Bell's theorem refuted via elementary probability theory

[gill1109]

Sorry Gordon, I told you I am not answering any more of your questions till you have answered a question of my own. I need to understand what the hell you are going on about by getting your clear answer to a question. I am not going into physics or metaphysics or philosophy here. I want to stick to: elementary probability theory.

First some preliminaries. Many (but not all) people agree (Joy Christian and Fred Diether disagree) that one can prove with elementary probability theory that there do not exist A, B and rho, such that

1) A is a function of a and lambda, taking the values +/- 1

2) B is a function of b and lambda taking the values +/-1

3) a and b are directions represented by unit vectors (whether in the plane or in space doesn't matter)

4) lambda takes values in a space Lambda on which there is defined a probability measure with probability density rho

5) int_{lambda in Lambda} rho(lambda)d lambda A(a, lambda) B(b, lambda) = a.b for all a and b.

My question to you:

Do you agree with that "elementary probability theory result", yes or no?

.
no: please show me your proof.
.

No. We are discussing your elementary probability theory, not mine.

So you think that functions A, B and rho, with all those properties, do exist?

[local]

Let's try to cut through this Gordonian knot.

My refutation of BT goes through: independent of the functions A and B

Here GW claims that Bell's integral integrates to -a.b independent of the functions. It's total nonsense. GW, if I present a set of simple functions that does NOT integrate to -a.b, will you finally admit the error of your ways?

Notwithstanding that, we can infer what functions you are using from your "proof". You claim those functions are "heuristically chosen". But simple testing of them with a simulation, or analysis with correct mathematics, does not produce -a.b.

You also claim that your sign error in equation (3) is just a "TYPO". That is more nonsense. If you correct that error in (3) you cannot simply reintroduce it in (4). So please give us your revised 2-page paper with your "TYPO" corrected. Don't use Richard's legitimate concerns about notation as an excuse to refuse that. Your notation is good enough at least for many of us to understand. Your proof is simply wrong. You have made an elementary sign error that is obvious even with your cherished high-school mathematics. Best to admit it and move on, rather than double down on nonsense.

Try to publish this proof in a respectable peer-reviewed journal. I can point you to several that are willing to publish solid papers challenging the mainstream views about Bell's work and nonlocality. If your argument withstands scrutiny it will be published. Your proof does not withstand scrutiny.

[Gordon Watson]

Sorry Gordon, I told you I am not answering any more of your questions till you have answered a question of my own. I need to understand what the hell you are going on about by getting your clear answer to a question. I am not going into physics or metaphysics or philosophy here. I want to stick to: elementary probability theory.

First some preliminaries. Many (but not all) people agree (Joy Christian and Fred Diether disagree) that one can prove with elementary probability theory that there do not exist A, B and rho, such that

1) A is a function of a and lambda, taking the values +/- 1

2) B is a function of b and lambda taking the values +/-1

3) a and b are directions represented by unit vectors (whether in the plane or in space doesn't matter)

4) lambda takes values in a space Lambda on which there is defined a probability measure with probability density rho

5) int_{lambda in Lambda} rho(lambda)d lambda A(a, lambda) B(b, lambda) = a.b for all a and b.

My question to you:

Do you agree with that "elementary probability theory result", yes or no?

.
no: please show me your proof.
.

No. We are discussing your elementary probability theory, not mine.

So you think that functions A, B and rho, with all those properties, do exist?

YES! Since 1989! There are many such functions: eg, the dichotomic (2-channel) polarizer-analyser function:

.

Any objections?

Gordon
.

[Gordon Watson]

Let's try to cut through this Gordonian knot.

My refutation of BT goes through: independent of the functions A and B

Here GW claims that Bell's integral integrates to -a.b independent of the functions. It's total nonsense. GW, if I present a set of simple functions that does NOT integrate to -a.b, will you finally admit the error of your ways?

Notwithstanding that, we can infer what functions you are using from your "proof". You claim those functions are "heuristically chosen". But simple testing of them with a simulation, or analysis with correct mathematics, does not produce -a.b.

You also claim that your sign error in equation (3) is just a "TYPO". That is more nonsense. If you correct that error in (3) you cannot simply reintroduce it in (4). So please give us your revised 2-page paper with your "TYPO" corrected. Don't use Richard's legitimate concerns about notation as an excuse to refuse that. Your notation is good enough at least for many of us to understand. Your proof is simply wrong. You have made an elementary sign error that is obvious even with your cherished high-school mathematics. Best to admit it and move on, rather than double down on nonsense.

Try to publish this proof in a respectable peer-reviewed journal. I can point you to several that are willing to publish solid papers challenging the mainstream views about Bell's work and nonlocality. If your argument withstands scrutiny it will be published. Your proof does not withstand scrutiny.

local

1. My correction of that typo leaves the next 6 equations unchanged.

2. So no need to change (4).

3. Please show me the error in the high-school math that refutes BI.

4. I'll welcome your pointer to those several journals.

5. May I offer you as a referee?

6. Please have a look at the function in my last post (above) and comment critically.

7. What functions did you infer, and which did you test.

8. Re "the revised 2-page paper with my "TYPO." Put the correction into (3) by hand for now; leave all else unchanged.

Gordon
.

[local]

You ignored my main question to you and responded with more nonsense. The function you cite is meaningless gobbledegook (a proper function set includes definitions for A, B, and rho). Since you are not serious and ignore my questions (seems Richard has the same problem with you), I'm no longer interested in engaging with you. Good luck getting your work published. One option is Physics Essays.

[Gordon Watson]

You ignored my main question to you and responded with more nonsense. The function you cite is meaningless gobbledegook (a proper function set includes definitions for A, B, and rho). Since you are not serious and ignore my questions (seems Richard has the same problem with you), I'm no longer interested in engaging with you. Good luck getting your work published. One option is Physics Essays.

local, I wasn't offering the function set. Given the hint, I thought you could complete that for yourself. BUT NOTE, by implication, B must deliver ±1: it is NOT any old function, as you seemed to suggest above!

PS: You offered several journals, but gave only one, the one I know. Please let me know the others.

Thanks; Gordon
.

[gill1109]

Sorry Gordon, I told you I am not answering any more of your questions till you have answered a question of my own. I need to understand what the hell you are going on about by getting your clear answer to a question. I am not going into physics or metaphysics or philosophy here. I want to stick to: elementary probability theory.

First some preliminaries. Many (but not all) people agree (Joy Christian and Fred Diether disagree) that one can prove with elementary probability theory that there do not exist A, B and rho, such that

1) A is a function of a and lambda, taking the values +/- 1

2) B is a function of b and lambda taking the values +/-1

3) a and b are directions represented by unit vectors (whether in the plane or in space doesn't matter)

4) lambda takes values in a space Lambda on which there is defined a probability measure with probability density rho

5) int_{lambda in Lambda} rho(lambda)d lambda A(a, lambda) B(b, lambda) = a.b for all a and b.

My question to you:

Do you agree with that "elementary probability theory result", yes or no?

.
no: please show me your proof.
.

No. We are discussing your elementary probability theory, not mine.

So you think that functions A, B and rho, with all those properties, do exist?

YES! Since 1989! There are many such functions: eg, the dichotomic (2-channel) polarizer-analyser function:

.

Any objections?

Gordon
.

Yes, I object, because I don’t see a definition of a function here. I think you need to look up the definition of “function”. A function has a domain and a range, and it consists of a rule which associates each element of the domain to an element of the range. Please show us your functions A, B and rho, and talk us through the computation of that integral.

I’m in entire agreement with “local” on this one.

[local]

it is NOT any old function, as you seemed to suggest above

You're the guy that said your proof goes through independent of the functions.

You offered several journals, but gave only one, the one I know. Please let me know the others.

My consulting rate is $300/hour. Send a PM.

[gill1109]

it is NOT any old function, as you seemed to suggest above

You're the guy that said your proof goes through independent of the functions.

You offered several journals, but gave only one, the one I know. Please let me know the others.

My consulting rate is $300/hour. Send a PM.

Mine is 250 Euro per hour!

[local]

Well duh, you're an Emeritus Professor and I'm just a bricklayer.

[gill1109]

Well duh, you're an Emeritus Professor and I'm just a bricklayer.

“Bricklayer” is a noble profession. And more important to society than “professor”. Our “ivory towers” are built of bricks and mortar, steel and reinforced concrete, stone.

[Gordon Watson]

it is NOT any old function, as you seemed to suggest above

You're the guy that said your proof goes through independent of the functions.

... in the context of Bell's theorem and his functions A(a,λ) = ±1, B(b,λ) = ±1, ....

Hope this is more to your liking and your interest in programming: https://vixra.org/pdf/2010.0068v5.pdf

Gordon
.

[local]

Interested only in your function set A, B, and rho that integrates to -a.b, which you refuse to provide. Who said I am interested in programming? Hey, I'm interested in proper drywall technique too, and how to unclog a mucked-up toilet, so what? Stop trying to distract us with nonsense. Your latest version is worse than the previous one. Your functions...where are they!?

[gill1109]

it is NOT any old function, as you seemed to suggest above

You're the guy that said your proof goes through independent of the functions.

... in the context of Bell's theorem and his functions A(a,λ) = ±1, B(b,λ) = ±1, ....

Hope this is more to your liking and your interest in programming: https://vixra.org/pdf/2010.0068v5.pdf

Gordon
.

The problem is your equation (7) and your abuse of your own notation. “P(A^+) is actually “P(A^+|a, b, Lamba^+)” in one instance, and “P(A^+|a, b, Lamba^-)” in the other. They add to 1/2 but certainly can’t both equal 1/2. Similarly for A^-.

[Gordon Watson]

it is NOT any old function, as you seemed to suggest above

You're the guy that said your proof goes through independent of the functions.

... in the context of Bell's theorem and his functions A(a,λ) = ±1, B(b,λ) = ±1, ....

Hope this is more to your liking and your interest in programming: https://vixra.org/pdf/2010.0068v5.pdf

Gordon
.

The problem is your equation (7) and your abuse of your own notation. “P(A^+) is actually “P(A^+|a, b, Lamba^+)” in one instance, and “P(A^+|a, b, Lamba^-)” in the other. They add to 1/2 but certainly can’t both equal 1/2. Similarly for A^-.

Thanks Richard,

It is, mistakenly, the old denouement carried down from an earlier version; so it's no problem to fix: so long as we agree that "they add to 1"?

EDIT: I prefer the earlier version: expanding Bell's definition of E(a, b) directly and avoiding the Λ subsets. So I'm planning to return to that. Any comment on that?

Thanks again; Gordon
.

[gill1109]

The problem is your equation (7) and your abuse of your own notation. “P(A^+) is actually “P(A^+|a, b, Lamba^+)” in one instance, and “P(A^+|a, b, Lamba^-)” in the other. They add to 1/2 but certainly can’t both equal 1/2. Similarly for A^-.

Thanks Richard,

It is, mistakenly, the old denouement carried down from an earlier version; so it's no problem to fix: so long as we agree that "they add to 1"?

EDIT: I prefer the earlier version: expanding Bell's definition of E(a, b) directly and avoiding the Λ subsets. So I'm planning to return to that. Any comment on that?

Thanks again; Gordon
.

My comment is: you are on a fool’s quest.

[Gordon Watson]

The problem is your equation (7) and your abuse of your own notation. “P(A^+) is actually “P(A^+|a, b, Lamba^+)” in one instance, and “P(A^+|a, b, Lamba^-)” in the other. They add to 1/2 but certainly can’t both equal 1/2. Similarly for A^-.

Thanks Richard,

It is, mistakenly, the old denouement carried down from an earlier version; so it's no problem to fix: so long as we agree that "they add to 1"?

EDIT: I prefer the earlier version: expanding Bell's definition of E(a, b) directly and avoiding the Λ subsets. So I'm planning to return to that. Any comment on that?

Thanks again; Gordon
.

My comment is: you are on a fool’s quest.

OK. But my question remains. Richard: do those probabilities add to 1, or not?

Gordon
.

[gill1109]

I already told you that in pairs they add to 1/2. So all four together add up to 1.

[local]

GW, where is your function set (A, B, and rho) that integrates to -a.b? You've claimed that your proof goes through independent of the functions, so it should be trivial to show a set that integrates to -a.b. But you just ignore the requests and try to obfuscate things with further silliness.

GW, put up or shut up. If you need help with integration, analytically or numerically, we will be happy to test your function set for you.

[local]

GW, given your failure to provide a function set integrating to -a.b, shall we conclude that you now accept that there is no such set, and that your "proof" must therefore be flawed?