Why is entanglement necessary for understanding quantum mechanics?

[Nugatory]

Do you say that because it's known that all photons have the same wavelength, or is there some other reason?

It is not true that "all photons have the same wavelength" (or even that they have a physically meaningful wavelength, although that digression will take us far off-topic).

Wavelength $\lambda$ and frequency $\nu$ of a wave traveling at speed $c$ are related by $c=\lambda\nu$, so to the extent that polarizers work the same way for a range of frequencies, they must also work the same way for a range of wavelengths - and that's what we observe. Because the energy of a photon is related to the frequency by $E=h\nu$, and the polarizers work the same way for a range of frequencies, they must also work the same way for the corresponding range of energies.

Also some of the Bell-type experiments that measure the polarization of polarization-entangled photons use the calcium atomic cascade (google for "calcium cascade photon") to generate their photons, and this process generates photons at specific frequencies. Thus, even if there were some dependency on frequency and wavelength, it wouldn't affect these experiments.

 

[Jabbu]

It is not true that "all photons have the same wavelength" (or even that they have a physically meaningful wavelength, although that digression will take us far off-topic).

Wavelength $\lambda$ and frequency $\nu$ of a wave traveling at speed $c$ are related by $c=\lambda\nu$, so to the extent that polarizers work the same way for a range of frequencies, they must also work the same way for a range of wavelengths - and that's what we observe. Because the energy of a photon is related to the frequency by $E=h\nu$, and the polarizers work the same way for a range of frequencies, they must also work the same way for the corresponding range of energies.

Suppose photon energy is proposed to be a "hidden variable". How do you show there can not exist a function involving this unknown which would duplicate experimental results?

Also some of the Bell-type experiments that measure the polarization of polarization-entangled photons use the calcium atomic cascade (google for "calcium cascade photon") to generate their photons, and this process generates photons at specific frequencies. Thus, even if there were some dependency on frequency and wavelength, it wouldn't affect these experiments.

theta_A = 0, theta_B = 0
A: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0
B: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0

Ok. So finally now I'm staring at the naked mystery face to face. Entangled photons polarization is random between pairs, but same for each pair. Their overall chance to pass through any polarizator angle remains 50% as it should. However, unexpectedly, both photon twins have the same chance at different locations as if it was one event with a single probability and not two separate events each with its own independent probability. Would this be a good description of the essence of the mystery, or is there even more to it?

 

[Nugatory]

Suppose photon energy is proposed to be a "hidden variable". How do you show there can not exist a function involving this unknown which would duplicate experimental results?

There's Bell's theorem: no local hidden variable theory can match the quantum mechanical prediction in all cases. Then there are the experiments of Alain Aspect and many others, showing that the quantum mechanical predictions are correct in these cases. Put them together, and we know that there is no possible local hidden variable theory which matches experiment.

Ok. So finally now I'm staring at the naked mystery face to face. Entangled photons polarization is random between pairs, but same for each pair. Their overall chance to pass through any polarizator angle remains 50% as it should. However, unexpectedly, both photon twins have the same chance at different locations as if it was one event with a single probability and not two separate events each with its own independent probability. Would this be a good description of the essence of the mystery, or is there even more to it?

That's a pretty good summary.

 

[Jabbu]

There's Bell's theorem: no local hidden variable theory can match the quantum mechanical prediction in all cases.

Original Bell's inequality... This simple form does have the virtue of being quite intuitive. It is easily seen to be equivalent to the following elementary result from probability theory. Consider three (highly correlated, and possibly biased) coin-flips X, Y, and Z, with the property that:

X and Y give the same outcome (both heads or both tails) 99% of the time
Y and Z also give the same outcome 99% of the time,

then X and Z must also yield the same outcome at least 98% of the time. The number of mismatches between X and Y (1/100) plus the number of mismatches between Y and Z (1/100) are together the maximum possible number of mismatches between X and Z (a simple Boole–Fréchet inequality).
http://en.wikipedia.org/wiki/Bell's_theorem


This looks like a nice simple explanation, I just don't get it. Why are they even talking about some third coin, wouldn't two photons correspond to only two coins?

 

[bhobba]

That's a pretty good summary.

Yes it is.

But I really am scratching my head about all the angst this has engendered.

Its simply the weirdness of the underlying vector space structure of QM which is the essence of entanglement.

Such is totally inexplicable classically so its hardly surprising its not explainable by classical analogues like Bertlmanns socks.

Bell cottoned onto it, and his paper is clear about it.

Thanks
Bill

 

[Jabbu]

Such is totally inexplicable classically so its hardly surprising its not explainable by classical analogues like Bertlmanns socks.

I'm still trying to put it into some sensible terms before I even begin thinking about what actual explanation there is for this sorcery.

A: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0...
B: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0...

For example, this is like every time two of us flip a coin and it's always a match. It's already impossible. What is there to think? It's like trying to divide by zero, it does not compute. The premise must be wrong, surely?

 

[StevieTNZ]

May I recommend the recently published book by Nicolas Gisin - http://www.springer.com/physics/quantum+physics/book/978-3-319-05472-8

 

[Nugatory]

I'm still trying to put it into some sensible terms before I even begin thinking about what actual explanation there is for this sorcery.

A: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0...
B: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0...

For example, this is like every time two of us flip a coin and it's always a match. It's already impossible. What is there to think? It's like trying to divide by zero, it does not compute. The premise must be wrong, surely?

It might be worth going back to the beginning of this thread, reading through it again... It started with johan0001 asking why there was anything strange going on at all, how measuring the polarization of two entangled photons and finding a correlation is any different than putting two gloves in two boxes then finding that the presence of a left-handed glove in one box is correlated with finding a right-handed glove in the other.

 

[bhobba]

I'm still trying to put it into some sensible terms before I even begin thinking about what actual explanation there is for this sorcery.

Mate - that's why we have Bells Theorem

Note that keyword THEOREM. It shows that classical analogues are not possible where classical means naive reality.

Why? In math I gave up aeons ago looking for the why behind theorems. What's the why behind the fundamental theorem of algebra? What's the why behind a Weiner process being continuous and non differentiable everywhere - even such a function exists is downright weird - little alone some physical process is modeled by such? Blowed if I know - the reason is the math.

Thanks
Bill

 

[Nugatory]

This looks like a nice simple explanation, I just don't get it. Why are they even talking about some third coin, wouldn't two photons correspond to only two coins?

We have two photons, entangled so that if one of them passes a filter at a given angle, the other one definitely will not pass a filter at that angle.

The three coins correspond to the possible results of measuring the polarization on any of three possible angles, A, B, and C. For example, heads/heads/tails corresponds to "the left hand-photon would pass a filter at angle A while the right-hand photon would not; the left hand-photon would pass a filter at angle B while the right-hand photon would not; the left hand-photon would not pass a filter at angle C while the right-hand photon would".

 

[Jabbu]

It might be worth going back to the beginning of this thread, reading through it again... It started with johan0001 asking why there was anything strange going on at all, how measuring the polarization of two entangled photons and finding a correlation is any different than putting two gloves in two boxes then finding that the presence of a left-handed glove in one box is correlated with finding a right-handed glove in the other.

I've actually read quite a bit about this stuff, but the crucial thing which eluded me is that photon polarization is supposed to be random, I thought it's constant. This is very subtle difference if you don't know it's implied. But what is fascinating I was reading through those experiments and it all actually made sense, it gives the same result, only there is no any mystery. Allegedly random photon polarization is a big news to me, it changes everything, and nothing makes sense anymore.

 

[billschnieder]

I've actually read quite a bit about this stuff, but the crucial thing which eluded me is that photon polarization is supposed to be random, I thought it's constant.

If you think about what "random" means you'll see there is some confusion in the way it is being used here. The only time it makes sense to talk of randomness with respect to the polarization of a single photon, has to do with inability to predict what it will be, but in that case it doesn't mean it won't be constant. For many different photons, you can say that their polarization directions are random, which simply means there is no discernible pattern from one photon to the other in the set. It does not mean each individual photon does not have a fixed constant polarization direction (although some people believe that). It is important to distinguish claims about individual photons, and claims about ensembles of photons.

 

[bhobba]

If you think about what "random" means you'll see there is some confusion in the way it is being used here.

Indeed there is.

But please bear in mind the polarisation is not random - its nothing at all - ie it doesn't even have the property of polarisation until observed. Its the act of observation that gives a random outcome. The weirdness is that it's always correlated with the other photon. But the other photon doesn't have the property of polarisation until observed either.

One may think some instantaneous communication went between the two photons, but what Bell's theorem shows is you don't have to view it that way. You can keep locality if you assume it doesn't have the property until observed - which is actually what the formalism says so really there is no issue. I personally go further and think there is some kind of communication, and the polarization don't exist until observed - which the theorem also allows. But that's just me - you don't have to do it.

Thanks
Bill

 

[Jabbu]

We have two photons, entangled so that if one of them passes a filter at a given angle, the other one definitely will not pass a filter at that angle.

You mean if they are orthogonally entangled? But if they are entangled with parallel polarization then whenever one goes through so must the other, like this:

theta_A = 0, theta_B = 0
A: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0
B: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0

Consider the first pair of photons from that sequence. Let's say they have 45 degrees polarization so they both have 50% chance to pass through their 0 degrees aligned polarizers. Photon A happens to go through, first, and informs his twin brother he must go through as well, or else! So then photon B finally meets with polarizer B, bribes it, and continues as planned. Even if the explanation is some instantaneous connection between the photons, it still doesn't explain why would second polarizer just go along with that deal.

 

[DrChinese]

Ok, all together it should now look like this:


theta_A = 0, theta_B = 0
A: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0
B: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0

sequence length = 20
matching pairs (00 or 11) = 20
mismatching pairs (01 or 10) = 0
Correlation = (match - mismatch) / sequence length = 20/20 = 100%


theta_A = 0, theta_B = 45
A: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0
B: 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1

sequence length = 20
matching pairs (00 or 11) = 15
mismatching pairs (01 or 10) = 5
Correlation = (match - mismatch) / sequence length = 10/20 = 50%


theta_A = 0, theta_B = 90
A: 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1
B: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0

sequence length = 20
matching pairs (00 or 11) = 10
mismatching pairs (01 or 10) = 10
Correlation = (match - mismatch) / sequence length = 0/20 = 0%

I just saw this post. Unfortunately, you have mixed up the entangled match percentages and correlation somewhat such that the above is not correct.

Correct is:
Theta=0 degrees, match=100%, correlation=1
Theta=0 degrees, match=50%, correlation=0
Theta=90 degrees, match=0%, correlation=-1

So the 2nd and 3rd patterns are inaccurate.

 

[PeterDonis]

Consider the first pair of photons from that sequence. Let's say they have 45 degrees polarization

Here is where you are going wrong: you are assuming that the photons have some definite polarization (45 degrees or anything else) before their polarization is measured. But that would mean that both photons started out in a polarization eigenstate; and that is a very restrictive assumption. There are *lots* of states of the photons which are *not* polarization eigenstates (and in the actual experiments that are done to test this, the photons are not in polarization eigenstates). When people say the polarization is "random", or that the photon does not have a definite polarization until it's observed, what they mean is that the photon's state at the start is not a polarization eigenstate.

 

[DrChinese]

You mean if they are orthogonally entangled? But if they are entangled with parallel polarization then whenever one goes through so must the other, like this:

theta_A = 0, theta_B = 0
A: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0
B: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0

...

There are 2 types of PDC producing entangled photon pairs: Type I and Type II. Type I produces pairs that are parallel, Type II produces pairs that are orthogonal. I prefer to discuss Type I because the examples are much easier to describe in posts. The fundamental principle is the same either way. In fact you can rotate either Type to act like the other Type.

So sometimes one poster is referring to one type when another poster is referring to the other. I do my best to label as Type I PDC and entangled so as to be clear.

 

[DrChinese]

Consider the first pair of photons from that sequence. Let's say they have 45 degrees polarization so they both have 50% chance to pass through their 0 degrees aligned polarizers. Photon A happens to go through, first, and informs his twin brother he must go through as well, or else! So then photon B finally meets with polarizer B, bribes it, and continues as planned. Even if the explanation is some instantaneous connection between the photons, it still doesn't explain why would second polarizer just go along with that deal.

As PeterDonis indicates, you must be careful when you assume that there is a pre-existing polarization as Bell's Theorem places restrictions on such.

However, your model WILL more or less work as described above. It is called a non-local model. Under such model, there is instantaneous communication from A to B (assuming A is measured first). In this hypothetical case, B conforms to A. The statistics work out fine and Bell's Theorem is not a problem. Further, you don't need to answer "WHY" it happens that way any more than you ask "why" the speed of light is c. It just is.

The problem with this interpretation (model) is that there is no other evidence of the signalling mechanism other than in entanglement, and it is not supported by the so-called "standard model". Accordingly, it requires a new force currently undiscovered - or other significant changes to our understanding of physics. There are several non-local interpretations that explicitly solve these issues. Bohmian Mechanics is one such, you can google that.

 

[DrChinese]

The premise must be wrong, surely?

Yes, but which premise?

That is what Bell helps us to understand. Usually the premises are:

1. QM is correct (this is strongly confirmed by experiment).
2. There is no action at a distance.
3. Quantum particles such as photons have well-defined properties independent of the act of observation.
4. There is causality (the future does not affect the past).

At least one of the above is incorrect, according to Bell's Theorem.

 

[Jabbu]

If you think about what "random" means you'll see there is some confusion in the way it is being used here. The only time it makes sense to talk of randomness with respect to the polarization of a single photon, has to do with inability to predict what it will be, but in that case it doesn't mean it won't be constant. For many different photons, you can say that their polarization directions are random, which simply means there is no discernible pattern from one photon to the other in the set. It does not mean each individual photon does not have a fixed constant polarization direction (although some people believe that). It is important to distinguish claims about individual photons, and claims about ensembles of photons.

That's why I'm asking about how actual data streams look like.

theta_A = 0, theta_B = 0
A: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0
B: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0

When there is always 50% ones and 50% zeroes in each individual sequence then according to Malus's law photon polarization is either random or constant at 45 degrees relative to polarizers. I thought photon polarization was constant and centered relative to polarizers, so that data stream for theta_A = 0, theta_B = 0 looks like this:

A: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
B: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

It turns out 100% correlation as well. Only this time it's not weird why sequence A coincides with sequence B, they simply both have 100% chance to go through. It's very subtle difference to distinguish if you don't look at some actual experimental data, which I can't find anywhere on the internet.

 

[Jabbu]

One may think some instantaneous communication went between the two photons, but what Bell's theorem shows is you don't have to view it that way. You can keep locality if you assume it doesn't have the property until observed - which is actually what the formalism says so really there is no issue. I personally go further and think there is some kind of communication, and the polarization don't exist until observed - which the theorem also allows. But that's just me - you don't have to do it.

Is there mathematically even any difference between "random" and "not existing - then existing"? I can conceive instantaneous interaction and stuff disappearing and reappearing in different locations, if I must. But that there is no Moon when I don't look at it, that's too much.

 

[Jabbu]

Here is where you are going wrong: you are assuming that the photons have some definite polarization (45 degrees or anything else) before their polarization is measured. But that would mean that both photons started out in a polarization eigenstate; and that is a very restrictive assumption. There are *lots* of states of the photons which are *not* polarization eigenstates (and in the actual experiments that are done to test this, the photons are not in polarization eigenstates). When people say the polarization is "random", or that the photon does not have a definite polarization until it's observed, what they mean is that the photon's state at the start is not a polarization eigenstate.

I don't think that changes the conclusion. Photon A interacts with polarizer A first, and the decision whether photon B will go through polarizer B is made right there and then. Ok? But even if the explanation is some instantaneous connection between the photons, it still doesn't explain why would second polarizer just go along with that deal.

 

[Jabbu]

As PeterDonis indicates, you must be careful when you assume that there is a pre-existing polarization as Bell's Theorem places restrictions on such.

However, your model WILL more or less work as described above. It is called a non-local model. Under such model, there is instantaneous communication from A to B (assuming A is measured first). In this hypothetical case, B conforms to A. The statistics work out fine and Bell's Theorem is not a problem. Further, you don't need to answer "WHY" it happens that way any more than you ask "why" the speed of light is c. It just is.

The problem with this interpretation (model) is that there is no other evidence of the signalling mechanism other than in entanglement, and it is not supported by the so-called "standard model". Accordingly, it requires a new force currently undiscovered - or other significant changes to our understanding of physics. There are several non-local interpretations that explicitly solve these issues. Bohmian Mechanics is one such, you can google that.

I thought instantaneous signaling is "standard model". If not that, what's the explanation then?

 

[DrChinese]

But that there is no Moon when I don't look at it, that's too much.

Type I entangled photons

A=0 degrees:
A: 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1

B=120 degrees:
B: 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0

Match rate above is 25%. If the moon is there when not observed, what is C below (had it been measured)?

C=240 degrees:
C: ? ? ? ...

 

[DrChinese]

I thought instantaneous signaling is "standard model". If not that, what's the explanation then?

Not really. The "standard model" is actually silent on the mechanism. There are also models where there is no instantaneous signalling.

The term you will sometimes hear is: "quantum non-locality". That means it sort of appears non-local, but strictly in a "quantum" manner - such that it does not conflict with relativity. Fully non-local models violate relativity.

 

[DrChinese]

PS regarding my post #164:

A-B match rate is 25%
A-C match rate should be 25%
B-C match rate should also be 25%

After all, theta is the same for all 3.

Good luck!

 

[PeterDonis]

Photon A interacts with polarizer A first, and the decision whether photon B will go through polarizer B is made right there and then.

But this way of looking at it is frame-dependent; there will be another frame in which photon B interacts first, and the decision whether photon A will go through is made right there and then. There is no invariant fact of the matter about which photon interacts first. That's why DrChinese said that fully non-local models violate relativity.

For what it's worth, quantum field theory has a somewhat different take on this, at least as I understand it. In QFT, "causality" does not mean that spacelike separated measurements can't be correlated, even to a degree that violates the Bell inequalities; it only means that spacelike separated measurements must commute, i.e., the results must not depend on which measurement happens first. The photon measurements satisfy this criterion, so QFT simply says "no problem".

 

[Jabbu]

I just saw this post. Unfortunately, you have mixed up the entangled match percentages and correlation somewhat such that the above is not correct.

Correct is:
Theta=0 degrees, match=100%, correlation=1
Theta=0 degrees, match=50%, correlation=0
Theta=90 degrees, match=0%, correlation=-1

So the 2nd and 3rd patterns are inaccurate.

After PeterDonis' post #132 I adjusted it to match the new formula:

correlation = (match - mismatch) / sequence length

...where "match" is number of 00 + 11 pairs, and "mismatch" is number of 01 + 10 pairs.


Originally this seemed to be the formula:

correlation = (match_0 + match_1) / sequence length

...where "match_0" is number 00 pairs, and "match_1" is number of 11 pairs.



What is your "match" formula?

 

[DrChinese]

After PeterDonis' post #132 I adjusted it to match the new formula:

correlation = (match - mismatch) / sequence length

...where "match" is number of 00 + 11 pairs, and "mismatch" is number of 01 + 10 pairs.Originally this seemed to be the formula:

correlation = (match_0 + match_1) / sequence length

...where "match_0" is number 00 pairs, and "match_1" is number of 11 pairs.
What is your "match" formula?

Type I Match: cos^2(theta)
Type I Correlation: cos^2(theta)-sin^(theta)

I did warn you in post #108, it is best to discuss matches and for Type I.

 

[Jabbu]

Type I entangled photons

A=0 degrees:
A: 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1

B=120 degrees:
B: 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0

Match rate above is 25%. If the moon is there when not observed, what is C below (had it been measured)?

C=240 degrees:
C: ? ? ? ...

True range is only from 0 to 90 degrees relative, from parallel to orthogonal. So both 120 and 240 are really just the same 60 degrees relative angle. Anyway, what I thought is that photon polarization is actually constant and deliberately centred between the two polarizers, so in the case of master_theta = 60 or 120 or 240:

theta_A = -30, theta_B = +30
A: 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1
B: 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1

Both photons now according to Malus have cos^2(30) = 75% chance to pass through, and therefore there is 75% ones and 25% zeros in each stream. So what is the chance of getting 11 or 00 matching pairs vs chance of getting 10 or 01 mismatching pairs?

chance of match: (0.75 * 0.75) + (0.25 * 0.25) = 0.625
chance of mismatch: (0.25 * 0.75) + (0.75 * 0.25) = 0.375
correlation: 0.625 - 0.375 = 25%

 

[Jabbu]

Type I Match: cos^2(theta)
Type I Correlation: cos^2(theta)-sin^(theta)

I did warn you in post #108, it is best to discuss matches and for Type I.

I'm not talking about any other experiment but what you call "Type I". cos^2(theta) is theoretical prediction equation. Correlation is calculated differently from experimental data, in terms of matching and mismatching pairs, along these lines:

correlation = (match - mismatch) / sequence length
...where "match" is number of 00 + 11 pairs, and "mismatch" is number of 01 + 10 pairs

correlation = (match_0 + match_1) / sequence length
...where "match_0" is number 00 pairs, and "match_1" is number of 11 pairs


The formula defines how actual data streams are supposed to look like, it makes all the difference, but the difference is very subtle, so it is important to get this formula straight.

 

[DrChinese]

The formula defines how actual data streams are supposed to look like, it makes all the difference, but the difference is very subtle, so it is important to get this formula straight.

And I keep telling you that the formula for matches and the formula for correlation are completely different. Forget correlation, you will simply make things more complicated than needed.

Matches at 60 degrees = matches at 120 degrees = 25%.

Before you start modeling things, you would find it beneficial to understand fully what happens experimentally. And many of your ideas about that are incorrect, especially most everything in post 170. For example, 1's are not more likely than 0's for entangled streams. They are equally likely. The correlation for 60 degrees is not 25%, it is -.5.

 

[bhobba]

Is there mathematically even any difference between "random" and "not existing - then existing"?

You are viewing it incorrectly.

When we say something exists we usually have the view of what's called naive reality - you can look up exactly what it is. I will not get into a philosophical discussion about what existing means except to say most assume some kind of naive reality.

Now QM is a theory about observations. It is silent on what's going on when not observed. Naive reality may apply - or it may not - the theory says nothing one way or the other - on the surface that is.

We can't say anything about the photons polarisation when it's not being observed. That is the key difference between your analogy, Bertlmanns socks vs QM. Both, being classical objects, obey naive reality.

What Bells theorem shows is QM is not only silent on the issue, but in fact rules out naive reality. That's the striking and interesting thing about it. The Bertlmann socks analogy is not correct.

Thanks
Bill

 

[bhobba]

it still doesn't explain why would second polarizer just go along with that deal.

That's the definition of correlated.

What Bell shows is classical correlations like Bertlmann's socks are different to quantum ones.

Why are they correlated?

Apply the Born Rule to 1/root 2 (|a>|b> + |b>|a>).

Its basic QM.

Thanks
Bill

 

[Jabbu]

Before you start modeling things, you would find it beneficial to understand fully what happens experimentally.

Can you point any document on the internet where we can see samples of actual experimental data?