The Mistakes by Bell and von Neumann are Identical

[Joy Christian]

I suggest you read your own references more carefully.

I suggest you read my paper instead of relying on authorities. Either you read my paper [Eq. (11)] and learn a few things, or remain deluded in your dogmatic beliefs. The choice is yours.

***

[gill1109]

I suggest you read your own references more carefully.

I suggest you read my paper instead of relying on authorities. Either you read my paper [Eq. (11)] and learn a few things, or remain deluded in your dogmatic beliefs. The choice is yours.

***

I prefer to rely on my mathematical training than on your “authority”! Just to remind you, I studied with J.H. Conway and S. Hawking, among others, at Gonville and Caius college, Cambridge, England. The college of the famous eugenist and founder of modern statistical science, Sir R.A. Fisher. I feel that Cambridge trumps Oxford, let alone Boston (somewhere in the US?). But feel free to your own opinion.

[Joy Christian]

I suggest you read your own references more carefully.

I suggest you read my paper instead of relying on authorities. Either you read my paper [Eq. (11)] and learn a few things, or remain deluded in your dogmatic beliefs. The choice is yours.

***

I prefer to rely on my mathematical training than on your “authority”! Just to remind you, I studied with J.H. Conway and S. Hawking, among others, at Gonville and Caius college, Cambridge, England. The college of the famous eugenist and founder of modern statistical science, Sir R.A. Fisher. I feel that Cambridge trumps Oxford, let alone Boston (somewhere in the US?). But feel free to your own opinion.

You are merely a statistician, not a physicist or a real mathematician. That is sufficient for me to distrust your "authority." I am not at all impressed by who you have rubbed shoulders with.

***

[gill1109]

I suggest you read your own references more carefully.

I suggest you read my paper instead of relying on authorities. Either you read my paper [Eq. (11)] and learn a few things, or remain deluded in your dogmatic beliefs. The choice is yours.

***

I prefer to rely on my mathematical training than on your “authority”! Just to remind you, I studied with J.H. Conway and S. Hawking, among others, at Gonville and Caius college, Cambridge, England. The college of the famous eugenist and founder of modern statistical science, Sir R.A. Fisher. I feel that Cambridge trumps Oxford, let alone Boston (somewhere in the US?). But feel free to your own opinion.

You are merely a statistician, not a physicist or a real mathematician. That is sufficient for me to distrust your "authority." I am not at all impressed by who you have rubbed shoulders with.

***

You can win the boasting competition: you have rubbed shoulders with John Bell, and I haven't. But anyway, don't trust anyone's "authority". Look at my argument and give your counter-argument. You seem very reluctant to get into mathematical details. Very reluctant. It's suspicious.

[Joy Christian]

I prefer to rely on my mathematical training than on your “authority”! Just to remind you, I studied with J.H. Conway and S. Hawking, among others, at Gonville and Caius college, Cambridge, England. The college of the famous eugenist and founder of modern statistical science, Sir R.A. Fisher. I feel that Cambridge trumps Oxford, let alone Boston (somewhere in the US?). But feel free to your own opinion.

You are merely a statistician, not a physicist or a real mathematician. That is sufficient for me to distrust your "authority." I am not at all impressed by who you have rubbed shoulders with.

***

You can win the boasting competition: you have rubbed shoulders with John Bell, and I haven't. But anyway, don't trust anyone's "authority". Look at my argument and give your counter-argument. You seem very reluctant to get into mathematical details. Very reluctant. It's suspicious.

If you think mathematics is at stake here, then you haven't understood the objection raised by Einstein and Bell ( both of whom were remarkable physicists ) against the "silly" theorem of von Neumann ( who was, of course, a mathematician par excellence ). No, mathematics is not an issue here. And as far as mathematics is relevant at all, it is amply provided in my paper.

***

[Joy Christian]

***
I have revised this paper once again: https://arxiv.org/abs/1704.02876. The slightly revised abstract reads:



***

[FrediFizzx]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.
.

[Joy Christian]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.

The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:



Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician.

***

[FrediFizzx]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.

The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:



Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician.

***

Proof??? What proof? There is no actual mathematical proof of Bell's junk physics theory since it is just a word "theorem".
.

[Joy Christian]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.

The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:



Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician.

***

Proof??? What proof? There is no actual mathematical proof of Bell's junk physics theory since it is just a word "theorem".

Sure. I am just trying to check whether they are consistent in their own wordgame.

But I have got the above equation wrong. That is not what they are assuming. What they are assuming is that Eq.(18) of my paper, with different indices in the sum of the four averages, is equivalent to Eq.(19) in my paper with the same index k for the four CHSH averages in the large N limit. They are probably right about that.

***

[gill1109]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.

The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:



Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician.

***

Joy, sometime we need to accept our differences, and work together, constructively. Yes, this is a question which some statisticians have already studied. I can certainly tell you that with only 256 events the margin of error is enormous. I know how big it is.

[gill1109]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.

The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:



Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician.

***

Proof??? What proof? There is no actual mathematical proof of Bell's junk physics theory since it is just a word "theorem".
.

Fred, can you enlighten me as to what you mean by a “word theorem”? Pythagoras theorem is a word theorem. Euclid wrote words, not formulas. I’ve given you references to several present day top mathematicians who have expressed Bell’s theorem as a formal mathematical theorem. No retractions yet. You may have heard of the name “Tsirelson”. (Boris. RIP). Klaas Landsman is another. The list could go on and on. I don’t think some British-Dutch statistician by the name of Gill had anything to do with all that, anything at all.

[Gordon Watson]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.

The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:



Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician.

***

Joy, perhaps I'm misreading it.

BUT it seems to me that there is a mistake in the above assumption; the one that you associate with the traditional proof of Bell's theorem.

Without any reference to QM, one finds, via the ordinary definition of an average or expectation, under EPR-Bohm (the experiment studied by Bell in 1964):

(1) The LHS = E(a,b) = -cos(a,b) ideally. (2) The RHS = E(a.b') = -cos(a,b') ideally.

THUS: The "questioned-equality" can be replaced by ≠ if b ≠ b'. And by = if b = b'.

PS: Please, can you show me where it occurs in Bell (1964) or in any other Bellian work?

And which equation are you referring to when you say you accept it in your paper?

Thanks; Gordon
.

[gill1109]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.

The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:



Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician.

***

Joy, perhaps I'm misreading it.

BUT it seems to me that there is a mistake in the above assumption; the one that you associate with the traditional proof of Bell's theorem.

Without any reference to QM, one finds, via the ordinary definition of an average or expectation, under EPR-Bohm (the experiment studied by Bell in 1964):

(1) The LHS = E(a,b) = -cos(a,b) ideally. (2) The RHS = E(a.b') = -cos(a,b') ideally.

THUS: The "questioned-equality" can be replaced by ≠ if b ≠ b'. And by = if b = b'.

PS: Please, can you show me where it occurs in Bell (1964) or in any other Bellian work?

And which equation are you referring to when you say you accept it in your paper?

Thanks; Gordon
.

Gordon: in an earlier post Joy writes “But I have got the above equation wrong. That is not what they are assuming. What they are assuming is that Eq.(18) of my paper, with different indices in the sum of the four averages, is equivalent to Eq.(19) in my paper with the same index k for the four CHSH averages in the large N limit. They are probably right about that.”

He’s right. This is the distinction between bound variables and free variables which we have talked about before. Some people talk about dummy variables. When you write e.g. integral over x in some range, of some function of x, d x, you can replace the “x” by any other symbol you like as long as it is not presently being used for something else.

[FrediFizzx]

...
Proof??? What proof? There is no actual mathematical proof of Bell's junk physics theory since it is just a word "theorem".
.

Fred, can you enlighten me as to what you mean by a “word theorem”? Pythagoras theorem is a word theorem. Euclid wrote words, not formulas. I’ve given you references to several present day top mathematicians who have expressed Bell’s theorem as a formal mathematical theorem. No retractions yet. You may have heard of the name “Tsirelson”. (Boris. RIP). Klaas Landsman is another. The list could go on and on. I don’t think some British-Dutch statistician by the name of Gill had anything to do with all that, anything at all.

viewtopic.php?f=6&t=441

It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.
.

[Gordon Watson]

Yeah, the Bell fans are finished and don't even know it. They think because they have moved the goalposts to Gill's "theorem" that they are not finished. But it is just junk physics like Bell's junk physics theory. It has nothing to do with comparing local models to quantum mechanics since QM can't predict individual event by event outcomes either.

The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:



Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician.

***

Joy, perhaps I'm misreading it.

BUT it seems to me that there is a mistake in the above assumption; the one that you associate with the traditional proof of Bell's theorem.

Without any reference to QM, one finds, via the ordinary definition of an average or expectation, under EPR-Bohm (the experiment studied by Bell in 1964):

(1) The LHS = E(a,b) = -cos(a,b) ideally. (2) The RHS = E(a.b') = -cos(a,b') ideally.

THUS: The "questioned-equality" can be replaced by ≠ if b ≠ b'. And by = if b = b'.

PS: Please, can you show me where it occurs in Bell (1964) or in any other Bellian work?

And which equation are you referring to when you say you accept it in your paper?

Thanks; Gordon
.

Gordon: in an earlier post Joy writes “But I have got the above equation wrong. That is not what they are assuming. What they are assuming is that Eq.(18) of my paper, with different indices in the sum of the four averages, is equivalent to Eq.(19) in my paper with the same index k for the four CHSH averages in the large N limit. They are probably right about that.”

He’s right. This is the distinction between bound variables and free variables which we have talked about before. Some people talk about dummy variables. When you write e.g. integral over x in some range, of some function of x, d x, you can replace the “x” by any other symbol you like as long as it is not presently being used for something else.

Thanks Richard, but Joy's comments do not match your explanation:

Joy writes: "The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:

Image

Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician."

By my reading of the defective "questioned-equality" such comments make no sense.

Gordon

[FrediFizzx]

...
Thanks Richard, but Joy's comments do not match your explanation:

Joy writes: "The traditional proof of Bell's theorem depends on the following assumption (without the question mark). Note that the indices j and k and the settings b and b' are not the same:

Image

Although I accept the above equality in my paper, I am curious whether it even holds for the real experiments where they have observed only 256 events. It is supposed to hold for large values of p and q. But how large would they have to be? Any way to check that? Perhaps this is a question for a statistician."

By my reading of the defective "questioned-equality" such comments make no sense.

Gordon

Oh, jeez. Ya just had to muck up this thread with stuff that doesn't matter at all! Stay off this thread until Gill responds to my last post.
.

[gill1109]

...
Proof??? What proof? There is no actual mathematical proof of Bell's junk physics theory since it is just a word "theorem".
.

Fred, can you enlighten me as to what you mean by a “word theorem”? Pythagoras theorem is a word theorem. Euclid wrote words, not formulas. I’ve given you references to several present day top mathematicians who have expressed Bell’s theorem as a formal mathematical theorem. No retractions yet. You may have heard of the name “Tsirelson”. (Boris. RIP). Klaas Landsman is another. The list could go on and on. I don’t think some British-Dutch statistician by the name of Gill had anything to do with all that, anything at all.

viewtopic.php?f=6&t=441

It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.
.

Dear Fred, you keep saying this, and I keep saying that I don’t agree (or I just don’t understand you). Experiments don’t “use an inequality”. Experiments observe four correlations. There is a mathematical theory which says that one minus the sum of the other three can’t exceed 2, under certain conditions; moreover, equality is possible. There is a different theory which says it can’t exceed 2 sqrt 2 under the same conditions, moreover, equality is possible. There is a third theory which says that under the same conditions it can’t exceed the natural bound, 4, which by definition of the correlation between binary outcomes, can’t exceed 4. And it could in principle attain the bound of 4. This is all mathematics. You can write it out as formally and rigorously as you like. Theory 1 is what Einstein had in mind. Theory 2 is called QM. Theory 3 is called “Rohrlich-Popescu” but nobody takes that theory seriously, it isn’t worked out in any detail at all. Do you need more references? Are you aware of Boris Tsirelson’s really impressive and deep mathematical work?

It’s all maths. It’s there. Physicists can do with it what they like. In 2015 physicists did very difficult experiments under very rigorous experimental conditions and observed 2.4 (Delft), 2.6 (Munich), 2.00001 (NIST, Vienna). One can have quite a few criticisms on the quality of those results. Since then, the experiments have been repeated and improved.

The experiments don’t “use an inequality”. They observe four correlations.

Richard

[FrediFizzx]

...
viewtopic.php?f=6&t=441

It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.
.

Dear Fred, you keep saying this, and I keep saying that I don’t agree (or I just don’t understand you). Experiments don’t “use an inequality”. Experiments observe four correlations. There is a mathematical theory which says that one minus the sum of the other three can’t exceed 2, under certain conditions; moreover, equality is possible. There is a different theory which says it can’t exceed 2 sqrt 2 under the same conditions, moreover, equality is possible. There is a third theory which says that under the same conditions it can’t exceed the natural bound, 4, which by definition of the correlation between binary outcomes, can’t exceed 4. And it could in principle attain the bound of 4. This is all mathematics. You can write it out as formally and rigorously as you like. Theory 1 is what Einstein had in mind. Theory 2 is called QM. Theory 3 is called “Rohrlich-Popescu” but nobody takes that theory seriously, it isn’t worked out in any detail at all. Do you need more references? Are you aware of Boris Tsirelson’s really impressive and deep mathematical work?

It’s all maths. It’s there. Physicists can do with it what they like. In 2015 physicists did very difficult experiments under very rigorous experimental conditions and observed 2.4 (Delft), 2.6 (Munich), 2.00001 (NIST, Vienna). One can have quite a few criticisms on the quality of those results. Since then, the experiments have been repeated and improved.

The experiments don’t “use an inequality”. They observe four correlations.

Richard

It is quite amazing that you don't understand the simple fact that NOTHING can exceed the Bell inequalities. Why are you going on about "...experiments don't use an inequality" when the experimenters claim they have exceeded the Bell inequalities? I didn't figure you would have a good answer because there is NO answer. The Bell inequalities are meaningless. Very simple.

However, there might be some meaning to your "theorem" that a local theory can't simulate Nature and the experiments. But I doubt it. Nature does it and we now know that even quantum mechanics is local for the EPR-Bohm scenario so Nature is most likely local in that scenario. Thus it should be possible to model Nature locally.
.

[Joy Christian]

It is oh so simple! It is mathematically and physically impossible for anything including quantum mechanics and the experiments to exceed the Bell inequalities. So, what is the very simple and very logical conclusion? Quantum mechanics and the experiments are using a different inequality with a higher bound! And you call yourself a mathematician. ??? Any mathematician should easily understand that. Thus, there can be no mathematical proof of Bell's junk physics theory. It is that simple.

Anyone with half a brain can understand that what you are saying is the simplest and most logical explanation of why the Bell inequalities seem to be exceeding in the experiments. But the trouble is that one does have to have half a brain to understand this.

***