, we still should have zero correlation; otherwise we have to accept that photons A and B don’t have the same polarization any more.

Bell's concept is no different from EPR's, and again you are totally delusional if you think Bell's minimal assumptions say anything about the specific probabilities we should expect in this experiment. Note that in both Bell and EPR's version, it's quite possible that particle #2's properties are changed in some way when it passes through the first polarizer at angle B, so that its probability of passing through C is different from what it would be if C was the first polarizer it had encountered. For example, if the angles of C and A are the same, and particle #1 made it through A, that doesn't necessarily mean that any entangled particle #2 that makes it through B must also make it through C, although we know it definitely would have made it through C if that was the first polarizer it had encountered.

 

[miosim]

However within the EPR paper (1935) there are no “classical” particles. Instead there are two independent QM entities (described by the individual wave function)

No! In QM there is no "individual wavefunction" for each one that allows them to be treated independently, instead there is a single wavefunction for the entangled 2-particle system.

Apparently Einstein didn’t know that. From EPR paper (1935)

“ … let us suppose that we have two systems I and II, which we permit to interact from the time t=0 to t=T, after which time we suppose that there is no longer any interaction between the two parts…
…We see therefore that, as a consequence of two different measurements performed upon the first system, the second system may be left in states with two different wave functions. On the other hand, since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system. This is, of cause, merely a statement of what is meant by the absence of an interaction between the two systems. Thus, it is possible to assign two different wave functions (…) to the same reality… “

Why Bell ‘stripped’ EPR particles from their QM privileges?

Because he wanted to investigate whether a local theory, which posited an objective reality independent of our measurements, could reproduce QM predictions. That was also what EPR and Einstein specifically were interested in. That's kind of the whole point …

So Bell was interested to see if there is any difference between original system and its reduced version ”stripped” from its key properties?

What does "EPR model" even mean? EPR don't suggest a specific model, they simply suggest that when you have a perfect correlation when you make the same measurement on both particles, then both particles must have local properties that predetermine what result they will give to that measurement…

As I understand there are four key properties of EPR model relevant to the Bell’s theorem:

1. After separation the particles have determined and perfectly correlated properties (spin, polarization, etc.).
2. The complementary particles don’t interact after separation.
3. Particle’s behavior is independent from each other and is described by the corresponding independent wave functions.

For example if you know particle #1 can pass it through a polarizer at angle A (assuming that's the first polarizer it encounters), then particle #2 must also have properties that predetermine it would pass through a polarizer at angle A as well … Why do you think that fact alone should tell us anything about the probability it will pass through two polarizers at different angles B and C?

I don’t worry about the particle #1 while applying the Malus’ law to the particle #2. Whlie passing two consecutive polarizers C (at 45 deg) and B (at 90 deg) the probability (intencity) to pass polarizer by the particle #2 is:

I(final) = I(max) * cos^2(45) * cos^2(90-45) = I(max)*0.25

To comply with Malus’ law particle #2, as I understand, must change its polarization, so the correlated photons #1 and #2 will have different polarizations. This isn’t a problem for EPR model but is prohibited for Bom’s entangled photons that must have identical polarization.

Bell's concept is no different from EPR's, and again you are totally delusional if you think Bell's minimal assumptions say anything about the specific probabilities we should expect in this experiment. Note that in both Bell and EPR's version, it's quite possible that particle #2's properties are changed in some way when it passes through the first polarizer at angle B, so that its probability of passing through C is different from what it would be if C was the first polarizer it had encountered. For example, if the angles of C and A are the same, and particle #1 made it through A, that doesn't necessarily mean that any entangled particle #2 that makes it through B must also make it through C, although we know it definitely would have made it through C if that was the first polarizer it had encountered.

So what is your prediction for the experiment I described in the previous post and repeated below:

Let’s test this assumption using Aspect’s experimental setup.
1). First let's fully align polarizers A and B and observe a maximum (say 100%) correlation.
2). Set polarizer A and B at 90 deg and observe zero correlation.
3). Let’s add one more polarizers (C) between polarizer B and the source of photon and set this polarizers at intermediate angle of 45 deg and monitor correlated photons.

According to EPR model we should observe about 25% of correlated photons, because EPR photons on B side will be rotated by polarizers (B and C) and the intensity/probability of these photons could be calculated according to Malus’ law.

What is your prediction for Bell’s entangled photons for the step 3). ?