## Pedagogical proofs of Bell's theorem

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### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:
Heinera wrote:
FrediFizzx wrote:What more does one need to know other than it is mathematically impossible for anything to exceed the inequalities! You Bell fans always choke on that simple fact.
.

So, what inequality do you think applies to the CHSH urn experiment?

There is no such thing as a "CHSH urn experiment."

Moreover, Bell's so-called "theorem" is nothing but a statistical swindle.

What else do the Bell fanatics have to do now other than talk about irrelevant junk now that they are all shot down?
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### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:
Heinera wrote:
FrediFizzx wrote:What more does one need to know other than it is mathematically impossible for anything to exceed the inequalities! You Bell fans always choke on that simple fact.
.

So, what inequality do you think applies to the CHSH urn experiment?

There is no such thing as a "CHSH urn experiment."

Moreover, Bell's so-called "theorem" is nothing but a statistical swindle.

Boole’s three correlation theorem is a swindle!? (Necessity and sufficiency of Bell’s three correlations inequalities). And Fine’s four correlations theorem? (Necessity and sufficiency of CHSH inequalities).

Of course there a CHSH urn experiment. Put eight slips of paper in an urn. Pick one at random. Toss two fair coins. The coins determine Alice and Bob’s setting 1 or setting 2. Call them a and b.

Each slip of paper has four numbers +/-1 written on it. Call them: x1, x2, y1, y2. Report outcomes: xa, yb.

Return slip of paper to urn, repeat…

This thought experiment can be performed in a classroom. It can be simulated on a computer. It can be studied mathematically using standard tools from probability theory and mathematical statistics.

Here are the eight slips of paper, using “0” and “1” to stand for “-1” and “+1” respectively:

"0000"
"0100"
"0110"
"1110"
"0001"
"1001"
"1011"
"1111"

Of course, you can fill the urn in other ways; and you can choose settings using biased coins or even correlated coins, if you like. The special “eight slip” urn I mentioned will give three correlations of +0.5 and one of -0.5, so a value of “S” of 2. In the limit of large N.

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:
FrediFizzx wrote:What more does one need to know other than it is mathematically impossible for anything to exceed the inequalities! You Bell fans always choke on that simple fact.
.

So, what inequality do you think applies to the CHSH urn experiment?

There is no such thing as a "CHSH urn experiment."

Moreover, Bell's so-called "theorem" is nothing but a statistical swindle.
.

### Re: Pedagogical proofs of Bell's theorem

FrediFizzx wrote:What more does one need to know other than it is mathematically impossible for anything to exceed the inequalities! You Bell fans always choke on that simple fact.
.

So, what inequality do you think applies to the CHSH urn experiment?

### Re: Pedagogical proofs of Bell's theorem

gill1109 wrote:
FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:@Heine It is up to you to find it.
.

Indeed, because you can't.

Actually, not at all interested in this irrelevant junk.

But you keep reacting to it!

Let’s get back on topic, folks. There are strictly mathematical results called, for better or for worse, Bell’s theorem. Some people say it should be called Boole’s theorem. Indeed, you can find it in his book from the 1850’s. It is legitimate to look for more pedagogical proofs than, say, Boole’s or Bell’s.

What more does one need to know other than it is mathematically impossible for anything to exceed the inequalities! You Bell fans always choke on that simple fact. It's irrelevant junk.
.

### Re: Pedagogical proofs of Bell's theorem

FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:@Heine It is up to you to find it.
.

Indeed, because you can't.

Actually, not at all interested in this irrelevant junk.

But you keep reacting to it!

Let’s get back on topic, folks. There are strictly mathematical results called, for better or for worse, Bell’s theorem. Some people say it should be called Boole’s theorem. Indeed, you can find it in his book from the 1850’s. It is legitimate to look for more pedagogical proofs than, say, Boole’s or Bell’s.

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:
FrediFizzx wrote:@Heine It is up to you to find it.
.

Indeed, because you can't.

Actually, not at all interested in this irrelevant junk.
.

### Re: Pedagogical proofs of Bell's theorem

FrediFizzx wrote:@Heine It is up to you to find it.
.

Indeed, because you can't.

### Re: Pedagogical proofs of Bell's theorem

@Heine It is up to you to find it.
.

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:FrediFizzx claims to have found a logical error in my first post, but refuses to tell us what it is.
FrediFizzx wrote:I don't think I ever claim that. I said this junk is irrelevant! Since Bell and Gill are shot down to pieces!
.

Well...
FrediFizzx wrote:It is all irrelevant since Joy shot it down in 2007. There is a flaw in your argument. It is up to you to find it. Time to get more up to date.
.

So, what's the flaw?

### Re: Pedagogical proofs of Bell's theorem

FrediFizzx wrote:
gill1109 wrote:
Heinera wrote:Let's me just summarize the discussion so far:
Joy disagrees with everything in the first post in this thread. He has not said anything about whether he believes the statistical long term upper bound of 2 will hold.
minkwe complains there is only one urn. Doesn't matter, since the upper bound will hold no matter how many urns you have, as long as you pick the urn independently of Alice and Bob's coin tosses.
FrediFizzx claims to have found a logical error in my first post, but refuses to tell us what it is.

I don't think I ever claim that. I said this junk is irrelevant! Since Bell and Gill are shot down to pieces!
Heinera wrote:Anything more that could be added?

gill1109 wrote:Joy has said that he's a physicist and couldn't care less about mathematics. His formulas are pictures, representing his physics dreams. FrediFizzx just keeps growing his spaghetti code which draws a negative cosine in ever more complicated ways. Michel's mind is made up; he's not going to study anybody's mathematics or look at anybody else's computer code, since he *knows* in advance that it will be bad physics. What these guys have in common is that they know from looking at Bell (1964) that Bell was wrong and they certainly aren't going to waste any of their time looking at works of Bell, or works of followers of Bell, which came later.
It's interesting that many Bell-deniers have a strong background in chemistry or (molecular)-biology or engineering, rather than in hardcore physics. I think this is correlated with a weaker mathematical background.

And then we have more rambling almost nonsense from the master nonsense maker.

You are right to call my ramblings "almost nonsense". They contain pearls of wisdom, one cannot expect everyone to appreciate them.

You said "I said this junk is irrelevant! Since Bell and Gill are shot down to pieces!" As you know, I believe that that's where you are completely wrong.

### Re: Pedagogical proofs of Bell's theorem

gill1109 wrote:
Heinera wrote:Let's me just summarize the discussion so far:

Joy disagrees with everything in the first post in this thread. He has not said anything about whether he believes the statistical long term upper bound of 2 will hold.

minkwe complains there is only one urn. Doesn't matter, since the upper bound will hold no matter how many urns you have, as long as you pick the urn independently of Alice and Bob's coin tosses.

FrediFizzx claims to have found a logical error in my first post, but refuses to tell us what it is.

I don't think I ever claim that. I said this junk is irrelevant! Since Bell and Gill are shot down to pieces!

Heinera wrote:Anything more that could be added?

gill1109 wrote:Joy has said that he's a physicist and couldn't care less about mathematics. His formulas are pictures, representing his physics dreams. FrediFizzx just keeps growing his spaghetti code which draws a negative cosine in ever more complicated ways. Michel's mind is made up; he's not going to study anybody's mathematics or look at anybody else's computer code, since he *knows* in advance that it will be bad physics. What these guys have in common is that they know from looking at Bell (1964) that Bell was wrong and they certainly aren't going to waste any of their time looking at works of Bell, or works of followers of Bell, which came later.

It's interesting that many Bell-deniers have a strong background in chemistry or (molecular)-biology or engineering, rather than in hardcore physics. I think this is correlated with a weaker mathematical background.

And then we have more rambling almost nonsense from the master nonsense maker.
.

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:Let's me just summarize the discussion so far:

Joy disagrees with everything in the first post in this thread. He has not said anything about whether he believes the statistical long term upper bound of 2 will hold.

minkwe complains there is only one urn. Doesn't matter, since the upper bound will hold no matter how many urns you have, as long as you pick the urn independently of Alice and Bob's coin tosses.

FrediFizzx claims to have found a logical error in my first post, but refuses to tell us what it is.

Anything more that could be added?

Joy has said that he's a physicist and couldn't care less about mathematics. His formulas are pictures, representing his physics dreams. FrediFizzx just keeps growing his spaghetti code which draws a negative cosine in ever more complicated ways. Michel's mind is made up; he's not going to study anybody's mathematics or look at anybody else's computer code, since he *knows* in advance that it will be bad physics. What these guys have in common is that they know from looking at Bell (1964) that Bell was wrong and they certainly aren't going to waste any of their time looking at works of Bell, or works of followers of Bell, which came later.

It's interesting that many Bell-deniers have a strong background in chemistry or (molecular)-biology or engineering, rather than in hardcore physics. I think this is correlated with a weaker mathematical background.

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:Let's me just summarize the discussion so far:

Joy disagrees with everything in the first post in this thread. He has not said anything about whether he believes the statistical long term upper bound of 2 will hold.

minkwe complains there is only one urn. Doesn't matter, since the upper bound will hold no matter how many urns you have, as long as you pick the urn independently of Alice and Bob's coin tosses.

FrediFizzx claims to have found a logical error in my first post, but refuses to tell us what it is.

Anything more that could be added?

Oh sure..., That you Bell fanatics are finished and don't even know it.

Perhaps I should explain how the analytical definitions from the paper match up with the code? Sure, might as well. But I believe it is already explained in the paper. Here is the current version of the quaternion version of the code.

https://www.wolframcloud.com/obj/fredif ... -forum3.nb
EPRsims/newCS-15-S3quat-prodcalc-forum3.pdf

And a link to the paper.

http://dx.doi.org/10.13140/RG.2.2.28311.91047/2

So, in the paper we have the main equations (13) and (20) which may be a little confusing at first until you go thru the other definitions. Think of just one event. Then A and B will just be equal to 1 of the 3 possibilities. The other 2 possibilities at that time will be "no result". This in the code here,

outA=Sort[Catenate[{listA4,outA2,listA6}],#1[[3]]<#2[[3]]&]; (*Combine lists and sort*) (completely local)
outB=Sort[Catenate[{listB4,outB2,listB6}],#1[[3]]<#2[[3]]&]; (*Combine lists and sort*)

Next we have the definitions that correspond to the code. For A1, A2, B1 and B2. The code is this,

outA1=Select[outAa,MemberQ[#,g1]&]; (*Split outAa into outA1 and outA2*)(completely local)
outA2=Select[outAa,MemberQ[#,f1]&];
outB1=Select[outBb,MemberQ[#,g2]&]; (*Split outBb into outB1 and outB2*)(completely local)
outB2=Select[outBb,MemberQ[#,f2]&];

What they do is separate the events for pre-result outAa and outBb into A1 and B1 events that are greater than the HV process and for A2 and B2, events that are less than the HV process. Exactly like it says in the paper for eqs. (14), (15), (21) and (22). Next in the paper we have A3 and B3 eqs. (16) and (23). The code for that is,

listB3=Select[outB1,Intersection[{#[[3]]},listbd3]!={#[[3]]}&];

And easy to see that it is for events from outA1 and outB1 that don't match via trial numbers via outA4 and outB4. Then of course we have A4 and B4 from eqs. (17) and (24) for which the code is,

listA4=Select[outA1,Intersection[{#[[3]]},list23]=={#[[3]]}&]; (completely local)
listB4=Select[outB1,Intersection[{#[[3]]},list13]=={#[[3]]}&];

Also easy to see that it is for events from outA1 and outB1 where the trial numbers do match. Perhaps we should reverse n3 and n4 to make the flow better in the paper. Then we have A5 and B5 in the paper eqs. (18) and (25) for which the code is,

$\text{A5}=\text{\lambda 2}[[i]] \text{sgn}(\xi +\text{qa}[[4]]);$ (completely local)
$\text{B5}=-\text{\lambda 2}[[i]] \text{sgn}(\xi +\text{qb}[[4]]);$

I should mention here that A5 and B5 are recorded as the 5th element for every event in the tables for the A and B sides. And these are for use in A6 and B6 eqs. (19) and (26). Which in the code are,

Do[If[listA3[[i]][[2]]==listA3[[i]][[5]],qaaq[[i]]=1,qaaq[[i]]=Re[listA36[[i]]**listA37[[i]]]];
listA6[[i]]={listA3[[i]][[1]],qaaq[[i]]*listA3[[i]][[2]],listA3[[i]][[3]],listA3[[i]][[4]],listA3[[i]][[5]],listA3[[i]][[6]],listA3[[i]][[7]]}, {i, M}](completely local)
Do[If[listB3[[i]][[2]]==listB3[[i]][[5]],qbbq[[i]]=1,qbbq[[i]]=Re[listB36[[i]]**listB37[[i]]]];
listB6[[i]]={listB3[[i]][[1]],qbbq[[i]]*listB3[[i]][[2]],listB3[[i]][[3]],listB3[[i]][[4]],listB3[[i]][[5]],listB3[[i]][[6]],listB3[[i]][[7]]}, {i, M2}](completely local)

Yep, those two are doozies but you can see the spinorial sign changes here qaaq[[i]]*listA3[[i]][[2]] and here qbbq[[i]]*listB3[[i]][[2]]. So, "emulates" comes out of the paper description. Ok, I think that is it. Questions?
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### Re: Pedagogical proofs of Bell's theorem

Let's me just summarize the discussion so far:

Joy disagrees with everything in the first post in this thread. He has not said anything about whether he believes the statistical long term upper bound of 2 will hold.

minkwe complains there is only one urn. Doesn't matter, since the upper bound will hold no matter how many urns you have, as long as you pick the urn independently of Alice and Bob's coin tosses.

FrediFizzx claims to have found a logical error in my first post, but refuses to tell us what it is.

Anything more that could be added?

### Re: Pedagogical proofs of Bell's theorem

gill1109 wrote:
FrediFizzx wrote:It's not sad, it is an irrelevant piece of junk.

Don’t insult Michel!

Yeah, right. I was talking about this whole thread by Heine is an irrelevant piece of junk since Bell's junk physics theory is shot down and Gill's junk theory is now shot down.
.

### Re: Pedagogical proofs of Bell's theorem

FrediFizzx wrote:It's not sad, it is an irrelevant piece of junk.

Don’t insult Michel!

### Re: Pedagogical proofs of Bell's theorem

It's not sad, it is an irrelevant piece of junk.
.

### Re: Pedagogical proofs of Bell's theorem

minkwe wrote:
gill1109 wrote:Michel, what do you mean by “independent”?
Are you using the word in its sense in elementary calculus, or in its sense in elementary statistics and probability?

Now you are pretending you don't know what I mean. I'm not interested in anything to do with settings or particles. Your proof has no settings or particles. It's just a mathematical tautology involving ONLY outcomes.

Each X, Y in your proof can be considered as the outcome of a coin toss. I already told you this previously and you decided to dodge. In that case, how many independent coin tosses are involved in Z? And how many independent coin tosses are involved in the Bell test experiment. This is exactly the same question and you understand it perfectly.

Simple answer: There are 4 independent coin tosses ($X_1,X_2,X_3,X_4$) in your proof
Simple answer: There are 8 independent coin tosses in a Bell test Experiment $X^1_1, Y^1_1, X^2_1, Y^2_2, X^3_2, Y^3_1, X^4_2, Y^4_2$ no need to play word games.

There is no such thing as a CHSH urn experiment.