### 1 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Sunday 18 december 2016
A practical application of testing Bell's theorem is described here:
https://en.wikipedia.org/wiki/Bell%27s_theorem Go to "contents" and select paragraph 7.

The results indicate the following (see text):
When we perform 72 tests each time and the angle between the two polarizers
1) is 0 degrees we get (on average) 36 times + + and 36 times - - This means correlation is 1
2) is 90 degrees we get: 36 times + - and 36 times - + This means correlation is -1
3) is 45 degrees we get: 18 * ++, 18 * +-, 18 * -- and 18 * -+ This means correlation is 0

With +- I mean Alice detects a +1 and Bob detects a -1

My question is what is the result with 22.5 degrees ?
My prediction is 27 * ++, 9 * +-, 27 * -- and 9 * -+ With 67.5 degrees my prediction is:
My prediction is 9 * ++, 27 * +-, 9 * -- and 27 * -+

Any comment?
In paragraph 2 "overview" a similar test is described but the angles are twice as large.
( 0 degrees corr = 1, 180 degrees corr = -1, 90 degrees corr = 0

Question 2 At what place exactly(?) are the photons measured?
IMO this is at the two polarizers.

### 2 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Wednesday 21 december 2016
On Sunday, 18 December 2016 22:37:18 UTC+1, Nicolaas Vroom wrote:
 > A practical application of testing Bell's theorem is described here: https://en.wikipedia.org/wiki/Bell%27s_theorem

 > My question is what is the result with 22.5 degrees ? My prediction is 27 * ++, 9 * +-, 27 * -- and 9 * -+ Any comment?

 > Question 2 At what place exactly(?) are the photons measured? IMO this is at the two polarizers. The text is not clear about this specific point

To start with the second questions I think that the photons are already measured at the polarizers. That is where each photon "decides" if it should go to the +1 or -1 detector. At each detector the photon is again measured (this depents) to show the result of the first measurement.

This means if there is some form of communication between the two photons it should be between the two polarizers and not between the detectors.

I doubt if there is any form of communication between the two polarizers.

Regarding the first question: The following table shows the predicted results between 0 and 90 degrees.

```++    +-   --   -+   correlation
0     36     0   36    0     1
15    30     6   30    6     0.6666
22.5  27     9   27    9     0.5
30    24    12   24   12     0.3333
45    18    18   18   18     0
67.5  12    24   12   24    -0.3333
75     6    30    6   30    -0,6666
90     0    36    0   36    -1
```

My question is primarily about the actual measured results for each angle. Are the predicted values as observed?

The above table also shows the correlations based on these results. The relation is lineair but that is not according to quantum mechanics which predicts a cos(2 teta) function. Any explanation?

Nicolaas Vroom

### 3 Two Questions about Bell's theorem

From: Jos Bergervoet
Datum: Wednesday 21 december 2016
On 12/21/2016 4:51 PM, Nicolaas Vroom wrote:
 > On Sunday, 18 December 2016 22:37:18 UTC+1, Nicolaas Vroom wrote:
 >> A practical application of testing Bell's theorem is described here: https://en.wikipedia.org/wiki/Bell%27s_theorem
 >
 >> My question is what is the result with 22.5 degrees ? My prediction is 27 * ++, 9 * +-, 27 * -- and 9 * -+

No, that seems to be the result for 30 degrees (correlation +0.5 if I follow your example correctly).

For 22.5 degrees the correlation should be sqrt(2)/2 = 0.7071... so the numbers would be 31, 5, 31, 5, approximately. In general the quantum correlation in this case is cos(2*phi), whereas you seem to be using 1-2*phi/Pi.

 >> Any comment?

What you are using is the classical correlation. If the photons are internally having a pointer in some direction that defines their polarization, are created with random polarization in matched pairs (pairs with equal polarization) and sorted by the polarizers by just forcing their polarization to the nearest of the two possible outcomes of that polarizer, then you get the classical correlation.

You do not need quantum mechanics for that procedure, some classical mechanical instrument could simply do it like that.

 >> Question 2 At what place exactly(?) are the photons measured? IMO this is at the two polarizers. The text is not clear about this specific point
 > To start with the second questions I think that the photons are already measured at the polarizers. That is where each photon "decides" if it should go to the +1 or -1 detector.

That is not how quantum field theory (QFT) describes the process. After the field excitation moves through the polarizer, there is still a superposition in the photon field of a field excitation moving along the +1 path and an excitation moving along the -1 path. I use "excitation", although I could call it "wave packet" but a quantum field is not a wave function so that would be misleading! It is a function of a wave function: a wave functional. It gives the quantum amplitude for each possible wave function. That's why it's a function of a function.

In particular: The wave functional can give a nonzero amplitude for a wave function which consists only of a packet going in the +1 direction, while also giving a nonzero amplitude for a wave function consisting only of a packet going in the -1 direction. And it will give zero amplitude for a wave function consisting of two packets, one in each direction. (If you would just add two wave packets into an ordinary wave function than this combined result would be possible. QFT rules it out!)

In that way the wave functional describes different possibilities for the wave function. That is what a quantum field is. It is a set of possible wave functions. So unlike what you suppose, the photon has *not* made a choice yet.

 > At each detector the photon is again measured (this depents) to show the result of the first measurement.

After the detectors have been reached, the photon field will have interacted with the matter field of the detectors. Still, quantum field theory will describe all the possibilities, each with a nonzero amplitude. Still the same possibilities we had, but transferred to the possible configurations of the matter field comprising the detector.

 > The following table shows the predicted results between 0 and 90 degrees. ``` ++ +- -- -+ correlation 0 36 0 36 0 1 15 30 6 30 6 0.6666 22.5 27 9 27 9 0.5 30 24 12 24 12 0.3333 45 18 18 18 18 0 67.5 12 24 12 24 -0.3333 75 6 30 6 30 -0,6666 90 0 36 0 36 -1 ```

No, that is again the classical correlation. The quantum correlation is higher.

 > My question is primarily about the actual measured results for each angle. Are the predicted values as observed?

As far as I know, the quantum correlation is always observed, so *not* the correlation of your table.

 > The above table also shows the correlations based on these results. The relation is lineair but that is not according to quantum mechanics which predicts a cos(2 teta) function. Any explanation?

Well, as I said, your correlation is the wrong one! It is not what you get if you compurte the amplitude of the different possibilities of the wave function shape, by using QFT (or similar quantum mechanical methods).

Of course quantum mechanics can only give this higher correlation because it does *not* describe the field as a simple wave function which would be polarized in a specific direction, but as a collection of possible wave functions, described by the wave functional. This gives a non-zero complex amplitude to each possible wave function, where the situation in different parts in space is correlated.

[NB: You can also describe it by wave functions of more than one particle position, a more old-fashioned approach to quantum field theory, which is easier for doing calculations and avoids the concept of a wave functional. That approach obviously also introduces correlations between things going on in different parts of space. Bottom line is: what happens at one detector is correlated to what happens at the other by complex numbers and not by correlated chances (positive real numbers), the quantum correlation is stronger than correlated chances!]

-- Jos

### 4 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Saturday 24 december 2016
On Wednesday, 21 December 2016 21:53:54 UTC+1, Jos Bergervoet wrote:
 > On 12/21/2016 4:51 PM, Nicolaas Vroom wrote:
 > > On Sunday, 18 December 2016 22:37:18 UTC+1, Nicolaas Vroom wrote:
 > >> A practical application of testing Bell's theorem is described here: https://en.wikipedia.org/wiki/Bell%27s_theorem
 > >
 > >> My question is what is the result with 22.5 degrees ? My prediction is 27 * ++, 9 * +-, 27 * -- and 9 * -+
 > No, that seems to be the result for 30 degrees (correlation +0.5 if I follow your example correctly). For 22.5 degrees the correlation should be sqrt(2)/2 = 0.7071... so the numbers would be 31, 5, 31, 5, approximately. In general the quantum correlation in this case is cos(2*phi), whereas you seem to be using 1-2*phi/Pi.
 > >> Any comment?
 > What you are using is the classical correlation.

Jos,

What I try to understand are the actual results of a "two channel" Bell test. As such I need a document which describes the results of an actual experiment. I need the raw results. In that sense I do not need the correlation factor nor the correlation function because there are many ways to calculate a correlation factor. The correlation factors 1,0 and -1 are clear. All the other ones can be "tricky" and depend about the specific mathematics used. In my case for each angle the correlation is calculated based on 72 "observations" in increments of 2.5 degrees.

 > > The following table shows the predicted results between 0 and 90 degrees. ``` ++ +- -- -+ correlation 0 36 0 36 0 1 15 30 6 30 6 0.6666 22.5 27 9 27 9 0.5 30 24 12 24 12 0.3333 45 18 18 18 18 0 67.5 12 24 12 24 -0.3333 75 6 30 6 30 -0,6666 90 0 36 0 36 -1 ```

At page 6 this document shows the measured results of 45 runs. The results show that in 24 cases the two lamps are identical (RR and GG) and in 21 cases the lamps are different (RG and GR) Because there are 8 varieties and 9 possible swith settings the total number of combinations is 72. When you investigate each of these combinations you get 48 runs where the two lamps are identical and 24 runs where they are different That means theoretical in 2/3 the lamps are identical and 1/3 not. This seems to be inconflict with the actual results of the test. However when you perform an actual simulation of 100 experiments with 45 runs 4 experiments are with 24 equal pairs or less. This means that the experiment does not give an answer on the question if the bell inequality is true or violated nor that quantum theorie is right or wrong.

For more details see: http://users.telenet.be/nicvroom/wik_Bell's_theorem.htm#par%2012

 > > My question is primarily about the actual measured results for each angle. Are the predicted values as observed?
 > As far as I know, the quantum correlation is always observed, so *not* the correlation of your table.

The correlation is not observed. The correlation is calculated. What is observed are possible counts at each of the detectors. These counts are the raw data (as a function of an angle)

Nicolaas Vroom

### 5 Two Questions about Bell's theorem

From: Jos Bergervoet
Datum: Sunday 25 december 2016
Translate message into English On 12/24/2016 11:07 AM, Nicolaas Vroom wrote:
 > On Wednesday, 21 December 2016 21:53:54 UTC+1, Jos Bergervoet wrote:
 >> On 12/21/2016 4:51 PM, Nicolaas Vroom wrote:
 >>> On Sunday, 18 December 2016 22:37:18 UTC+1, Nicolaas Vroom wrote:
 >>>> A practical application of testing Bell's theorem is described here: https://en.wikipedia.org/wiki/Bell%27s_theorem
 >>>
 >>>> My question is what is the result with 22.5 degrees ? My prediction is 27 * ++, 9 * +-, 27 * -- and 9 * -+
 >> No, that seems to be the result for 30 degrees (correlation +0.5 if I follow your example correctly). For 22.5 degrees the correlation should be sqrt(2)/2 = 0.7071... so the numbers would be 31, 5, 31, 5, approximately. In general the quantum correlation in this case is cos(2*phi), whereas you seem to be using 1-2*phi/Pi.
 >>>> Any comment?
 >> What you are using is the classical correlation.
 > Jos, What I try to understand are the actual results of a "two channel" Bell test.

Then you are looking for an explanation!

 > As such I need a document which describes the results of an actual experiment.

No, you need a document that explains how this particular process (the experiment with photon pairs) works.

 > I need the raw results.

No, you would only need those if you were trying to check if the explanations were correct, after reading them (and perhaps not wanting to believe them?!)

But, although you do not strictly *need* the raw results, I agree with you that having them would be interesting.

 > In that sense I do not need the correlation factor nor the correlation function because there are many ways to calculate a correlation factor.

That is like saying you do not need the tables of multiplication because there are many ways to get the result of multiplying two numbers, and you only want a list of raw results of example calculations that others have done. Again, that sounds like you are refusing to accept some well-known theory and want to challenge it!

 > The correlation factors 1,0 and -1 are clear. All the other ones can be "tricky" and depend about the specific mathematics used.

No, they are not tricky at all in the case you discuss: The result is cos(2*phi). Period.

 > In my case for each angle the correlation is calculated based on 72 "observations" in increments of 2.5 degrees.

So what is your question then?! You would need

```N++   =  18 * (1 + cos(2 phi))
N--   =  18 * (1 + cos(2 phi))
N+-   =  18 * (1 - cos(2 phi))
N-+   =  18 * (1 - cos(2 phi))
```
which would give cos(2 phi) as correlation. Just subtract the anti-coincidence cases from the coincidence cases: (N++ + N-- - N+- - N-+) / 72 = cos(2phi)

...
 > There exists a different document by N. David Mermin. See: http://cp3.irmp.ucl.ac.be/~maltoni/PHY1222/mermin_moon.pdf

Mermin seems to describe one of the early experiments (by Alain Aspect). It's from 1985, much more has been verified since then. Quantum mechanics is right. (Forget your hopes of refuting it!)

..
 > That means theoretical in 2/3 the lamps are identical and 1/3 not. This seems to be inconflict with the actual results of the test. However when you perform an actual simulation of 100 experiments with 45 runs 4 experiments are with 24 equal pairs or less.

Mermin's numbers seem to come from a "gedanken demonstration" (see p. 4). If he has made an error in his table (and I did not check) then it's his fault.

 > This means that the experiment does not give an answer on the question if the bell inequality is true or violated nor that quantum theorie is right or wrong.

We do not need an old discussion from 1985 for that. Aspect's experiment and many varieties of it have been repeated many times since then.

...
 >>> My question is primarily about the actual measured results for each angle. Are the predicted values as observed?
 >> As far as I know, the quantum correlation is always observed, so *not* the correlation of your table.
 > The correlation is not observed. The correlation is calculated. What is observed are possible counts at each of the detectors.

The counts are observed as predicted. A correlation calculated from it is also as predicted.

The counts are not as in your table but they are as in the expressions that I wrote above (if you average over a large enough sample and the particle pairs are created exactly as they should, and other experimental errors are dealt with!)

 > These counts are the raw data (as a function of an angle)

Yes, and the angle can be chosen *just before* the particles reach the polarizers. At that point in time the situation is the most interesting! The state of the photon field must contain all the information to produce all the different count results for all the different angles that Alice and Bob are still free to choose at that moment! And there *cannot* be any communication between those regions of space at that late stage in time.

As I wrote earlier, only QM can encode this information. Either in a two-position wave function, or in a distribution of ordinary single-position E-field waves as given by the QFT wave functional. This state, just before the polarizers are reached is essential to understand things!

Mermin's document gives some hints at page 9, but for photons the proper 2-particle wave function for spin-singlet would be:

E_Ah(x)*E_Bv(x')-E_Av(x)*E_Bh(x')-E_Bh(x)*E_Av(x')+E_Bv(x)*E_Ah(x')

whereas your Wikipedia case of *aligned* spins would give:

E_Av(x)*E_Bv(x')+E_Ah(x)*E_Bh(x')+E_Bh(x)*E_Ah(x')+E_Bv(x)*E_Av(x')

where E_Ah is a wave packet towards Alice with horizontal polarization, E_Bv a wave packet towards Bob with vertical polarization, E_Av towards Alice with vertical pol., etc. Both cases are symmetric under particle exchange as boson functions should be. The first one is anti-symmetric in the polarization as the spin-singlet state it contains should be. (Don't make it simpler than that, Mermin is confusing things by starting with light and then going to spin-1/2 fermion states..)

-- Jos

### 6 Two Questions about Bell's theorem

From: ben...@hotmail.com
Datum: Sunday 25 december 2016
Nicolaas Vroom wrote: ......
 >> My prediction is 27 * ++, 9 * +-, 27 * -- and 9 * -+

I agree with Jos that:

 > seems to be the result for 30 degrees (correlation +0.5). For 22.5 degrees the correlation should be sqrt(2)/2 = 0.7071... so the numbers would be 31, 5, 31, 5, approximately. In general the quantum correlation in this case is cos(2*phi) ...

For QM data, I calculate the numbers as:

```angle        n11
0        36
15        33.58845727
22.5        30.72792206
30        27
45        18
67.5        5.272077939
75        2.411542732
90        0
```

The formula that I used for n11 is 72 * (1+COS(2*angle))/4, where angle is in radians. The correlation is COS(2*angle).

Your table of angles is not completely symmetric up versus down as you have included 30 degrees but excluded 06 degrees. Maybe this asymmetry in the table was unhelpful.

### 7 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Monday 26 december 2016
On Sunday, 25 December 2016 04:42:08 UTC+1, Jos Bergervoet wrote:
 > On 12/24/2016 11:07 AM, Nicolaas Vroom wrote:
 > > Jos, What I try to understand are the actual results of a "two channel" Bell test.
 > Then you are looking for an explanation!
 > > As such I need a document which describes the results of an actual experiment.
 > No, you need a document that explains how this particular process (the experiment with photon pairs) works.
 > > I need the raw results.
 >

1) When the polarization of both photons is measured in the same direction, both give the same outcome: perfect correlation.
2) When measured at directions making an angle 45 degrees with one another, the outcomes are completely random (uncorrelated).
3) Measuring at directions at 90 degrees to one another, the two are perfectly anti-correlated.
4) In general, when the polarizers are at an angle phi to one another, the correlation is cos(2*phi).

Line 1 indicates that apparently someone has performed this experiment 100 times with angle is zero and the result is 50++ and 50 --
Line 2 indicates that with 45 degrees and 100 times the result is (on average) 25++ 25+- 25-- and 25-+
Line 3 indicates that with 90 degrees the result is: 50+- and 50-+ The correlation factors are with 0, 45 and 90 degrees: 1, 0 and -1

In order to understand line 4 the first angles to study are 22.5 and 67.5 degrees. That is why I asked the question: Is there anyone who has performed this experiment and what are the results. I'am not so much interesting in the correlation factors.

 > But, although you do not strictly *need* the raw results, I agree with you that having them would be interesting.

That is not interesting: that is very important. That is the only way to verify if the Bell inequality is violated or if the quantum theory (in this respect) is correct.

 > Again, that sounds like you are refusing to accept some well-known theory and want to challenge it!

What I want to understand which of the two theories is correct. The only way is to compare the predicted outcomes of the experiments by each theory with the actual outcome.

 > > The correlation factors 1,0 and -1 are clear. All the other ones can be "tricky" and depend about the specific mathematics used.
 > No, they are not tricky at all in the case you discuss: The result is cos(2*phi). Period.

You are already sure that line 4 is correct. I do not say that line 4 is wrong. The point is I want to study the results of actual experiments which show that the correlation is this cos(2*phi) function.

 > > There exists a different document by N. David Mermin. See: http://cp3.irmp.ucl.ac.be/~maltoni/PHY1222/mermin_moon.pdf
 > Mermin seems to describe one of the early experiments (by Alain Aspect). It's from 1985, much more has been verified since then. Quantum mechanics is right. (Forget your hopes of refuting it!)

The main reason why I show this document is because it starts with the results of an actual experiment.

When you study the Alain Aspect document of 1979, it also starts with an actual experiment.

I do not want to refute something. I do not understand. It is very difficult to find clear and simple documents.
The Alain Aspect 1979 is very clear to some extend except when they realy come to what I should call the highlight of the document then there is silence.
This document is also "difficult" to understand: http://users.telenet.be/nicvroom/wik_Principle_of_locality.htm#ref1 IMO it should be possible to use simpler experiments to demonstrate the difference between clasical physics and quantum physics assuming there are such differences.

Nicolaas Vroom

### 8 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Monday 26 december 2016
On Sunday, 25 December 2016 04:42:08 UTC+1, Jos Bergervoet wrote:
 > On 12/24/2016 11:07 AM, Nicolaas Vroom wrote:
 > > Jos, What I try to understand are the actual results of a "two channel" Bell test.
 > Then you are looking for an explanation!
 > > As such I need a document which describes the results of an actual experiment.
 > No, you need a document that explains how this particular process (the experiment with photon pairs) works.
 > > I need the raw results.
 >

1) When the polarization of both photons is measured in the same direction, both give the same outcome: perfect correlation. 2) When measured at directions making an angle 45 degrees with one another, the outcomes are completely random (uncorrelated). 3) Measuring at directions at 90 degrees to one another, the two are perfectly anti-correlated. 4) In general, when the polarizers are at an angle =CE=B8 to one another, the correlation is cos(2=CE=B8).

Line 1 indicates that apparently someone has performed this experiment 100 times with angle is zero and the result is 50++ and 50 -- Line 2 indicates that with 45 degrees and 100 times the result is (on average) 25++ 25+- 25-- and 25-+ Line 3 indicates that with 90 degrees the result is: 50+- and 50-+ The correlation factors are with 0, 45 and 90 degrees: 1, 0 and -1

In order to understand line 4 the first angles to study are 22.5 and 67.5 degrees. That is why I asked the question: Is there anyone who has performed this experiment and what are the results. I'am not so much interesting in the correlation factors.

 > But, although you do not strictly *need* the raw results, I agree with you that having them would be interesting.

That is not interesting: that is very important. That is the only way to verify if the Bell inequality is violated or if the quantum theory (in this respect) is correct.

 > Again, that sounds like you are refusing to accept some well-known theory and want to challenge it!

What I want to understand which of the two theories is correct. The only way is to compare the predicted outcomes of the experiments by each theory with the actual outcome.

 > > The correlation factors 1,0 and -1 are clear. All the other ones can be "tricky" and depend about the specific mathematics used.
 > No, they are not tricky at all in the case you discuss: The result is cos(2*phi). Period.

You are already sure that line 4 is correct. I do not say that line 4 is wrong. The point is I want to study the results of actual experiments which show that the correlation is this cos(2*phi) function.

 > > There exists a different document by N. David Mermin. See: http://cp3.irmp.ucl.ac.be/~maltoni/PHY1222/mermin_moon.pdf
 > Mermin seems to describe one of the early experiments (by Alain Aspect). It's from 1985, much more has been verified since then. Quantum mechanics is right. (Forget your hopes of refuting it!)

The main reason why I show this document is because it starts with the results of an actual experiment.

When you study the Alain Aspect document of 1979, it also starts with an actual experiment. For more information see: http://users.telenet.be/nicvroom/wik_Bell's_theorem.htm#par%2012

I do not want to refute something. I do not understand. It is very difficult to find clear and simple documents. The Alain Aspect 1979 is very clear to some extend except when they realy come to what I should call the highlight of the document then there is silence. This document is also "difficult" to understand: http://users.telenet.be/nicvroom/wik_Principle_of_locality.htm#ref1 IMO it should be possible to use simpler experiments to demonstrate the difference between clasical physics and quantum physics assuming there are such differences.

Nicolaas Vroom

### 9 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Monday 26 december 2016
[Moderator's note: Unfortunately I let this posting through after moderation, not realizing that it is distorted from bad character encoding. Here it's in better readable form again. Note that in the Usenet only ASCII characters are supposed to be used and displayed correctly.]

On Sunday, 25 December 2016 04:42:08 UTC+1, Jos Bergervoet wrote:
 > On 12/24/2016 11:07 AM, Nicolaas Vroom wrote:
 >> Jos, What I try to understand are the actual results of a "two channel" Bell test.
 > Then you are looking for an explanation!
 >> As such I need a document which describes the results of an actual experiment.
 > No, you need a document that explains how this particular process (the experiment with photon pairs) works.
 >> I need the raw results.
 >

1) When the polarization of both photons is measured in the same direction, both give the same outcome: perfect correlation.
2) When measured at directions making an angle 45 degrees with one another, the outcomes are completely random (uncorrelated).
3) Measuring at directions at 90 degrees to one another, the two are perfectly anti-correlated.
4) In general, when the polarizers are at an angle ? to one another, the correlation is cos(2?).

Line 1 indicates that apparently someone has performed this experiment 100 times with angle is zero and the result is 50++ and 50 -- Line 2 indicates that with 45 degrees and 100 times the result is (on average) 25++ 25+- 25-- and 25-+ Line 3 indicates that with 90 degrees the result is: 50+- and 50-+ The correlation factors are with 0, 45 and 90 degrees: 1, 0 and -1

In order to understand line 4 the first angles to study are 22.5 and 67.5 degrees. That is why I asked the question: Is there anyone who has performed this experiment and what are the results. I'am not so much interesting in the correlation factors.

 > But, although you do not strictly *need* the raw results, I agree with you that having them would be interesting.

That is not interesting: that is very important. That is the only way to verify if the Bell inequality is violated or if the quantum theory (in this respect) is correct.

 > Again, that sounds like you are refusing to accept some well-known theory and want to challenge it!

What I want to understand which of the two theories is correct. The only way is to compare the predicted outcomes of the experiments by each theory with the actual outcome.

 >> The correlation factors 1,0 and -1 are clear. All the other ones can be "tricky" and depend about the specific mathematics used.
 > No, they are not tricky at all in the case you discuss: The result is cos(2*phi). Period.

You are already sure that line 4 is correct. I do not say that line 4 is wrong. The point is I want to study the results of actual experiments which show that the correlation is this cos(2*phi) function.

 >> There exists a different document by N. David Mermin. See: http://cp3.irmp.ucl.ac.be/~maltoni/PHY1222/mermin_moon.pdf
 > Mermin seems to describe one of the early experiments (by Alain Aspect). It's from 1985, much more has been verified since then. Quantum mechanics is right. (Forget your hopes of refuting it!)

The main reason why I show this document is because it starts with the results of an actual experiment.

When you study the Alain Aspect document of 1979, it also starts with an actual experiment. For more information see: http://users.telenet.be/nicvroom/wik_Bell's_theorem.htm#par%2012

I do not want to refute something. I do not understand. It is very difficult to find clear and simple documents. The Alain Aspect 1979 is very clear to some extend except when they realy come to what I should call the highlight of the document then there is silence. - show quoted text -

### 10 Two Questions about Bell's theorem

From: Jos Bergervoet
Datum: Wednesday 28 december 2016
On 12/26/2016 5:16 PM, Nicolaas Vroom wrote: ..
 >> But, although you do not strictly *need* the raw results, I agree with you that having them would be interesting.
 > That is not interesting: that is very important. That is the only way to verify if the Bell inequality is violated or if the quantum theory (in this respect) is correct.

That's the same, actually. Quantum theory violates Bell's inequality! The Bell inequality is saying how classical theory behaves. And quantum theory behaves differently, in a way that can violate the inequality (not always, but sometimes it does).

So it is not: QM is correct *or* the inequality is violated, but it is: QM is correct *and* the inequality is violated.

..
 >> Again, that sounds like you are refusing to accept some well-known theory and want to challenge it!
 > What I want to understand which of the two theories is correct.

You mean QM and some other theory? What other theory do you have?? Note that classical electrodynamics will not help you, it does not describe single photon states or pairs of photons so how would you use it for this experiment?

 > The only way is to compare the predicted outcomes of the experiments by each theory with the actual outcome.

Why? The experimenters themselves already compared the results with the predicted outcomes and told us that they agreed with quantum mechanics. Why do you think that you have to do that comparison again?

Are you also personally going to compare the experiments about Newton's laws of motion and Maxwell's theory of EM with the predicted results of those theories?

...
 > I do not want to refute something. I do not understand. It is very difficult to find clear and simple documents. The Alain Aspect 1979 is very clear to some extend except when they realy come to what I should call the highlight of the document then there is silence.

Perhaps, but in the mean time you know exactly what the claim is! The photon detectors fire with: 1) A fraction (1+cos(2*phi))/2 of events are aligned, 2) A fraction (1-cos(2*phi))/2 of events anti-aligned.

 > IMO it should be possible to use simpler experiments to demonstrate the difference between clasical physics and quantum physics assuming there are such differences.

I think the 2-photon experiment with angles 0, 22.5 and 45 degrees is one of the simplest, actually.

The experiment described in the earlier EPR paradox is *not* sufficient, it would allow to have information hidden in the particles to instruct each of them how to react on the measurements. EPR use the paradox only to conclude that the the QM wave function possibly has to be made more complex to contain more information. They say: "QM is not complete".

For the Aspect experiment it is logically impossible to ever come up with two separate particle descriptions (as wave functions or otherwise!) that gives the observed results, as Mermin tries to illustrate with his example. That is why it does *not work correctly*. It is Mermin's intention to show that this approach must fail! Conclusion: QM cannot be made complete in the way EPR would like it.

So the Aspect experiment is one of the simplest to show that QM results require correlated descriptions of different regions in space. Perhaps you can make classical mechanics do the same, but then you have to alter 'conventional' classical mechanics into something else. (Probably making it equivalent to QM..)

-- Jos

### 11 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Friday 30 december 2016
On Wednesday, 28 December 2016 16:43:37 UTC+1, Jos Bergervoet wrote:
 > On 12/26/2016 5:16 PM, Nicolaas Vroom wrote: ..
 > >> But, although you do not strictly *need* the raw results, I agree with you that having them would be interesting.
 > > That is not interesting: that is very important. That is the only way to verify if the Bell inequality is violated or if the quantum theory (in this respect) is correct.
 > That's the same, actually.

When I follow the information at page 160 of this document: https://www.scientificamerican.com/media/pdf/197911_0158.pdf I want to verify if Local Realistic Theories (Classical theories) are correct or if Quantum mechanics is correct. IMO in order to do that you need at least the raw results.

 > >> Again, that sounds like you are refusing to accept some well-known theory and want to challenge it!
 > > What I want to understand which of the two theories is correct.
 > You mean QM etc
See above. Classical Theory versus Quantum Theory

 > > The only way is to compare the predicted outcomes of the experiments by each theory with the actual outcome.
 > Why? The experimenters themselves already compared the results with the predicted outcomes and told us that they agreed with quantum mechanics.

That is a certain type of "believe" I do not share. I need something more convincing.

When you go to page 159 there is an observer with a drawing board which shows the raw data of an actual experiment. The raw data clearly shows negative correlation. My interpretation is that in this case Bell's inequality is valid.

Page 174 also shows the results of an actual experiment but in this case not the raw data but the correlation factors. I have no problem with this picture in general, but there is no way for me to clearly understand if this representation is correct because I do not have the raw data.

Part of the problem is I do not know how the correlation values are actual calculated (based on observations)

When you go to https://en.wikipedia.org/wiki/Bell%27s_theorem#Bell_inequalities there are already three ways to calculate correlation factors. Only one Ce (the first) is clearly based on observations.

The SA article starts with the sentence:
"Any succesful theory in physical sciences is expected to make accurate predictions."
I prefer something slightly different: A theory is a set of relations or a mathematical model which are a description (explanation) of observations or experiments. Newton's Law is a mathematical description of the planets in our solar system Next we read:
"Given some well-defined experiment, the theory should correctly specify the outcome or should at least assign the correct probabilities of all the possible outcomes" This sentence is "wrong". The experiment comes first. Next come "all the possible outcomes"" The theory should specify all these outcomes. When new outcomes become available you should adapt your theory. This also happened in the realm of quantum mechanics. As a consequence quantum mechanics becomes (is) succesful. Now read next sentences in article.

At page 158 near the picture at page 159 is written:
(b) he observes a stict negative correlation.
My interpretation of the experiment depicted at page 159 that it comes in two flavours: One in which there is a negative correlation and a different experiment where there is no correlation. The issue is what exactly is the difference between those two experiments. IMO it is in the source more specific in the reaction that generates the two photons.

The explanation is that in case the outcome is random the two protons are not correlated and when there is negative correlation the two protons are entangled. In fact this experiment can be used to clasify the reaction involved (and be used as a source for additional experiments) That means the difference is in what is called realism or the physical reality. You do not need faster than light communication to explain this difference, because how should such communication operate different in two almost identical processes? Nor can be explained when the proton reaches the detector.

Nicolaas Vroom

### 12 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Tuesday 3 january 2017
On Wednesday, 28 December 2016 16:43:37 UTC+1, Jos Bergervoet wrote:
 > On 12/26/2016 5:16 PM, Nicolaas Vroom wrote:
 > > IMO it should be possible to use simpler experiments to demonstrate the difference between clasical physics and quantum physics assuming there are such differences.
 > For the Aspect experiment it is logically impossible to ever come up with two separate particle descriptions (as wave functions or otherwise!) that gives the observed results, as Mermin tries to illustrate with his example. That is why it does *not work correctly*. It is Mermin's intention to show that this approach must fail! Conclusion: QM cannot be made complete in the way EPR would like it.

When you want to study quantum mechanics you should start from something simple and go to more complex. Suppose you want to study the following reaction:

Sr38 --> Rb37 + 1p
In this particular reaction 1 proton is released. To detect the proton you build a circle of 360 proton detectors around the reaction and you monitor each event when some detector is hit.
You can get a sequence like 11, 255, 31, 174, 333, 205, 5, 221 etc This looks a random sequence. Nothing special?

Next you study the following reaction:

Zr40 --> Sr38 + 2p
In this imaginary reaction 2 protons are released. In this particular case you get a sequence of each time two numbers:
(11, 167) (31,245), (1,71) (167,289) (95,332) (245,311) (119,258)
Also here all the numbers are more or less random.

Next you study the following reaction:

Mo42 --> Zr40 + 2p
In this imaginary reaction 2 protons are released. In this particular case you get a sequence of each time two numbers:
(11, 191) (31,211), (1,181) (167,347) (95,274) (64,245) (119,298)
In this particle case the first number is random but the second number is 180 (degrees) higher. That means they fly away in opposite directions.

IMO this is a physical process and nothing special.

You can also do similar reaction using photons. For example the imaginary reaction Sr38 --> Sr37 + 1 photon and Zr40 --> Zr38 + 2 photons and Mo42--> Mo40 + 2 photons Also here you can build a circle of 360 photon detectors and observe if the reaction generates 1 or 2 photons and in the last case if the directions are correlated.

When you have a set of reactions which generates 2 photons and which "fly" away in opposite directions you can also test if it makes a difference how large the circle is. You do this by keeping half the same and increasing only the opposite side. My prediction is that this does not make a difference in the direction correlation.

You can also test if the two photons are polarised. To do that you should start with an appartus which generates two photons in opposite directions. In one direction you immediate place a photon detector L and in the other direction a beam splitter with two detectors R1 and R2. Now you should get a sequence like:
(L,R1) (L,R1) (L,R2) (L,R1), (L,R1) (L,R2) (L,R2) (L,R1)

Next you replace detector L with a beam splitter and two detectors L1,L2 and you could get a sequence like:
(L2,R1) (L2,R1) (L1,R2) (L2,R1), (L2,R1) (L1,R2) (L1,R2) (L2,R1) That means the photons are correlated i.e. entangled.

The cause of this correlation, entanglement is directly in the reaction itself and established by means of 1000 experiments. There is no additional communication of any kind involved when any of the parameters of one of the particles is measured or changed by additional actions or reactions.

In order to explain entanglement you do not need the concept of (collapse) a wave function because then either IMO you also need that same concept in all the other experiments or you have to explain why only to explain entanglement.

The same issue is if you think that faster than light communication is involved. Why only in this case and not in all the other experiments?

 > > The Alain Aspect 1979 is very clear to some extend except when they realy come to what I should call the highlight of the document then there is silence.
 > Perhaps, but in the mean time you know exactly what the claim is! The photon detectors fire with: 1) A fraction (1+cos(2*phi))/2 of events are aligned, 2) A fraction (1-cos(2*phi))/2 of events anti-aligned.

And how do you know this exactly?
By first perfoming 1000 experiments and monitoring the raw measured data values.
Secondly by performing mathematics i.e. calculating correlation factors.

Nicolaas Vroom

### 13 Two Questions about Bell's theorem

From: ben...@hotmail.com
Datum: Friday 3 february 2017
On Wednesday, December 28, 2016 at 3:43:37 PM UTC, Jos Bergervoet wrote:
 > .. Perhaps, but in the mean time you know exactly what the claim is! The photon detectors fire with: 1) A fraction (1+cos(2*phi))/2 of events are aligned, 2) A fraction (1-cos(2*phi))/2 of events anti-aligned. ......

but won't that give an overall positive correlation instead of a negative correlation when (say) phi = 45 degrees.

### 14 Two Questions about Bell's theorem

From: ben...@hotmail.com
Datum: Saturday 4 february 2017
- show quoted text - I would like to add that I am not merely pointing out the sign error here, if indeed there is one. My main reason for posting is that I believe I have found a similar sign error in one of Susskind's online lectures on entanglement. Susskind sets out to prove that QM can break the Bell Inequality AB' + BC'
 > = AC' for electrons,
where Alice measures at 0, Bob at 45 and Charlie at 90 degrees.

Looking at the 2x2 table of measurements of A and B, the four cells are (+ +), (+ -), (- +) and (- -). Since the table is symmetric wrt Alice and Bob, there is only one degree of freedom for filling in the table. And if you say that the correlation must be - 1/ sqrt 2, then there are no degrees of freedom left and the four cells must be 0.073, 0.427, 0.427 and 0.073, respectively, as proportions, using simple algebra rather than QM. The proportion in the (+ +) cell is 0.073 and that is what Susskind calculates using Projection Operators in a QM calculation except that he calculates that value for AB' which seems to me to be the wrong cell. I equate AA with (+ +), AB' with (+ -), A'B with (- +) and B'B' with (- -). Where AB' means A AND NOT_B.

In a simulation with one million pairs of particles, using hidden variables, I also found 0.073 but for cell (+ +) i.e. not for AB'.

For electrons the formula for cell (+ +) is different than for photons being 0.25*(1 - cos phi). So did Susskind make a mistake? What inequality did he break, if any?

AND

TRANSCRIPT Notes on Susskind=E2=80=99s lecture 5, courtesy of pa...@lecture-notes.co.uk http://www.lecture-notes.co.uk/susskind/quantum-entanglements/lecture-5/violation-of-bells-theorem/

### 15 Two Questions about Bell's theorem

From: Jos Bergervoet
Datum: Monday 6 february 2017
On 2/4/2017 5:43 PM, ben...@hotmail.com wrote:
 > On Friday, February 3, 2017 at 10:24:42 PM UTC, ben...@hotmail.com wrote:
 >> On Wednesday, December 28, 2016 at 3:43:37 PM UTC, Jos Bergervoet wrote:
 >>> .. Perhaps, but in the mean time you know exactly what the claim is! The photon detectors fire with: 1) A fraction (1+cos(2*phi))/2 of events are aligned, 2) A fraction (1-cos(2*phi))/2 of events anti-aligned. ......
 >> but won't that give an overall positive correlation instead of a negative correlation when (say) phi = 45 degrees.

phi=45 gives exactly 0 for the correlation. (This was about measuring photon polarizations, resulting in "H" or "V".)

 > I would like to add that I am not merely pointing out the sign error here, if indeed there is one.

With the answer being 0, there cannot be a sign error. For other angles, it depends on whether you start with anti-aligned or aligned photon pairs. (OP of this thread references a Wikipedia example with *aligned* photon pairs which makes the correlation positive for phi < 45 deg.)

 > My main reason for posting is that I believe I have found a similar sign error in one of Susskind's online lectures on entanglement. Susskind sets out to prove that QM can break the Bell Inequality AB' + BC' >= AC' for electrons,

Be aware that for electrons the angular variation is only half of that for photons. So the correlation there is 0 for phi=90 degrees. If the electrons are initially in aloigned pairs (like the photons above) then we will have positive correlation between detector results for < 90 deg. angle between detector orientations, in particular we have full correlation for phi=0.

If, however, the electrons come in anti-aligned pairs (as in the 'singlet state') then it is the opposite: negative correlation for less than 90 degrees orientation difference between the detectors and complete anti-correlation (-1) with angle phi = 0 between detectors.

I didn't look up the Susskind lecture you refer to, but for electrons, this second possibility is often used:

sqrt(1/2) * ( |+-> - |-+> )

It is of course also possible to start with the other possibility (aligned instead of anti-aligned), although it may be more difficult to prepare experimentally.

..
 > For electrons the formula for cell (+ +) is different than for photons being 0.25*(1 - cos phi).

In any case the variation with angle phi is with half the rate. And the sign may also be different if the prepared electron pairs are anti-aligned and you compare them with photon pairs that are created aligned.

 > So did Susskind make a mistake?

I expect it is a matter of comparing different cases..

 > What inequality did he break, if any?

You already wrote that it was about Bell's inequality. That means he broke the inequality that describes the limits of possible classical behavior. What Bell's inequality does is telling you what is possible with classical physics. More is possible in QM.

-- Jos

### 16 Two Questions about Bell's theorem

From: ben...@hotmail.com
Datum: Wednesday 8 february 2017
On Monday, February 6, 2017 at 5:57:47 AM UTC, Jos Bergervoet wrote:
 > On 2/4/2017 5:43 PM, ben6993 wrote: .....

 > phi=45 gives exactly 0 for the correlation. (This was about measuring photon polarizations, resulting in "H" or "V".)

Yes, agreed. Cos(2*45 degrees) = 0. I am too used to thinking about electrons rather than photons in this context. So the four cells of the 2x2 table would all be 0.25. But for phi = say 22.5 degrees then the minus cosine term needs to be in the (+, +) cell if you need to make the correlation negative.

 > For other angles, it depends on whether you start with anti-aligned or aligned photon pairs. (OP of this thread references a Wikipedia example with *aligned* photon pairs which makes the correlation positive for phi < 45 deg.)

Also agreed. I want only to refer to anti-correlated singlet electron-positron pairs as in Susskind's example.

 > Be aware that for electrons the angular variation is only half of that for photons. So the correlation there is 0 for phi=90 degrees. If the electrons are initially in aloigned pairs (like the photons above) then we will have positive correlation between detector results for < 90 deg. angle between detector orientations, in particular we have full correlation for phi=0.

Agreed. I do know that but when I quoted the 45 degree case above my mind was still set on halving, which I did instead of doubling! Oops.

 > If, however, the electrons come in anti-aligned pairs (as in the 'singlet state') then it is the opposite: negative correlation for less than 90 degrees orientation difference between the detectors and complete anti-correlation (-1) with angle phi = 0 between detectors.

This is the case I am interested in.

 > I didn't look up the Susskind lecture you refer to, but for electrons, this second possibility is often used: sqrt(1/2) * ( |+-> - |-+> )

OK

 > It is of course also possible to start with the other possibility (aligned instead of anti-aligned), although it may be more difficult to prepare experimentally.

I have sometimes prepared aligned singlets in a computer simulation, but I did not realise that it was possible to prepare them in the lab. I mean exactly aligned rather than aligned to be pointing in the same hemisphere.

 > ..
 > > For electrons the formula for cell (+ +) is different than for photons being 0.25*(1 - cos phi).
 > In any case the variation with angle phi is with half the rate. And the sign may also be different if the prepared electron pairs are anti-aligned and you compare them with photon pairs that are created aligned.

Completely agree with all of this.

 > > So did Susskind make a mistake?
 > I expect it is a matter of comparing different cases..

 >
 > > What inequality did he break, if any?
 > You already wrote that it was about Bell's inequality. That means he broke the inequality that describes the limits of possible classical behavior. What Bell's inequality does is telling you what is possible with classical physics. More is possible in QM.

I am quite convinced that Susskind did not break the inequality that he set out to break which is AB' + BC' >= AC' using singlet electron pairs. Where a=0, b=45 and c=90 degrees.

He used QM calculations to find AB' = BC' = 0.073, where AC' = 0.25. So it is certainly true that 0.073 + 0.073 is not >= 0.25.

But using his values one gets a correlation of +0.707 instead of -0.707. So he seems to have broken some inequality or other involving AB = BC = 0.073 and AC = 0.25.

Also, I found the value 0.073 using a computer simulation where the compute program knows the particles' hidden variables which are the particles exact vectors (p). But I found that value 0.073 for cells (+ +) and (- -) whereas Suskind found that value for cells (+ -) and (- +).

I calculated p dot a and p dot b for each particle pair and the correlated these data. The correlation was -0.707. To get 0.073, I accumulated values where p dot a was positive for particle 1 and p dot b was positive for the partner particle. So I calculated with hidden variables the same values as did Sussking using QM.

What neither Susskind nor I did was to calculate -0.707 using integer values of A and B which of course is expected to be 0.5 in the long run. We both started out with integer values but then took fractional values of them when projected onto exact detector vectors. QM may not have done this as explicitly as I did but it found the same result. That is excellent for QM as it managed to do so without using individual particles' hidden vectors. But it did use projection operators to find 0.073 which gives a clue that QM was doing something similar in intent.

What is puzzling me after my calculations which match Susskind's is why finding 0.073 by QM leads one to think that you can get a correlation of -0.707 for a 2x2 table of integer values of A and B? The proportions in the 2X2 table are (or have the same value as) accumulations of fractional loadings on exact detector vectors. IMO to break Bell's Inequality you need to correlate Alice's and Bob's integer measurements direct as -0.707 and not mess with them first. My calculation could not beat 0.5. Whatever led QM to think that a direct correlation of integer measurements could break the barrier?

### 17 Two Questions about Bell's theorem

From: John Heath
Datum: Sunday 12 february 2017
On Wednesday, February 8, 2017 at 1:32:26 PM UTC-5, ben...@hotmail.com wrote:
 > On Monday, February 6, 2017 at 5:57:47 AM UTC, Jos Bergervoet wrote:
 > > On 2/4/2017 5:43 PM, ben6993 wrote: .....
 > Thanks for the reply Jos.
 > > phi=45 gives exactly 0 for the correlation. (This was about measuring photon polarizations, resulting in "H" or "V".)
 > Yes, agreed. Cos(2*45 degrees) = 0. I am too used to thinking about electrons rather than photons in this context. So the four cells of the 2x2 table would all be 0.25. But for phi = say 22.5 degrees then the minus cosine term needs to be in the (+, +) cell if you need to make the correlation negative.
 > > For other angles, it depends on whether you start with anti-aligned or aligned photon pairs. (OP of this thread references a Wikipedia example with *aligned* photon pairs which makes the correlation positive for phi < 45 deg.)
 > Also agreed. I want only to refer to anti-correlated singlet electron-positron pairs as in Susskind's example.
 > > Be aware that for electrons the angular variation is only half of that for photons. So the correlation there is 0 for phi degrees. If the electrons are initially in aloigned pairs.

 > Where a=0, b=45 and c degrees.
There are times when one is too close to a problem to solve it. Good time to step back for a broader picture.

Entanglement has empirical evidence on it's side with 5/9 correlation when it should be 5/10 however it comes with baggage of star trek thoughts of action faster than light. If entanglement is true then it follows that we should have quantum computers. Do we have quantum computers? I have a rule of thumb formula to answer this question with (N + W + M)^3 .

N average Number of letters in words , scale 1 to 10
W White lab coat with formulas in the background , scale 1 to 10
M does he want Money , scale 1 to 10
N=2 + W=2 + M=2 = 6^3 216 good stuff should take notes
N=5 + W=5 + M=5 = 15^3 3375 maybe
N=8 + W=8 + M=8 = 24^3 13824 red flag , extreme caution

Presentations I have seen on the new qubit quantum computers are in the N=8 , W=8 and M=8 range. Time to reconsider. It can not be Bell as the thinking is clear with little room to argue. In any event a functioning quantum computer is not in our near future according to the NWM scale. Maybe a second look at the finer details of how a Bell test is done is in order.

### 18 Two Questions about Bell's theorem

From: ben...@hotmail.com
Datum: Monday 13 february 2017
On Sunday, February 12, 2017 at 4:26:38 PM UTC, John Heath wrote:
 > On Wednesday, February 8, 2017 at 1:32:26 PM UTC-5, ben wrote: .....

 > There are times when one is too close to a problem to solve it. Good time to step back for a broader picture. .... If entanglement is true then it follows that we should have quantum computers. Do we have quantum computers? I have a rule of thumb formula to answer this question with (N + W + M)^3 . N average Number of letters in words , scale 1 to 10 W White lab coat with formulas in the background , scale 1 to 10 M does he want Money , scale 1 to 10 N=2 + W=2 + M=2 = 6^3 216 good stuff should take notes N=5 + W=5 + M=5 = 15^3 3375 maybe N=8 + W=8 + M=8 = 24^3 13824 red flag , extreme caution Presentations I have seen on the new qubit quantum computers are in the N=8 , W=8 and M=8 range.

I agree with the sentiments but I am just an amateur. I have a vixra paper on the matters I have raised above at http://vixra.org/abs/1610.0327 for which I would guess N=1, W=2, M=0.

 > Time to reconsider. It can not be Bell as the thinking is clear with little room to argue.

Not so sure about that. Real experiments seem to have broken inequalities but there are loopholes continually being raised. A 2015 experiment had results based on only 245 pairs of particles.

 > In any event a functioning quantum computer is not in our near future according to the NWM scale. Maybe a second look at the finer details of how a Bell test is done is in order.

I have a draft paper looking at the CHSH statistic used in real experiments and seeing how sensitive the statistic is to experimental error.

### 19 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Wednesday 15 february 2017
[[Mod. note -- 1. I have manually rewrapped some overly-long lines. 2. Some characters of this article were garbled in transit [Hint to everyone: Usenet news is NOT 8-bit clean! Stick to 7-bit ASCII and you'll be ok.]
I don't know what the original characters were which got garbled into "=C2=B11". :( -- jt]]

On Saturday, 4 February 2017 17:43:02 UTC+1, ben...@hotmail.com wrote:

 > I would like to add that I am not merely pointing out the sign error here, if indeed there is one. My main reason for posting is that I believe I have found a similar sign error in one of Susskind's online lectures on entanglement. Susskind sets out to prove that QM can break the Bell Inequality AB' + BC'
 > > = AC' for electrons,

The problem is not so much with the mathematics involved but with the physical interpretations. A typical case is: Lecture 2: Classical observables: Classical vs. quantum observables In that paragraph we read:

"In quantum mechanics, observables are not real-valued functions, but a specific set of linear operators called Hermitian matrices that act on quantum states and allow us to calculate the probabilities of particular outcomes."
The problem is: first you need observations and based on these observations you can calculate the Hermitan matrices. The next step is: using these matrices you can make new predictions.

The same problem is also in the following section:
Lecture 5: Example states : Non-entangled states In that paragraph we read:

"This means that, for a product state, there is always a direction along which you will measure the spin of the first electron to be +-1 with 100% certainty, and there is always a direction along which you will measure the spin of the second electron to be +-1 with 100% certainty. This is equivalent to saying that each electron can be measured independently."
Also here first you have to measure and then you can claim: its a product state

Also here: Lecture 5: Example states : Entangled states

"By definition, these states are systems where the second electron is in the opposite configuration to the first. If one of electrons is measured to be up along a given direction, then the other will definitely be down without the need for measurement. A pair of electrons in this state are said to be entangled."
First you have to demonstrate that when one electron is up always the other one is down (or reverse). Next you know that they are entangled.

Lecture 5: Violation of Bell's theorem: Bell's theorem shows Bell's theorem: N(1)+N(2)+N(3)+N(4)>= N(1)+N(2)
This theorem can easily be demonstrated when you use three coins 1,2 and 3 state 1 means H,H and H resp for coins 1,2 and 3
state 2 means H,H and T resp for coins 1,2 and 3 etc.
Putting all the three coins in a bag and mixing them will demonstrate that the theorem is correct when you perform this experiment 1000 times.

In the next paragraph the probability 2P[z^,w^] = 0.146 is calculated. Again here you have to demonstrate that this is correct for certain "types" of electron pairs. What that means is that the mathematics used is correct. Next the probability P[z^,x^] = 0,25 is calculated. Again here you have to demonstrate that this correct, for the same "type" of electron pairs. What this means is that the mathematics is correct.

Finally you can claim that this is in disagreement with Bell's theorem. That is true. The problem is that in some sense we are comparing here apples with pears. You are comparing the behaviour of coins with the behaviour of entangled electrons and that does not make sense.

What I want to emphasize is that there are many experiments which results are in agreement with the Bell's theorem.

In the same document we read:

" It shouldn't be too surprising, since states in quantum theory are complex vectors, rather than elements of sets. The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. Historically, this was known before Bell, but his theorem is perhaps the most elegant demonstration."
The problem is that there are many experiments which do not agree with the Bell's theorem but that does not immediate validate the claim that quantum mechanics is correct. Anyway what is quantum mechanics? What is entanglement?
Mathematics is a tool to describe entanglement, but it does not explain what it is.
When two particles are entangled at large distance, the cause is the (local) reaction that created the two particles. No faster than light communication is involved in this process. Also the claim that the entanglement is always 100% is too strong because external influences can influence the state (spin) of the particles involved (at larger distances).

Nicolaas Vroom

### 20 Two Questions about Bell's theorem

From: ben...@hotmail.com
Datum: Thursday 16 february 2017
[[Mod. note -- I have manually rewrapped over-long lines. -- jt]]

On Wednesday, February 15, 2017 at 3:36:11 PM UTC, Nicolaas Vroom wrote:
 > On Saturday, 4 February 2017 17:43:02 UTC+1, ben...@hotmail.com wrote:

 > The lecture notes by Prof Susskind on entanglement are very interesting but they raises also certain questions. See: http://www.lecture-notes.co.uk/susskind/quantum-entanglements/ ...

 > Lecture 5: Violation of Bell's theorem: Bell's theorem shows Bell's theorem: N(1)+N(2)+N(3)+N(4)>= N(1)+N(2)

Yes, IMO that inequality is trivially true when using coins which are always say H or T and you are not performing more than counts and overall proportions on them. Or abstract this to -1s and +1s instead of coins.

 > In the next paragraph the probability 2P[z^,w^] = 0.146 is calculated. Again here you have to demonstrate that this is correct for certain "types" of electron pairs. What that means is that the mathematics used is correct. Next the probability P[z^,x^] = 0,25 is calculated. Again here you have to demonstrate that this correct, for the same "type" of electron pairs. What this means is that the mathematics is correct. Finally you can claim that this is in disagreement with Bell's theorem. That is true. The problem is that in some sense we are comparing here apples with pears. You are comparing the behaviour of coins with the behaviour of entangled electrons and that does not make sense. What I want to emphasize is that there are many experiments which results are in agreement with the Bell's theorem.

The calculation of 0.146( = 2* 0.073) is not the result of simple counts of +1s and -1s with a simple overall proportion. I have found this value without using QM but using a computer simulation with hidden variables (i.e. the particles' exact vectors) using dot products which take fractions of the 1s and -1s first and then add those fractions. In Lecture 5, Susskind does not really break Bell's Inequality because he (and QM) messes too much with the integer measurements by fractionalizing them. One cannot fractionalize the measurements in a real experiment to try to break the inequality. For example the CHSH S statistic used in real experiments seems fine to me and it does not fractionalize the data in the same way that QM does.

I have another small simulation for AB' + BC' >= AC' where the integer values are (1 + 1) + (1 + 1) >= 1 + 1 + 1 + 1 which does not break the inequality but the fractionalized version is
(0 + 0.707) + (0 + 0.707) >= (0.7070 + 0 + 1 + 0.707)
which does break the inequality as 1.414 is not >= 2.414. In fact, this small example reduces by simple proportional scaling to give the correct exact values 0.073 + 0.073 is not >= 0.25 as found by QM.

What puzzles me is why a QM calculation using fractionalized measurements which can supposedly 'break' the inequality could ever have led someone to think that they could break the inequality using integer measurements in a real experiment. Unless maybe this was 'discovered' experimentally first?

### 21 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Monday 20 february 2017
On Thursday, 16 February 2017 20:32:43 UTC+1, ben...@hotmail.com wrote:
 > On Wednesday, February 15, 2017 at 3:36:11 PM UTC, Nicolaas Vroom wrote:
 > > On Saturday, 4 February 2017 17:43:02 UTC+1, ben...@hotmail.com wrote:
 >
 > > The lecture notes by Prof Susskind on entanglement are very interesting but they raises also certain questions. See: http://www.lecture-notes.co.uk/susskind/quantum-entanglements/ ...
 >
 > > Lecture 5: Violation of Bell's theorem: Bell's theorem shows Bell's theorem: N(1)+N(2)+N(3)+N(4)>= N(1)+N(2)
 > Yes, IMO that inequality is trivially true when using coins which are always say H or T and you are not performing more than counts and overall proportions on them. Or abstract this to -1s and +1s instead of coins.

I agree that this theorem with coins is rather trivial.

 > > Finally you can claim that this is in disagreement with Bell's theorem. That is true. The problem is that in some sense we are comparing here apples with pears. You are comparing the behaviour of coins with the behaviour of entangled electrons and that does not make sense. What I want to emphasize is that there are many experiments which results are in agreement with the Bell's theorem.
 > In Lecture 5, Susskind does not really break Bell's Inequality because he (and QM) messes too much with the integer measurements by fractionalizing them.

IMO the issue is not so much if a specific experiment is in agreement with Bell's theorem as described above. The issue is if the mathematical description of the behaviour of two (entangled) electrons is in agreement with the outcome of actual experiments.
In Lecture 5 Susskind uses complex numbers to describe the physical reality. IMO (I guess) other mathematical equations are also possible to describe the same. What ever you do the results of the predictions should be in accordance with observations.
Computer simultions in general are not enough if not supported by (additional) observations.

Nicolaas Vroom.

### 22 Two Questions about Bell's theorem

From: ben...@hotmail.com
Datum: Wednesday 22 february 2017
On Monday, February 20, 2017 at 8:04:38 PM UTC, Nicolaas Vroom wrote:
 > On Thursday, 16 February 2017 20:32:43 UTC+1, ben...@hotmail.com wrote: ....
 > > In Lecture 5, Susskind does not really break Bell's Inequality because he (and QM) messes too much with the integer measurements by fractionalizing them.
 >

 > IMO the issue is not so much if a specific experiment is in agreement with Bell's theorem as described above. The issue is if the mathematical description of the behaviour of two (entangled) electrons is in agreement with the outcome of actual experiments. In Lecture 5 Susskind uses complex numbers to describe the physical reality. IMO (I guess) other mathematical equations are also possible to describe the same. What ever you do the results of the predictions should be in accordance with observations. Computer simultions in general are not enough if not supported by (additional) observations. Nicolaas Vroom.

I agree that the maths must agree with the experimental observations and I need to know more about the experimental results.

The 2015 Delft experiment only used 245 pairs of particles which does not seem enough, by itself, to sustain a belief in experimental observations breaking an inequality, whatever the result's p value is (significant but not exceedingly so). That experiment was trying to simultaneously close loopholes so I guess that is why the number of pairs was small.

One experiment reported sig levels at about 20 sigma. But only 5% of the pairs were captured.

Susskind's QM formulae do not convince me at all that he has broken the inequality as his result matched mine which was based on hidden variables. And the hidden variables method did not break the inequality as the integer nature of A and B measurements were compromised in a way that cannot be done in a real experiment.

### 23 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Sunday 26 february 2017
On Wednesday, 22 February 2017 21:32:07 UTC+1, ben...@hotmail.com wrote:

 > I agree that the maths must agree with the experimental observations and I need to know more about the experimental results.

But what is more each different experiment has its own math.

 > The 2015 Delft experiment only used 245 pairs of particles which does not seem enough, by itself, to sustain a belief in experimental observations breaking an inequality, whatever the result's p value is (significant but not exceedingly so). That experiment was trying to simultaneously close loopholes so I guess that is why the number of pairs was small.

The Delft experiment also has its own math to describe its results. My understanding is that generally speaking you cannot use the math of one to validate or invalidate the math of an other one. As such you cannot use the math of an experiment using electrons (its spin) to (in)validate the math using coins which can be described using classical mechanics.

Part of this reasoning stems from the fact that coins are not correlated (can not be entangled) while electrons (its spin) can.

Nicolaas Vroom.

### 24 Two Questions about Bell's theorem

From: ben...@hotmail.com
Datum: Tuesday 28 february 2017
On Sunday, February 26, 2017 at 4:47:58 AM UTC, Nicolaas Vroom wrote:
 > On Wednesday, 22 February 2017 21:32:07 UTC+1, ben...@hotmail.com wrote: ....
 > > I agree that the maths must agree with the experimental observations and I need to know more about the experimental results.
 > .... But what is more each different experiment has its own math. ....

Experiments need to be analysed using maths, so OK.

 > The Delft experiment also has its own math to describe its results.

OK again. There is a lot of physics and maths in in the Delft experiment that I have not followed yet. But the maths of the main result is a calculation of a CHSH S statistic which is basically a sum of four correlation coefficients between Alice's and Bob's measurements. Where each different correlation is based on one pair of magnet angle settings.

If S=2, that points to an average correlation of 0.5. If S=2.828, that points to an average correlation of 0.707 in which case the experiment breaks the Bell Inequality. I am just looking for evidence that loophole-free experiments truly break the inequality.

 > My understanding is that generally speaking you cannot use the math of one to validate or invalidate the math of an other one. As such you cannot use the math of an experiment using electrons (its spin) to (in)validate the math using coins which can be described using classical mechanics. Part of this reasoning stems from the fact that coins are not correlated (can not be entangled) while electrons (its spin) can. Nicolaas Vroom.

As I wrote above, the S statistic is based on a simple correlation coefficient and the size of the coefficient determines if the equality is broken (S --> 2.828) or not broken (S --> 2.0).

I think it is slightly more complicated that that as there may be a feeling that S = 2 does not break the inequality whereas any S > 2 does break the inequality. I have been simulating the CHSH statistic for robustness under experimental error of measurement, and I can get S changing from 2 to >2 through adding error to the simulated measurements. It is very odd that adding error can increase the correlation! Like decreasing entropy? But only for small numbers of pairs. For large numbers of pairs S goes back to 2. Also my simulation to obtain S=2 for a small number of pairs assumes zero error of measurement and that is also odd. But I am still working on this.

### 25 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Friday 3 march 2017
On Tuesday, 28 February 2017 09:02:33 UTC+1, ben...@hotmail.com wrote:

 > If S=2, that points to an average correlation of 0.5. If S=2.828, that points to an average correlation of 0.707 in which case the experiment breaks the Bell Inequality. I am just looking for evidence that loophole-free experiments truly break the inequality.
 > > My understanding is that generally speaking you cannot use the math of one to validate or invalidate the math of an other one. As such you cannot use the math of an experiment using electrons (its spin) to (in)validate the math using coins which can be described using classical mechanics. Part of this reasoning stems from the fact that coins are not correlated (can not be entangled) while electrons (its spin) can. Nicolaas Vroom.
 >

My whole point is: First you have to demonstrate the Bell inequality (is correct) This requires at least one experiment which is in agreement with the Bell inequality. For example an experiment without entanglement. The next thing is you want invalidate the Bell inequality. This requires a different experiment. For example an experiment with entanglement. The description requires different mathematics (using quantum mechanics) The next thing is you have to demonstrate that this mathematics is correct by performing the experiment 1000 times. Suppose that this mathematics violates the Bell inequality does that immediate mean that this mathematics is a correct description of the second experiment. No it does not.

More important it does not explain what entanglement is.

The last sentence in this document http://www.lecture-notes.co.uk/susskind/quantum-entanglements/lecture-5/violation-of-bells-theorem/ is: Clearly, hence we have shown that the singlet state violates Bell's theorem. That is true in the mathematical sense but not directly in the physical sense.

Nicolaas Vroom.

### 26 Two Questions about Bell's theorem

From: Rich L.
Datum: Saturday 4 march 2017

On Thursday, March 2, 2017 at 10:03:00 PM UTC-6, Nicolaas Vroom wrote: ...
 > My whole point is: First you have to demonstrate the Bell inequality (is correct) This requires at least one experiment which is in agreement with the Bell inequality.
...
 > Nicolaas Vroom.

The Bell Inequality is a mathematical theorem. You should read Bell's paper on this. There is no physical reasoning involved in its derivation.

The APPLICATION of Bell's inequality to physics involves an interpretation of the physics and an application of the inequality to the physics. By testing the physics against the inequality you test the assumptions of that interpretation and your understanding of the physics. Bell's Inequality has been proven by mathematical theorem. You do not need to, and cannot, prove or disprove it experimentally.

Rich L.

### 27 Two Questions about Bell's theorem

From: Nicolaas Vroom
Datum: Tuesday 7 march 2017
On Saturday, 4 March 2017 08:25:15 UTC+1, Rich L. wrote:
 > On Thursday, March 2, 2017 at 10:03:00 PM UTC-6, Nicolaas Vroom wrote: ...
 > > My whole point is: First you have to demonstrate the Bell inequality (is correct) This requires at least one experiment which is in agreement with the Bell inequality.
 > ...
 > > Nicolaas Vroom.
 > The Bell Inequality is a mathematical theorem. You should read Bell's paper on this. There is no physical reasoning involved in its derivation.

I fully agree that there is no physical reasoning involved in its derivation. That is strictly mathematics. At the same the Bell Inequality is not stictly mathematics. Its basis is physics.

 > The APPLICATION of Bell's inequality to physics involves an interpretation of the physics and an application of the inequality to the physics.
This is all rather vaque.
 > By testing the physics against the inequality you test the assumptions of that interpretation and your understanding of the physics.
Also vaque. My understanding has nothing to do with this.

 > Bell's Inequality has been proven by mathematical theorem. You do not need to, and cannot, prove or disprove it experimentally.

An interesting article to read is the document "The Quantum Theory and Reality" by Bernard d'Espagnat in Scientific Amarican of November 1979 See https://www.scientificamerican.com/media/pdf/197911_0158.pdf In that document at page 162 (or 132) you can read: "The inequality applies to particles that have stable properties A,B,C each of which can have the values plus and minus. Thus there are 2^3 or 8 possible classes of particles etc." The inequality is derived as: n[A+B+] =< n[A+C+]+n[B+C+] In order to demonstrate (prove) the inequality you do the following: 1) You take three coins and mark one with as A, one as B, and one as C
2) You put three coins in a bag, shake and throw them on a table.
3) You take a sheet of paper, on which you write three columns: [A+B+] , n[A+C+] and [B+C+]. A+ means Coin A head. A- means coin A tail.
4) When you observe the combination A+,B+ (A head, Bhead) you make a cross in column [A+B+]. The same for A head C head in column [A+C+] and the same for B head C head in column [B+C+]
5) Next you you repeat this experiment 100 times and you will observe on average in each column 25 crosses. This results validates the inequality using coins.

IMO the whole article by Bernard d'Espagnat is around experiments.

My point of view is that you cannot use the inequality as a yardstick to demonstrate that if the result of a certain new experiment violates the Bell inequality that the Bell inequality (Classical mechanics) is wrong and this new experiment (involving entanglement) based on quantum mechanics is right. IMO this new experiment requires its own mathematics and experiments to validate the predictions of quantum mechanics.

Nicolaas Vroom