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

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

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?

15 Two Questions about Bell's theorem

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:

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

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=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

>	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

>

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.

19 Two Questions about Bell's theorem

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,

20 Two Questions about Bell's theorem

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

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

>

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

>	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

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

>	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.

26 Two Questions about Bell's theorem

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

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.