## Why the upper bound on CHSH is 2\/2 and not 4 ?

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Re: Why the upper bound on CHSH is 2\/2 and not 4 ?

Gordon Watson wrote:When I first saw the heading for this thread I was going to suggest (as I now do) that it be changed to: Why the EXPERIMENTAL upper bound on CHSH is 2√2 and not 4?

Although I see where you are coming from, and although I agree with Michel's classification above, I disagree with your suggestion. The title is fine just as it is. By CHSH I simply mean the string of four expectation values. I have a theoretical model that analytically gives the bound of $2\sqrt{2}$ on the string of four expectation values. See, for example, Eq. (5) of this paper. This theoretical bound is more generally referred to as Tsirel’son's bound, and that is what I have in mind in the title of this thread. In short, as Fred also indicates, $2\sqrt{2}$ is not just an experimental bound. It is also a theoretical bound (more precisely, it is a physical bound).
Joy Christian
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### Re: Why the upper bound on CHSH is 2\/2 and not 4 ?

minkwe wrote:You should understand the difference between intended meaning and actual meaning. There is no doubt that the intended meaning is what you say. But it is also evident that the actual meaning is what I say.

The intended meaning is the only meaning there is. If a definition says something else then there is an error in the definition, which can be detected by comparison to the actual use of the term.

It doesn't make sense to use two different definitions of the CHSH, in order to give the false impression that their intended meaning matches their actual meaning.

Use of different meanings can be confusing, but you cant help that with introduction of one more.
Mikko

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### Re: Why the upper bound on CHSH is 2\/2 and not 4 ?

Mikko wrote:The intended meaning is the only meaning there is.

That may be true in politics or gossip but not in mathematics, where the actual meaning is the only meaning. That many have not yet discerned the difference between the two meanings does not change this fact. And that you continue to ignore the gulf between the two meanings does not make it disappear, it just shows that you too are making the subtle error Bell and the authors of CHSH made.

If a definition says something else then there is an error in the definition, which can be detected by comparison to the actual use of the term.

There is no error in the definitions. The error is simply failing to discern the difference between, the actual meaning implied by the algebra, and the meanings of the other similar looking expressions. Too bad you don't see it yet. I've given a few articles above to help you see it, there are whole threads here dedicated to helping people see it, for example this one.viewtopic.php?f=6&t=181#p4923

Use of different meanings can be confusing, but you cant help that with introduction of one more.

I haven't introduced anything. Bell did by calculating a different expression from QM than the expression he had just derived. Almost everyone since sheepishly repeats the error. Now it is rich of you to accuse me of introducing a new definition when all I've done is identify the different expressions the authors are confused about. Are you denying that the expressions have different meanings, or are you denying that the authors use them interchangeably as if they had the same meaning? You have to pick just one, though both positions are demonstrably false. What's your pleasure?
minkwe

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### Re: Why the upper bound on CHSH is 2\/2 and not 4 ?

Gordon, Joy,
Please the distinction between experimental and theoretical bounds is a red herring. All the bounds are theoretical. And you can do experiments strictly adherring to the meaning of each expression, and even then, you will never obtain a violation. The idea that an experiment would have a different upper bound than a theory is wrongheaded. You look at the experimental expression and decide what it's upper bound should be, or you look at the theoretical expression and decide precisely what experiment to do. If your results don't agree, then an error has been made. You can't look at an experimental expression and compare it to a theoretical expression with a different meaning.

Fred,
I don't think you can say "mainstream" CHSH. The problem is that according to the mainstream, all those expressions are one and the same expression. That is why they are still confused when they derive a limit of 2 and measure 2 root 2. They do not yet appreciate that they measured something different. They like mysticism so they project their ignorance to spookiness in nature.
minkwe

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### Re: Why the upper bound on CHSH is 2\/2 and not 4 ?

minkwe wrote:And you can do experiments strictly adherring to the meaning of each expression,

That is not how experiments are performed. Experiments seek to find out facts. Meanings are irrelevant. First something is done and some results are recorded. Then some numbers are computed from the observations. These observations and computed numbers are facts. In order to compare with a theory, you must describe the experiment as actually performed in a way that the theory can be applied. The relevant meanings come from experiment, not from definitions.
Mikko

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### Re: Why the upper bound on CHSH is 2\/2 and not 4 ?

FrediFizzx wrote:Ok, here it is.
Code: Select all
//Adaptation of Albert Jan Wonnink's original code//http://challengingbell.blogspot.com/2015/03/numerical-validation-of-vanishing-of.htmlfunction getRandomLambda() {     if( rand()>0.5) {return 1;} else {return -1;}}batch test(){     set_window_title("Test of Joy Christian's CHSH derivation");     N=20000; //number of iterations (trials)     I=e1^e2^e3;     s=0;     a1=sin(0)*e1 + cos(0)*e2 + 0.000*e3;     b1=sin(pi/4)*e1 + cos(pi/4)*e2 + 0.000*e3;     a2=sin(pi/2)*e1 + cos(pi/2)*e2 + 0.000*e3;     b2=sin(3*pi/4)*e1 + cos(3*pi/4)*e2 + 0.000*e3;     for(nn=0;nn<N;nn=nn+1) //perform the experiment N times     {          lambda=getRandomLambda(); //lambda is a fair coin                                                 //resulting in +1 or -1          mu=lambda * I;  //calculate the lambda dependent mu          C1=-I.a1;  //C = {-a_j B_j}          D1=I.b1;   //D = {b_k B_k}          C2=-I.a2;  //C = {-a_j B_j}          D2=I.b2;   //D = {b_k B_k}          E1=mu.a1;  //E = {a_k B_k(L)}          F1=mu.b1;  //F = {b_j B_j(L)}          A1=C1 E1;  //eq. (1) of arXiv:1103.1879, A(a, L) = {-a_j B_j}{a_k B_k(L)}           B1=F1 D1;  //eq. (2) of arXiv:1103.1879, B(b, L) = {b_j B_j(L)}{b_k B_k}          E2=mu.a2;  //E = {a_k B_k(L)}          F2=mu.b2;  //F = {b_j B_j(L)}          A2=C2 E2;  //eq. (1) of arXiv:1103.1879, A(a, L) = {-a_j B_j}{a_k B_k(L)}           B2=F2 D2;  //eq. (2) of arXiv:1103.1879, B(b, L) = {b_j B_j(L)}{b_k B_k}          q=0;          if(lambda==1) {q=((-C1) (A1 B1) (-D1))-((-C1) (A1 B2) (-D2))+((-C2) (A2 B1) (-D1))+((-C2) (A2 B2) (-D2));}           else {q=((-D1) (B1 A1) (-C1))-((-D2) (B2 A1) (-C1))+((-D1) (B1 A2) (-C2))+((-D2) (B2 A2) (-C2));}          s=s+q;     }     Joy_CHSH=abs(s/N);     print(Joy_CHSH, "f");      prompt();}

And the result is,

Joy_CHSH = 2.828427

So it comes out the same as taking the shortcut.

Fred, your revised correlation plot on the other thread does not seem to be using scalar outcomes --- I mean this one: viewtopic.php?f=6&t=200&p=5550#p5514.

Is it possible to use scalar outcomes as above for the correlation plot? It should be possible, it seems.
Joy Christian
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### Re: Why the upper bound on CHSH is 2\/2 and not 4 ?

Mikko wrote:Experiments seek to find out facts. Meanings are irrelevant.
... [blah blah blah ] ...
The relevant meanings come from experiment

You should review Adenier's paper: http://arxiv.org/abs/quant-ph/0006014
Adenier wrote:Bell's Theorem was developed on the basis of considerations involving a linear combination of spin correlation functions, each of which has a distinct pair of arguments. The simultaneous presence of these different pairs of arguments in the same equation can be understood in two radically different ways: either as strongly objective,' that is, all correlation functions pertain to the same set of particle pairs, or as weakly objective,' that is, each correlation function pertains to a different set of particle pairs.
It is demonstrated that once this meaning is determined, no discrepancy appears between local realistic theories and quantum mechanics: the discrepancy in Bell's Theorem is due only to a meaningless comparison between a local realistic inequality written within the strongly objective interpretation (thus relevant to a single set of particle pairs) and a quantum mechanical prediction derived from a weakly objective interpretation (thus relevant to several different sets of particle pairs).

And my previous discussion with a fellow named Richard Gill, in which he stumbled on the same question:
viewtopic.php?f=6&t=63&hilit=Strongly+objective#p2632
minkwe

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### Re: Why the upper bound on CHSH is 2\/2 and not 4 ?

Joy Christian wrote:
FrediFizzx wrote:And the result is,

Joy_CHSH = 2.828427

So it comes out the same as taking the shortcut.

Fred, your revised correlation plot on the other thread does not seem to be using scalar outcomes --- I mean this one: viewtopic.php?f=6&t=200&p=5550#p5514.

Is it possible to use scalar outcomes as above for the correlation plot? It should be possible, it seems.

Albert Jan used the shortcut for that simulation also. It should work also with the full formulation.
FrediFizzx
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