Experiment confirms my local-realistic model for EPR-Bohm

[Gordon Watson]

Gordon,

All I am saying is that quantum mechanics makes no prediction whatsoever for the Bell-CHSH quantity E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’)

for a single run of the EPR-Bohm type experiment, because no experiment can be performed that can measure that quantity for a single run.

The point I am making is rather trivial to understand: a, b, a', and b' are mutually exclusive, or physically incompatible observation directions.

***
As for your question: "How did Bell-CHSH get it so wrong?", my answer, as many on this forum know, has to do with the wrong choice of a co-domain they
chose for the measurement functions, as I have explained in great detail on this page of my blog: http://libertesphilosophica.info/blog/d ... orem-book/

***

Joy,

1. If that is now all that you are saying (limiting your statement to a single run of the EPRB experiment rather than a single run of an experiment known as a Bell-test), then this statement of yours remains false: "It [QM] makes no prediction whatsoever for the Bell-CHSH quantity E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’), because no experiment can ever be performed (even by "God") which can measure that quantity."

2. I look forward to an explanation of this statement of yours: "The point I am making is rather trivial to understand: a, b, a', and b' are mutually exclusive, or physically incompatible observation directions."

Thanks; Gordon

[thray]

" ... a, b, a', and b' are mutually exclusive, or physically incompatible observation directions."

Why is this so hard for otherwise intelligent people to understand?

Joy, Tom, Fred:

What is currently hard for me to understand is this: Why do you make such a statement?

Having regard to the following facts, I'd welcome your explanation.

a and a' are mutually exclusive, b and b' are mutually exclusive; but a does not exclude b or b', and a' does not exclude b or b', etc.

Thus the following combinations of detector settings are relevant, valid and physically compatible angles: (a, b), (a, b'), (a', b), (a', b'); being the angles between physically compatible detector settings.

Gordon, do you agree with the statement: "No observation in any experiment was ever made except in some direction"?

I hope you agree that is trivial.

When measurements are made based on detector settings, they do not assume direction; Richard Gill explains it thus: "The experiment is about 'counting'. There are two measurement devices which have binary settings ("1" or "2"). There is a binary outcome. ("+" or "-") At the end of the experiment you have 16 counts. So many times you saw outcome "++" and the setting was "11", so many times "+-" and the setting was "12" ... so many times "--" and the setting was "22". Quantum mechanics predicts the probabilities of outcomes given settings e.g. Prob("-+" | "21"). The physicist's correlation is just the the probability of equal outcomes minus the probability of different outcomes."

He then accuses Joy Christian of inventing his own correlation: "Christian decides to redefine correlation by dividing the average of the product of the outcomes by bivectorial 'standard deviations'. His famous model actually has the outcome on Alice's side always opposite to the outcome on Bob's side so in ordinary terms it predicts a correlation of -1 independently of the settings on each side."

Except that isn't at all what Joy has done. Remember the elementary calculus rule: "the product of limits equals the limit of products"? As with all calculus, this rests on the principles of limit and function. A continuous function of this sort on the 3-sphere measure space reverses sign continually in a regular sine wave pattern; you say that "a and a' are mutually exclusive, b and b' are mutually exclusive; but a does not exclude b or b', and a' does not exclude b or b', etc.", yes it must. Even though the trajectories are independently random (binary) the result manifestly orients the measure space to pairwise certainty. Not to a "correlation of -1 independently of the settings on each side" as Gill claims, but +/- 1 depending on the topological orientation in the observer's view -- orientation built into the structure of the space, and not chosen by the observer.

Bell's experiment has no measure space -- were it prescribed, one would find insufficient degrees of freedom to account for the results.

[Gordon Watson]

" ... a, b, a', and b' are mutually exclusive, or physically incompatible observation directions."

Why is this so hard for otherwise intelligent people to understand?

Joy, Tom, Fred:

What is currently hard for me to understand is this: Why do you make such a statement?

Having regard to the following facts, I'd welcome your explanation.

a and a' are mutually exclusive, b and b' are mutually exclusive; but a does not exclude b or b', and a' does not exclude b or b', etc.

Thus the following combinations of detector settings are relevant, valid and physically compatible angles: (a, b), (a, b'), (a', b), (a', b'); being the angles between physically compatible detector settings.

Gordon, do you agree with the statement: "No observation in any experiment was ever made except in some direction"?

I hope you agree that is trivial.

When measurements are made based on detector settings, they do not assume direction; Richard Gill explains it thus: "The experiment is about 'counting'. There are two measurement devices which have binary settings ("1" or "2"). There is a binary outcome. ("+" or "-") At the end of the experiment you have 16 counts. So many times you saw outcome "++" and the setting was "11", so many times "+-" and the setting was "12" ... so many times "--" and the setting was "22". Quantum mechanics predicts the probabilities of outcomes given settings e.g. Prob("-+" | "21"). The physicist's correlation is just the the probability of equal outcomes minus the probability of different outcomes."

He then accuses Joy Christian of inventing his own correlation: "Christian decides to redefine correlation by dividing the average of the product of the outcomes by bivectorial 'standard deviations'. His famous model actually has the outcome on Alice's side always opposite to the outcome on Bob's side so in ordinary terms it predicts a correlation of -1 independently of the settings on each side."

Except that isn't at all what Joy has done. Remember the elementary calculus rule: "the product of limits equals the limit of products"? As with all calculus, this rests on the principles of limit and function. A continuous function of this sort on the 3-sphere measure space reverses sign continually in a regular sine wave pattern; you say that "a and a' are mutually exclusive, b and b' are mutually exclusive; but a does not exclude b or b', and a' does not exclude b or b', etc.", yes it must. Even though the trajectories are independently random (binary) the result manifestly orients the measure space to pairwise certainty. Not to a "correlation of -1 independently of the settings on each side" as Gill claims, but +/- 1 depending on the topological orientation in the observer's view -- orientation built into the structure of the space, and not chosen by the observer.

Bell's experiment has no measure space -- were it prescribed, one would find insufficient degrees of freedom to account for the results.

Thanks Tom, but I am talking about detector-settings (unit-vectors in 3-space), not observations. So my need for a satisfactory explanation of the Joy-Tom-Fred position re the detector-settings still stands.

[Joy Christian]

1. If that is now all that you are saying (limiting your statement to a single run of the EPRB experiment rather than a single run of an experiment known as a Bell-test), then this statement of yours remains false: "It [QM] makes no prediction whatsoever for the Bell-CHSH quantity E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’), because no experiment can ever be performed (even by "God") which can measure that quantity."

2. I look forward to an explanation of this statement of yours: "The point I am making is rather trivial to understand: a, b, a', and b' are mutually exclusive, or physically incompatible observation directions."

I find this discussion quite tedious, not the least because we (all of us in this forum) have beaten these issues to death, many times over. But let us indulge in it again:

It is quite obvious that (a, b), (a, b’), (a’, b), and (a’, b’) are mutually exclusive pairs of measurement directions. Each pair can be used by Alice and Bob for a given experiment, for all runs, but no two of the four pairs can be used by Alice and Bob simultaneously. This is simply because Alice and Bob do not have a miraculous ability to be in London and Paris at the same time (i.e., on the same space-like hypersurface). If you don't agree with this paragraph, then this discussion ends here.

Now consider the following averages E(a, b), E(a, b’), E(a’, b), and E(a’, b’). Each of these averages is well defined and observable. I believe we agree about this.

Let me now unpack E(a, b) to explain what it means: E(a, b) = < A(a) B(b) > , where < > stands for ordinary average of the product A(a)B(b) of numbers A(a) and B(b).

Now, for a single run of a given experiment, consider the quantity A(a) B(b) + A(a) B(b' ) + A(a' ) B(b) - A(a' ) B(b' ). This quantity is actually meaningless because it is not observable for a single run of a given experiment, because (a, b), (a, b’), (a’, b), and (a’, b’) are mutually exclusive pairs of measurement directions, as agreed.

Now consider several different runs of the experiment and the corresponding un-observable quantities similar to A(a) B(b) + A(a) B(b' ) + A(a' ) B(b) - A(a' ) B(b' ).

For clarity, let us label the runs by numbers 1, 2, 3, ... n, so that we have the following set of n un-observable quantities altogether:

A_1(a) B_1(b) + A_1(a) B_1(b' ) + A_1(a' ) B_1(b) - A_1(a' ) B_1(b' )

A_2(a) B_2(b) + A_2(a) B_2(b' ) + A_2(a' ) B_2(b) - A_2(a' ) B_2(b' )

A_3(a) B_3(b) + A_3(a) B_3(b' ) + A_3(a' ) B_3(b) - A_3(a' ) B_3(b' )

*
*
*

A_n(a) B_n(b) + A_n(a) B_n(b' ) + A_n(a' ) B_n(b) - A_n(a' ) B_n(b' ).

Since each of these n quantities is an un-observable quantity, their average,

< A_k(a) B_k(b) + A_k(a) B_k(b' ) + A_k(a' ) B_k(b) - A_k(a' ) B_k(b' ) >

(where the summation is over the index k going from 1 to n),

is also an un-observable quantity.

But the above average is often what is meant by the expression E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’) in the CHSH discussions, which surreptitiously assumes

E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’) = < A_k(a) B_k(b) + A_k(a) B_k(b' ) + A_k(a' ) B_k(b) - A_k(a' ) B_k(b' ) > ......................... (1).

Hence my statement you keep quoting: "It [QM] makes no prediction whatsoever for the Bell-CHSH quantity E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’), because no experiment can ever be performed (even by "God") which can measure that quantity."

Just in case there is still some confusion, let me stress that, individually, each of the averages ,

E(a, b) = < A_k(a) B_k(b) > ,

E(a, b’) = < A_k(a) B_k(b' ) > ,

E(a’, b) = < A_k(a' ) B_k(b) > ,

E(a’, b’) = < A_k(a' ) B_k(b' ) > ,

is a perfectly good, observable quantity. Each E(a, b) can be computed for a given choice (a, b) of a pair of observable directions, on a given space-like hyper-surface.

But if one sticks to individual averages only, then the upper bound of 2 on CHSH cannot be derived. The upper bound of 2 can be derived only by cheating, as in Eq. (1)

***

[FrediFizzx]

For clarity, let us label the runs by numbers 1, 2, 3, ... n, so that we have the following set of n un-observable quantities altogether:

A_1(a) B_1(b) + A_1(a) B_1(b' ) + A_1(a' ) B_1(b) - A_1(a' ) B_1(b' )

A_2(a) B_2(b) + A_2(a) B_2(b' ) + A_2(a' ) B_2(b) - A_2(a' ) B_2(b' )

A_3(a) B_3(b) + A_3(a) B_3(b' ) + A_3(a' ) B_3(b) - A_3(a' ) B_3(b' )

*
*
*

A_n(a) B_n(b) + A_n(a) B_n(b' ) + A_n(a' ) B_n(b) - A_n(a' ) B_n(b' ).

Since each of these n quantities is an un-observable quantity, their average,

< A_k(a) B_k(b) + A_k(a) B_k(b' ) + A_k(a' ) B_k(b) - A_k(a' ) B_k(b' ) >

(where the summation is over the index k going from 1 to n),

is also an un-observable quantity.
***

For further clarity what the QM prediction and the experiments are doing is,

A_1(a) B_1(b)

A_2(a) B_2(b')

A_3(a') B_3(b)

A_4(a') B_4(b')
***
But not necessarily in that order and we will need 1 and 2 labels for the a's and b's giving,

A_1(a1) B_1(b1)

A_2(a1) B_2(b2)

A_3(a2) B_3(b1)

A_4(a2) B_4(b2)
*
*
*
A_n(a_i) B_n(b_j)

Where i and j = 1 or 2. Then when doing the CHSH string of expectations, they do a1's and b1's to get <A_k(a1) B_k(b1)> = E(a, b), etc. But it is easy to see that if we just had the four runs and added the expectation terms together it is possible to get,

1 + 1 +1 - (-1) = 4

That is the basis for a different inequality. It is not the Bell-CHSH inequality with a bound of 2 that QM and the experiments use. Neither QM nor the experiments have ever violated a Bell inequality. It is mathematically impossible.
.

[Joy Christian]

***
Here is another simple way to see the glaring mistake made by Bell and CHSH, and continue being made by their ardent followers like the statistician Richard D. Gill:

For clarity, let me rewrite my Eq. (1) above, namely

E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’) = < A_k(a) B_k(b) + A_k(a) B_k(b' ) + A_k(a' ) B_k(b) - A_k(a' ) B_k(b' ) > ......................... (1),

as follows:

< A_k(a) B_k(b) > + < A_k(a) B_k(b' ) > + < A_k(a' ) B_k(b) > - < A_k(a' ) B_k(b' ) > = < A_k(a) B_k(b) + A_k(a) B_k(b' ) + A_k(a' ) B_k(b) - A_k(a' ) B_k(b' ) > ... (2).

Now the bound of 2 on the RHS of the above equation can be easily derived:

| < A_k(a) B_k(b) + A_k(a) B_k(b' ) + A_k(a' ) B_k(b) - A_k(a' ) B_k(b' ) > | = | < A_k(a) [ B_k(b) + B_k(b' ) ] + A_k(a' ) [ B_k(b) - B_k(b' ) ] > | = 2 ............... (3),

because all A's and B's are = +1 or -1.

But notice that this seemingly innocent derivation requires the un-physical assumption stated in Eq. (2), making it a compete nonsense. The LHS of Eq. (2) is a sum of four averages of four perfectly legitimate, observable physical quantities; namely A_k(a) B_k(b), A_k(a) B_k(b' ), A_k(a' ) B_k(b), and - A_k(a' ) B_k(b' ). The RHS of Eq. (2), however, is a single average of an un-observable and hence un-physical quantity; namely A_k(a) B_k(b) + A_k(a) B_k(b' ) + A_k(a' ) B_k(b) - A_k(a' ) B_k(b' ) (see my previous post).

So in Eq. (2) Bell, CHSH, and their followers are surreptitiously replacing four perfectly observable quantities with one un-observable, and hence un-physical quantity to derive the bound of 2. If they don't take this illegitimate step, then the bound on CHSH is 4, not 2, as Fred also pointed about above. Note also that 4 is > 2\/2.

How on earth such a blatant slight of hand by Bell and his followers has been swallowed up by seemingly intelligent people within the physics community?

***

[thray]

Gordon Watson: " ... I am talking about detector-settings (unit-vectors in 3-space), not observations."

No observations = no physics.

[Joy Christian]

***
Thanks to Gordon's questions, I was inspired to write up my views expressed above in somewhat formal way. I have posted a new paper here on Academia.Edu.

In the past some people had difficulty downloading papers from Academia.Edu. In that case you can download the paper directly from my blog, in PDF format:

"On the Fatal Mistake Made by John S. Bell in the Proof of His Famous Theorem": http://libertesphilosophica.info/blog/w ... /Fatal.pdf

Note that this paper is only two pages long. I hope it is still understandable.

***

[ajw]

Your publication is very clear. However, looking at the referenced literature, it is less clear for me where exactly the error by Bell or CHSH is made. Is it the difference in notation, or follow up literature that is not mentioned?

[Joy Christian]

Your publication is very clear. However, looking at the referenced literature, it is less clear for me where exactly the error by Bell or CHSH is made. Is it the difference in notation, or follow up literature that is not mentioned?

Thank you, Albert Jan.

I have updated the paper on Academia with an additional reference to a specific page of Bell's book where he makes the fatal error. His notation is a bit different from mine, but it is quite clear on that page how he slips-in the replacement I talk about in my paper.

[Gordon Watson]

***
Thanks to Gordon's questions, I was inspired to write up my views expressed above in somewhat formal way. I have posted a new paper here on Academia.Edu.

In the past some people had difficulty downloading papers from Academia.Edu. In that case you can download the paper directly from my blog, in PDF format:

"On the Fatal Mistake Made by John S. Bell in the Proof of His Famous Theorem": http://libertesphilosophica.info/blog/w ... /Fatal.pdf

Note that this paper is only two pages long. I hope it is still understandable.

***

Joy, many thanks for going to the trouble of spelling out your view on one of Bell's problems. HOWEVER, in my view, you are dealing with a consequence of his opening "Fatal Mistake" -- ie, Bell's assumption of "objectivity or classicality" (via his interpretation of EPR "elements of physical reality"). That is, Bell assumes that each "measurement" reveals an "objective" pre-measurement property of each fermion AND (with admirable consistency) his equations reflect that mistake.

A nice reference to this assumption is given in CH (1974; footnote #11):

"Even though we have introduced λ as the state of a specific single system, the assumed objectivity of the system described by this state allows us to consider an ensemble of these, physically identical to the extent that they are all characterised by the same λ. Clearly, this procedure is conceptually sound, even in cases where we cannot in practice prepare the pure λ ensemble." (My bolding.)

So imho you should amend your notation to enhance the clarity and relevance of your paper. Here's what I would do [for starters]:

To be consistent with your later important and realistic conversion of " k " "to a specific run of the experiment" -- after eqn (7):

1. Rewrite eqn (1) using the index i where i denotes the i-th run of the experiment.

2. Rewrite eqn (3) over the indices i, j, k, l. Let i range from 1 to n (as above), j range from n+1 to 2n, k range 2n +1 to 3n, l range from 3n +1 to 4n.

3. Some consequential re-writing is then needed; maybe leaving out Spinoza's god. For Bell's Fatal Mistake is his "classicality" assumption: his equations simply reflect that assumption; an assumption known to be false from the time of QM's founding.

HTH, with best regards; Gordon

[Joy Christian]

***
Thanks to Gordon's questions, I was inspired to write up my views expressed above in somewhat formal way. I have posted a new paper here on Academia.Edu.

In the past some people had difficulty downloading papers from Academia.Edu. In that case you can download the paper directly from my blog, in PDF format:

"On the Fatal Mistake Made by John S. Bell in the Proof of His Famous Theorem": http://libertesphilosophica.info/blog/w ... /Fatal.pdf

Note that this paper is only two pages long. I hope it is still understandable.

***

Joy, many thanks for going to the trouble of spelling out your view on one of Bell's problems. HOWEVER, in my view, you are dealing with a consequence of his opening "Fatal Mistake" -- ie, Bell's assumption of "objectivity or classicality" (via his interpretation of EPR "elements of physical reality"). That is, Bell assumes that each "measurement" reveals an "objective" pre-measurement property of each fermion AND (with admirable consistency) his equations reflect that mistake.

A nice reference to this assumption is given in CH (1974; footnote #11):

"Even though we have introduced λ as the state of a specific single system, the assumed objectivity of the system described by this state allows us to consider an ensemble of these, physically identical to the extent that they are all characterised by the same λ. Clearly, this procedure is conceptually sound, even in cases where we cannot in practice prepare the pure λ ensemble." (My bolding.)

So imho you should amend your notation to enhance the clarity and relevance of your paper. Here's what I would do [for starters]:

To be consistent with your later important and realistic conversion of " k " "to a specific run of the experiment" -- after eqn (7):

1. Rewrite eqn (1) using the index i where i denotes the i-th run of the experiment.

2. Rewrite eqn (3) over the indices i, j, k, l. Let i range from 1 to n (as above), j range from n+1 to 2n, k range 2n +1 to 3n, l range from 3n +1 to 4n.

3. Some consequential re-writing is then needed; maybe leaving out Spinoza's god. For Bell's Fatal Mistake is his "classicality" assumption: his equations simply reflect that assumption; an assumption known to be false from the time of QM's founding.

HTH, with best regards; Gordon

Thanks for your comments, Gordon.

I am afraid I am unable to agree with any of your suggestions, at least on my first reading.

I will think about them further, but it seems to me from your suggestions that you have misunderstood both Bell's original argument as well as my criticism of it.

***

[Gordon Watson]

***
Thanks to Gordon's questions, I was inspired to write up my views expressed above in somewhat formal way. I have posted a new paper here on Academia.Edu.

In the past some people had difficulty downloading papers from Academia.Edu. In that case you can download the paper directly from my blog, in PDF format:

"On the Fatal Mistake Made by John S. Bell in the Proof of His Famous Theorem": http://libertesphilosophica.info/blog/w ... /Fatal.pdf

Note that this paper is only two pages long. I hope it is still understandable.

***

Joy, many thanks for going to the trouble of spelling out your view on one of Bell's problems. HOWEVER, in my view, you are dealing with a consequence of his opening "Fatal Mistake" -- ie, Bell's assumption of "objectivity or classicality" (via his interpretation of EPR "elements of physical reality"). That is, Bell assumes that each "measurement" reveals an "objective" pre-measurement property of each fermion AND (with admirable consistency) his equations reflect that mistake.

A nice reference to this assumption is given in CH (1974; footnote #11):

"Even though we have introduced λ as the state of a specific single system, the assumed objectivity of the system described by this state allows us to consider an ensemble of these, physically identical to the extent that they are all characterised by the same λ. Clearly, this procedure is conceptually sound, even in cases where we cannot in practice prepare the pure λ ensemble." (My bolding.)

So imho you should amend your notation to enhance the clarity and relevance of your paper. Here's what I would do [for starters]:

To be consistent with your later important and realistic conversion of " k " "to a specific run of the experiment" -- after eqn (7):

1. Rewrite eqn (1) using the index i where i denotes the i-th run of the experiment.

2. Rewrite eqn (3) over the indices i, j, k, l. Let i range from 1 to n (as above), j range from n+1 to 2n, k range 2n +1 to 3n, l range from 3n +1 to 4n.

3. Some consequential re-writing is then needed; maybe leaving out Spinoza's god. For Bell's Fatal Mistake is his "classicality" assumption: his equations simply reflect that assumption; an assumption known to be false from the time of QM's founding.

HTH, with best regards; Gordon

Thanks for your comments, Gordon.

I am afraid I am unable to agree with any of your suggestions, at least on my first reading.

I will think about them further, but it seems to me from your suggestions that you have misunderstood both Bell's original argument as well as my criticism of it.

***

OK. Sticking with what I've written, I'll be happy to read and reply to your more considered response.

NB: At the moment, in your own terms, three of your eqns (9) - (12) are "physically meaningless". Just like Bell's!

G

[Joy Christian]

NB: At the moment, in your own terms, three of your eqns (9) - (12) are "physically meaningless". Just like Bell's!

Sorry, Gordon. Your comment above only confirms my suspicion that you have misunderstood both Bell's original argument as well as my latest criticism of it.

As I have stressed in the paper, eqns (9) - (12) are perfectly meaningful. They define four counterfactually performed averages over well defined physical quantities.

***

[Gordon Watson]

NB: At the moment, in your own terms, three of your eqns (9) - (12) are "physically meaningless". Just like Bell's!

Sorry, Gordon. Your comment above only confirms my suspicion that you have misunderstood both Bell's original argument as well as my latest criticism of it.

As I have stressed in the paper, eqns (9) - (12) are perfectly meaningful. They define four counterfactually performed averages over well defined physical quantities.

***

Joy, you now say: "As I have stressed in the paper, eqns (9) - (12) are perfectly meaningful. They define four counterfactually performed averages [sic] over well defined physical quantities."

Alas Joy, in your own terms, three of your eqns (9) - (12) remain "physically meaningless" because (just like Bell's consequential mistake) they are counterfactual.

NB, again in your terms: "Here the index k = 1 now represents a specific run of the experiment"! BUT you have k ranging from 1 to n in each of your (9) - (12).

Thus, in my terms, you need another 3 "specific runs of the experiment" (say, over the indices i, j, l) to deliver the total of 4 specific terms that you need to exceed the CHSH bounds.

G

[Joy Christian]

***
Gordon, thanks again for your comments. At this point it is best that we agree to disagree.

***