Bell's theorem refuted via elementary probability theory

[gill1109]

Richard,

1. My P(A^-B^-) versus P(A = -1),P(B = -1))? Decorations or rigorous and convenient short-cut identifiers?

2. No matter what you want to talk about, say (a, b) or (c, d): it seems to me that Λ_+ and Λ_- are self-determining and clear from the context.

3. Please provide the other abominables that you have in mind. I can then get on with improving things. Thanks

Gordon
.

Gordon, I still have no idea what “self determining” means. But more important: I’ve told you the complaints I have with your notations. I suspect most mathematicians would agree with me. You want people like me to read your paper. So this is your problem, not mine.

As “local” points out, and as I agreed, your two pages have zero content, because they do not specify A, B and rho. So there is, so far, nothing to read, nothing to check. So far all we have seen is your attempt to prove the elementary, well known, fact: if X is a random variable which only takes the values +/-1, then E(X) = P(X = 1) - P(X = -1).

You will find it hard to complete the paper. It’s a well known theorem that a triple (A, B, rho) of functions satisfying your conditions does not exist. There is a nice proof by Steven Gull which does not use CHSH at all, which is being being discussed in another thread here. https://physics.stackexchange.com/questions/547039/help-understanding-prof-steve-gulls-explanation-of-bells-theorem

[Gordon Watson]

Richard,

1. My P(A^-B^-) versus P(A = -1),P(B = -1))? Decorations or rigorous and convenient short-cut identifiers?

2. No matter what you want to talk about, say (a, b) or (c, d): it seems to me that Λ_+ and Λ_- are self-determining and clear from the context.

3. Please provide the other abominables that you have in mind. I can then get on with improving things. Thanks

Gordon
.

Gordon, I still have no idea what “self determining” means. But more important: I’ve told you the complaints I have with your notations. I suspect most mathematicians would agree with me. You want people like me to read your paper. So this is your problem, not mine.

As “local” points out, and as I agreed, your two pages have zero content, because they do not specify A, B and rho. So there is, so far, nothing to read, nothing to check. So far all we have seen is your attempt to prove the elementary, well known, fact: if X is a random variable which only takes the values +/-1, then E(X) = P(X = 1) - P(X = -1).

You will find it hard to complete the paper. It’s a well known theorem that a triple (A, B, rho) of functions satisfying your conditions does not exist. There is a nice proof by Steven Gull which does not use CHSH at all, which is being being discussed in another thread here. https://physics.stackexchange.com/questions/547039/help-understanding-prof-steve-gulls-explanation-of-bells-theorem

Richard and, it seems, local,

A: Re my notation:

1. You suggested my extensive use of β was overkill, so I reduced it.

2. As to your suggestion re +1 and -1, I've shown above the benefits of my A^± and B^± notation.

3. So, please, what else are you talking about?

4. Since every equation is numbered, and the notation is consistent throughout: please rewrite a few equations in the way you are advocating.

5. Otherwise I'll have NO idea what you are talking about.

B: Re my 2 pages of "zero" content:

1. From eqn (1), Bell's inequality, I arrive in eqn (5) at a valid alternative (text-book) specification of E(a, b). So there's some content there.

2. From (4) I proceed via ordinary probability theory and hypotheses about natural laws to a refutation of Bell's theorem in (9). As in Aspect, QM and his experiment confirm my hypotheses there. In GHZ QM also agrees with my hypotheses there.

3. I then offer additional content by refuting Bell's inequality -- his own supposed proof of his now refuted theorem -- in a few lines of high-school math. So, given its simplicity, there's some content for you there.

C: As for your well-known "triple of functions":

1. NOTE: I show -- via eqn (3) -- that whatever the functions or even if there are none: Bell's theorem is refuted.

2. Further, wrt (3): are you suggesting -- now the typo is fixed -- that it is false?

3.As requested above: I'd welcome your definition of locality and realism

Thanks; Gordon
.

[gill1109]

Bell argues that local realism implies the existence of functions A, B and rho such that ... Notice, that lambda does not have to be thought of as "located" at the source and then travelling to the measurement locations. Rather, it stands for all the micro-variables throughout the entire experimental set-up which influence the final result. The idea is that God does throw super-dice, but classical ones, in the sense that the classically conceived outcome of the toss of a die is a deterministic function of initial conditions (Newton's laws of mechanics, etc etc). Moreover, "local realism" is about mathematical models of reality, not about reality itself. It's not philosophy. It's physics, or possibly meta-physics. So the realism part of local realism really means "is susceptible to a deterministic description". The local part is self-explanatory, I think. There is a big slightly hidden assumption of freedom and separability, or control: the settings come from outside, and can in principle be anything, and whatever they are chosen to be, is not statistically dependent on lambda. It is all totally uncontroversial and is just the world view of pre-quantum physics.

In order to refute Bell's theorem you have to show that functions A, B and rho, with the desired background properties (the measurement functions take the values +/-1; the probability density rho is nonnegative and integrates to 1), do exist. Bell's theorem seen in this way is a piece of pure mathematics: there are no functions satisfying .... such that ... . To disprove it you must show that they do exist. The fast way to do that is by figuring out what they could be and writing them down. You can even program them and run a computer simulation to prove that you have got something. You will get the Nobel prize since you will have overthrown fifty years of modern physics, and because you can post your programs on internet, and everyone can test them, no establishment conspiracy can stop the news from getting out.

[gill1109]

Your “hypotheses about natural laws” is the assumption that what you want to prove is true. You hypothesise that local realism is true and you hypothesise that Malus’ law is true. On that hypothesis, Bell’s theorem must be false. In ither words, you hypothesise that Bell’s theorem is false. Given your hypothesis, your proof is indeed rather short, and crystal clear. “A and B” is true implies that “not [A and B]” is false.

[Gordon Watson]

Bell argues that local realism implies the existence of functions A, B and rho such that ... Notice, that lambda does not have to be thought of as "located" at the source and then travelling to the measurement locations. Rather, it stands for all the micro-variables throughout the entire experimental set-up which influence the final result. The idea is that God does throw super-dice, but classical ones, in the sense that the classically conceived outcome of the toss of a die is a deterministic function of initial conditions (Newton's laws of mechanics, etc etc). Moreover, "local realism" is about mathematical models of reality, not about reality itself. It's not philosophy. It's physics, or possibly meta-physics. So the realism part of local realism really means "is susceptible to a deterministic description". The local part is self-explanatory, I think. There is a big slightly hidden assumption of freedom and separability, or control: the settings come from outside, and can in principle be anything, and whatever they are chosen to be, is not statistically dependent on lambda. It is all totally uncontroversial and is just the world view of pre-quantum physics.

In order to refute Bell's theorem you have to show that functions A, B and rho, with the desired background properties (the measurement functions take the values +/-1; the probability density rho is nonnegative and integrates to 1), do exist. Bell's theorem seen in this way is a piece of pure mathematics: there are no functions satisfying .... such that ... . To disprove it you must show that they do exist. The fast way to do that is by figuring out what they could be and writing them down. You can even program them and run a computer simulation to prove that you have got something. You will get the Nobel prize since you will have overthrown fifty years of modern physics, and because you can post your programs on internet, and everyone can test them, no establishment conspiracy can stop the news from getting out.

Many thanks Richard, for the clarity.

Now: since I'm here to learn, and (thus) am not be embarrassed or frightened or put off by errors, crudity, polemic, etc., are you satisfied that my "abominable" notation, etc, provides a "sound-enough" basis for our discussion to proceed.

If not, please show how you would like my notation changed. For, noting that I will not be changing my argument: surely we can agree about an adequate notation for starters?

In that way: the basis for my argument will be clear and we can focus on whether my "not-possible" function does the job.

PS: Note that, in analysing EPRB, Aspect, GHZ, I do not use Malus' Law directly. I simply follow his leadership (as I understand it) and conjecture about the related Laws of Nature in the experiments I am studying.

Then, as that old philosopher said: we can now together search for the refutation.

Thus, to be clear: I'm Ok with that: SO LONG as the notation in that 2-page PDF is pre-settled and we waste no more time on that notation.

OK?

For then I'll provide an updated version, with the typo corrected and notation touched-up; and move on ... .

Thanks again; Gordon

[Gordon Watson]

Your “hypotheses about natural laws” is the assumption that what you want to prove is true. You hypothesise that local realism is true and you hypothesise that Malus’ law is true. On that hypothesis, Bell’s theorem must be false. In ither words, you hypothesise that Bell’s theorem is false. Given your hypothesis, your proof is indeed rather short, and crystal clear. “A and B” is true implies that “not [A and B]” is false.

For now, let's not get bogged down here. In short: As an engineer, I take relativistic causality to be true. The rest follows.

BUT PLEASE, as earlier requested, now define the terms "local" and "realism" -- also nonlocality.

Thanks: Gordon

[gill1109]

Your “hypotheses about natural laws” is the assumption that what you want to prove is true. You hypothesise that local realism is true and you hypothesise that Malus’ law is true. On that hypothesis, Bell’s theorem must be false. In ither words, you hypothesise that Bell’s theorem is false. Given your hypothesis, your proof is indeed rather short, and crystal clear. “A and B” is true implies that “not [A and B]” is false.

For now, let's not get bogged down here. In short: As an engineer, I take relativistic causality to be true. The rest follows.

BUT PLEASE, as earlier requested, now define the terms "local" and "realism" -- also nonlocality.

Thanks: Gordon

Sorry, Gordon, this is not getting bogged down. I am not going to define anything for you. You wrote down some math assumptions and definitions and you did some calculus. You wrote down the math hypotheses in your paper. You assumed Malus law and you assumed a math framework copied from Bell. You wrote down Bell’s conclusion: Malus law can’t hold. You say: but I know it does hold. Well, yes, that’s exactly the point Bell was making.

If you build bridges doing math this way, they’ll fall down.

[Gordon Watson]

Your “hypotheses about natural laws” is the assumption that what you want to prove is true. You hypothesise that local realism is true and you hypothesise that Malus’ law is true. On that hypothesis, Bell’s theorem must be false. In ither words, you hypothesise that Bell’s theorem is false. Given your hypothesis, your proof is indeed rather short, and crystal clear. “A and B” is true implies that “not [A and B]” is false.

For now, let's not get bogged down here. In short: As an engineer, I take relativistic causality to be true. The rest follows.

BUT PLEASE, as earlier requested, now define the terms "local" and "realism" -- also nonlocality.

Thanks: Gordon

Sorry, Gordon, this is not getting bogged down. I am not going to define anything for you. You wrote down some math assumptions and definitions and you did some calculus. You wrote down the math hypotheses in your paper. You assumed Malus law and you assumed a math framework copied from Bell. You wrote down Bell’s conclusion: Malus law can’t hold. You say: but I know it does hold. Well, yes, that’s exactly the point Bell was making.

If you build bridges doing math this way, they’ll fall down.

1. I did NOT assume Malus' Law under β; it served heuristically.

2. What does this mean: "You wrote down Bell’s conclusion: Malus law can’t hold. You say: but I know it does hold. Well, yes, that’s exactly the point Bell was making." ??

You seem to be saying that Bell concluded that "Malus law can’t hold" and then you seem to say that "exactly the point Bell was making" was that Malus' Law does hold?

3. To be clear, where do I say this: "You wrote down Bell’s conclusion: Malus law can’t hold."?
...

[gill1109]

Bell was saying that that simple model with A, B and rho with those standard properties cannot generate anything close to Malus’ law.

We do observe Malus’ law in the lab. And it is predicted (I won’t say “explained”) by QM.

Your two page summary is not clear. You do not express things well, I think. You have your own idiosyncratic notations and conventions coming from your education and life long experience as an engineer. We don’t all have the same background as you.

One thing I am pretty sure of, your two pages don’t *prove* anything novel.

[Austin Fearnley]

This thread is interesting as it refers to Malus and Gull. I do not think there is a separate thread on these topics.

1. I am not interested in theoretical proofs of Bell's Theorem. I am glad some people are, but I leave it to them. IMO Bell's Theorem is correct because I cannot get the absolute value of the correlation to be 0.707 and only get 0.5 in a basic simulation using unpolarised beams.

2. I like Gull's simplified approach because that is the kind of simple simulation that I have used. CHSH may be important for real experiments to cut down on bias but I prefer to simulate r=0.707 rather than S=2.8.

3. Failure to simulate r=0.707 tells me that Alice and Bob are not measuring unpolarised beams. (Unpolarised beams are simulated by the random on a sphere method as used by Chantal Roth.) This means that unpolarised beams contain some pairs of particles that would not be generated in nature in a real Bell experiment. And some pairs are not generated when they should be.

3. The quantum Randi challenge tells me that there is not a deterministic formula to calculate a measurement by Alice or Bob. There is a statistical element to the measurement. (I.e. no counterfactual definiteness.)

4. There is a duality between the 2x1 results table in Malus and in the 2x2 results table in a simple Bell experiment. As Malus's Law depends on an incoming polarised beam, this suggests that in a Bell experiment Alice and Bob are measuring polarised beams. This points a finger at hidden communication of some sort.

5. This summarises as: Malus's Law can agree with QM and nature because its beams are polarised. Bells experiment using unpolarised beams would break the Bell Inequalities. Bell's Experiment actually works in nature because the beams are actually polarised. I like the ending of Gull's hand notes as they point to a hidden communication being used in the Bell experiment.

6. This scenario downplays the role of entanglement. It is necessary, but not spooky (nothing is spooky). Polarised beams are the key (and IMO they are not spooky though I cannot prove that).

7. Gull's notes also point at the Wheeler/Feynman idea of advanced and retarded waves. Where the advanced waves are moving backwards in time. This is also related to antiparticles moving backwards in time in Feynman diagrams and in his derivation of QED. Always with the proviso that it is just a mathematical trick as an e- travelling backwards in time is equivalent to an e+ travelling forwards in time. But if an e+ actually was an e- travelling backwards in time then that would completely resolve the Bell experiment's hidden communication route and show why QM can predict the 0.707 correlation. There may be some mathematical equivalence but backwards in time is not the same as forwards in time when it comes to the outcome of a measurement.

8. So, using my own idea of how to generate polarised beams, I have simulated Malus's Law using hidden variables. That is almost identical to solving Bell's experiment using polarised beams and backwards-in-time antiparticles. In doing so I have generated a program which can output beam intensities in a sequence of S-G measurements.

There are unsolved problems in my simulation of course, despite now getting the 0.707 correlation. The biggest IMO is that I can simulate the spin vectors of a polarised beam after a simulated measurement of a beam, but I cannot follow an individual particle through a measurement and know that particular spin vector after measurement. That is because of the measurement problem /or/ the statistical element in the measurement ourcome /or/ the lack of counterfactual definiteness.

Another problem is that I have IMO found, in classical physics, the static spin vector distribution of a polarised beam beam: easily derived via Malus's Law. It is a crescent moon shape (i.e. concavo-convex shape). This crescent shape explains why random-on-a-sphere does not work. But just how much dynamism is there within that shape? Just as the climate is more predictable than the weather. I oddly feel that gyroscopes should be stable, so is there chaos, and how much?

Since the polarised beam works particle at a time, with spaced out events, the whole of the nature of polarisation must be contained within each particle. This suggests that a spin vector cycles through the entire crescent moon distribution and the measurement outcome could depend on any vector. The spin vector of a particle would spend more time pointing at the polarisation vector than at any other vector.

[Gordon Watson]

1. Bell was saying that that simple model with A, B and rho with those standard properties cannot generate anything close to Malus’ law.

2. We do observe Malus’ law in the lab. And it is predicted (I won’t say “explained”) by QM.

3. Your two page summary is not clear. You do not express things well, I think. You have your own idiosyncratic notations and conventions coming from your education and life long experience as an engineer. We don’t all have the same background as you.

4. One thing I am pretty sure of, your two pages don’t *prove* anything novel.

????

Response 1. Using high-school math and notation, I claim to refute BI (and you point to no error); nor consider the consequences: recall that BI was the result that Bell used to prove his theorem (BT).

So is his BI an error and BT still true? No; despite the fact that it uses a standard definition of an expectation. Yet again, using elementary probability theory and notation, I claim to refute BT (and you point to no error).

R2. OK. So do you now see that I use Malus' Law heuristically -- in many experiments -- and my conjectures are not refuted: they are confirmed via QM and experiment. Watson 1, Gill 0.

R3. Taking math to be the best logic, I like math to do the talking. So what is not clear? What is idiosyncratic? Point to an equation or an explanation. Otherwise, how can I ever learn to clarify/simplify elementary math and PT to meet your requirements?

R4. Pretty sure? Bell, (as he said), living on the horns of a dilemma, half-expected some silliness in his work, and was rightly concerned that he may have thrown the baby out with the bath water?

Where to from here?

Gordon

[gill1109]

Gordon, I point to no error, *since I see no proof*. I just see some disconnected remarks, following some elementary and principally notational preliminaries.

How can I point to an error in your claim when you make a claim but do not prove it????? Or you don't even make any claim at all???????

Do you agree that Bell claims that functions A, B and rho do *not* exist [subject to the standard restrictions] which can reproduce the singlet correlations by a formula like:

E(product of outcomes | settings a, b) = int_{lambda in Lambda) rho(lambda) d lambda A(a, lambda) B(b, lambda)

Do you claim that this particular claim of Bell is wrong? Or do you claim something else entirely?

Case 1: you think that functions A, B, rho *do* exist? OK, show us an example of such functions, explicitly.
Case 2: you want to say something else entirely. Well for God's sake, man, make up your mind, and tell us what you think is wrong with Bell's work

[Gordon Watson]

Gordon, I point to no error, *since I see no proof*. I just see some disconnected remarks, following some elementary and principally notational preliminaries.

How can I point to an error in your claim when you make a claim but do not prove it????? Or you don't even make any claim at all???????

Do you agree that Bell claims that functions A, B and rho do *not* exist [subject to the standard restrictions] which can reproduce the singlet correlations by a formula like:

E(product of outcomes | settings a, b) = int_{lambda in Lambda) rho(lambda) d lambda A(a, lambda) B(b, lambda)

Do you claim that this particular claim of Bell is wrong? Or do you claim something else entirely?

Case 1: you think that functions A, B, rho *do* exist? OK, show us an example of such functions, explicitly.
Case 2: you want to say something else entirely. Well for God's sake, man, make up your mind, and tell us what you think is wrong with Bell's work

Richard,

To your questions:

I am endeavouring to remain within the bounds of a 2-page poster:* wherein, taking math to be the best logic, I let my math do the talking.

(If your math differs from mine: show me where and we'll let experiments decide!)

Here are the claims and related math in the current two pages:

1. Bell's 1964 theorem refuted: the math begins with his 1964 theorem and uses elementary PT to refute it.

2. Bell's inequality refuted: the math begins with his inequality and uses high-school math to refute it.

3. Bell's error located: via high-school math.

4. A variation of Bell's 1974 theorem, Bell 1975, will be addressed elsewhere. However, since the math there is similar to that above: I WANT TO NAIL THE ABOVE DOWN before I refute Bell 1975 for you!! Reason: Just as I'm boxing myself in, I need to box you in!

Examples: (1) You're still not clear on the claims that I make!?? (2) You thus excuse yourself for not pointing to errors. (3) You've not yet responded to my request: please define locality and realism; indeed any other terms that you regard as essential if one is to see BT and BI, etc., the way you do!

E(product of outcomes | settings a, b) = int_{lambda in Lambda) rho(lambda) d lambda A(a, lambda) B(b, lambda)

Do you claim that this particular claim of Bell is wrong? Or do you claim something else entirely?

Yes -- me taking it that you are talking about E(a,b) -- and no, respectively.

So, Richard, what do you not understand in -- and/or where do I breach -- elementary PT and high-school math?

* since you already have a heavy-duty background in the Bellian lit.

Gordon

[gill1109]

Gordon, I point to no error, *since I see no proof*. I just see some disconnected remarks, following some elementary and principally notational preliminaries.

How can I point to an error in your claim when you make a claim but do not prove it????? Or you don't even make any claim at all???????

Do you agree that Bell claims that functions A, B and rho do *not* exist [subject to the standard restrictions] which can reproduce the singlet correlations by a formula like:

E(product of outcomes | settings a, b) = int_{lambda in Lambda) rho(lambda) d lambda A(a, lambda) B(b, lambda)

Do you claim that this particular claim of Bell is wrong? Or do you claim something else entirely?

Case 1: you think that functions A, B, rho *do* exist? OK, show us an example of such functions, explicitly.
Case 2: you want to say something else entirely. Well for God's sake, man, make up your mind, and tell us what you think is wrong with Bell's work

Richard,

To your questions:

I am endeavouring to remain within the bounds of a 2-page poster:* wherein, taking math to be the best logic, I let my math do the talking.

(If your math differs from mine: show me where and we'll let experiments decide!)

Here are the claims and related math in the current two pages:

1. Bell's 1964 theorem refuted: the math begins with his 1964 theorem and uses elementary PT to refute it.

2. Bell's inequality refuted: the math begins with his inequality and uses high-school math to refute it.

3. Bell's error located: via high-school math.

4. A variation of Bell's 1974 theorem, Bell 1975, will be addressed elsewhere. However, since the math there is similar to that above: I WANT TO NAIL THE ABOVE DOWN before I refute Bell 1975 for you!! Reason: Just as I'm boxing myself in, I need to box you in!

Examples: (1) You're still not clear on the claims that I make!?? (2) You thus excuse yourself for not pointing to errors. (3) You've not yet responded to my request: please define locality and realism; indeed any other terms that you regard as essential if one is to see BT and BI, etc., the way you do!

E(product of outcomes | settings a, b) = int_{lambda in Lambda) rho(lambda) d lambda A(a, lambda) B(b, lambda)

Do you claim that this particular claim of Bell is wrong? Or do you claim something else entirely?

Yes -- me taking it that you are talking about E(a,b) -- and no, respectively.

So, Richard, what do you not understand in -- and/or where do I breach -- elementary PT and high-school math?

* since you already have a heavy-duty background in the Bellian lit.

Gordon

You breach elementary logic. You say you have proven something, but you have proven nothing, because you fail to exhibit a particular suite of functions which reproduces Malus’ law.

[FrediFizzx]

Ok, this thread is going around in circles. I'm going to lock it if you keep it up.
.

[Gordon Watson]

Gordon, I point to no error, *since I see no proof*. I just see some disconnected remarks, following some elementary and principally notational preliminaries.

How can I point to an error in your claim when you make a claim but do not prove it????? Or you don't even make any claim at all???????

Do you agree that Bell claims that functions A, B and rho do *not* exist [subject to the standard restrictions] which can reproduce the singlet correlations by a formula like:

E(product of outcomes | settings a, b) = int_{lambda in Lambda) rho(lambda) d lambda A(a, lambda) B(b, lambda)

Do you claim that this particular claim of Bell is wrong? Or do you claim something else entirely?

Case 1: you think that functions A, B, rho *do* exist? OK, show us an example of such functions, explicitly.
Case 2: you want to say something else entirely. Well for God's sake, man, make up your mind, and tell us what you think is wrong with Bell's work

Richard,

To your questions:

I am endeavouring to remain within the bounds of a 2-page poster:* wherein, taking math to be the best logic, I let my math do the talking.

(If your math differs from mine: show me where and we'll let experiments decide!)

Here are the claims and related math in the current two pages:

1. Bell's 1964 theorem refuted: the math begins with his 1964 theorem and uses elementary PT to refute it.

2. Bell's inequality refuted: the math begins with his inequality and uses high-school math to refute it.

3. Bell's error located: via high-school math.

4. A variation of Bell's 1974 theorem, Bell 1975, will be addressed elsewhere. However, since the math there is similar to that above: I WANT TO NAIL THE ABOVE DOWN before I refute Bell 1975 for you!! Reason: Just as I'm boxing myself in, I need to box you in!

Examples: (1) You're still not clear on the claims that I make!?? (2) You thus excuse yourself for not pointing to errors. (3) You've not yet responded to my request: please define locality and realism; indeed any other terms that you regard as essential if one is to see BT and BI, etc., the way you do!

E(product of outcomes | settings a, b) = int_{lambda in Lambda) rho(lambda) d lambda A(a, lambda) B(b, lambda)

Do you claim that this particular claim of Bell is wrong? Or do you claim something else entirely?

Yes -- me taking it that you are talking about E(a,b) -- and no, respectively.

So, Richard, what do you not understand in -- and/or where do I breach -- elementary PT and high-school math?

* since you already have a heavy-duty background in the Bellian lit.

Gordon

You breach elementary logic. You say you have proven something, but you have proven nothing, because you fail to exhibit a particular suite of functions which reproduces Malus’ law.

.
Richard, please stop ducking the issue and chickening out!

1. Please read the first line of the Refutation section.

2. My refutation of BT goes through: independent of the functions A and B; which might also be operations.

3. Bell, possibly aware of #2, modified his 1964 theorem in 1975! That's where the suite-of-functions issue arises.

4. That's where Bell walks away from his 1964. You seem to have missed this!?

5. If you would stop ducking the issue and answer my questions: you'll get to see how he walks away in his 1975.

6. You'll also see his new (1975) theorem refuted too.

7. Richard, please answer my questions. My present essay is a 2-page poster -- given that I assumed you to be well-acquainted with the Bellian lit. I want to use it as the preamble to another 2-page poster:

Bell’s 1975 theorem refuted via elementary probability theory!

Gordon

[gill1109]

I have answered your questions. You are ducking the issue which I raised. You did not refute BT. Try to convince someone else, someone who can rewrite your argument and let them have another try at converting me.

If you are right, this will happen eventually. I’m in no hurry and I see no point in putting more energy into this. We are in a loop. It was fun for a while but now it’s just annoying.

[Gordon Watson]

I have answered your questions. You are ducking the issue which I raised. You did not refute BT. Try to convince someone else, someone who can rewrite your argument and let them have another try at converting me.

If you are right, this will happen eventually. I’m in no hurry and I see no point in putting more energy into this. We are in a loop. It was fun for a while but now it’s just annoying.

Richard,

1.The issue that you raise stems from Bell (1975).

Of course I've addressed it: but I wanted to avoid further polemics and games, like you seem to enjoy.

We are in an annoying loop of your making: you have NOT answered my questions.

Examples: Where in Bell (1964) does your issue arise?

Where are the errors in my use of PT?

Ditto ... high-school math?

What are the links that you can't follow?

Where are your definitions of key bellian terms; like locality and realism?

2. Correction: TYPO 2 posts above; should read. "A variation of Bell's 1964 [-- not 1974 -- ] theorem, Bell 1975 ..."

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?

[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.
.