minkwe's challenge

[Heinera]

Heinera,
Both you and Richard claim QM/non-locality/non-realism/statistical error can violate the above theorem but LHV can not. The challenge quite simply is to produce the non-local/non-real/statistical dataset which demonstrates the violation. Richard claims to have written the simulation, we will see if it holds up. We will calculate delta from his dataset, and obtain the appropriate upper bound using his theorem. Hopefully for Richard, his claim will hold up because all his papers and claims are at stake.

Ok, so let us try this again: I can produce a non-local hidden variable model that beats the CHSH inequality by a safe margin; in fact it gives the same value for the inequality as QM does. It uses no data rejection, no loopholes.

And furthermore, all the four correlations can be computed on the same set of hidden variables. No disjoint sets.

Would that be of interest?

Please proceed. We will use Richard's LG theorem to calculate the appropriate bound and we will see if your non-local model holds up. If it is calculated on the same set then delta will be zero and the upper bound will be 2. But no need to explain just provide the dataset and we'll see.

Here is the model:

http://rpubs.com/heinera/16727

It is a simple non-local HV model without data rejection of any kind; no loopholes. It beats the CHSH inequality with a safe margin, even when all four correlations are computed on the same set of hidden variables.

Hopefully this example will make you realise that the CHSH inequality only applies to LHV models.

[minkwe]

Here is the model:

http://rpubs.com/heinera/16727

It is a simple non-local HV model without data rejection of any kind; no loopholes. It beats the CHSH inequality with a safe margin, even when all four correlations are computed on the same set of hidden variables.

Hopefully this example will make you realise that the CHSH inequality only applies to LHV models.

Heinera,
I don't think you understand what the challenge is all about to begin with, or you seem not to have earned anything from this thread (viewtopic.php?f=6&t=39). You are calculating an expression of the form

S= <a1b1> + <a2b2> - <a3b3> - <a4b4>

with 4 different pairs of outcomes. The "a" in "<a1b1>" is completely different from the "a" in "<a2b2>". So you need to go back and study that thread, to find out what the appropriate upper bound of that expression is. You can ask Richard, if you do not know.

Here is your simulation translated to python, for those interested. I've added one additional calculation of S at the bottom to show you what your model produces for a joint case:

Code: Select all

import numpy
M = 1e6
t = numpy.random.uniform(-1, 1, M)

def obs(a, b, hv):
    s = numpy.sign(hv)
    hv = numpy.abs(hv)
    L = (1 + (a*b).sum())/4
    o = numpy.ones_like(s)
    o[hv < L + 0.5] = -1
    o[hv < 2*L] = -s[hv < 2*L]
    o[hv < L] = s[hv < L]
    return o

def outcomes(alpha, beta, t):
    alpha = numpy.radians(alpha)
    beta =  numpy.radians(beta)
    a = numpy.array([numpy.cos(alpha), numpy.sin(alpha)])
    b = numpy.array([numpy.cos(beta), numpy.sin(beta)])
    ca = obs(a, b,  t)
    cb = obs(a, b, -t)
    return ca, cb
   

ca1, cb1 = outcomes(0,45, t)
ca2, cb2 = outcomes(0,135, t)
ca3, cb3 = outcomes(90,45, t)
ca4, cb4 = outcomes(90,135, t)

print "DISJOINT (delta=0): S<=4, S=", -(ca1*cb1).mean() + (ca2*cb2).mean() - (ca3*cb3).mean() - (ca4*cb4).mean()
print "JOINT (delta=1): S<=2, S=",  -(ca1*cb1).mean() + (ca1*cb2).mean() - (ca3*cb1).mean() - (ca3*cb2).mean()

output:

Code: Select all

DISJOINT: S<=4, S= 2.829348
JOINT: S<=2, S= 1.414512

Hopefully, this example will make you finally understand that expressions such as the CHSH are universally valid and can never be violated by anything (unless a mathematical error is made), not even non-local models like yours. Or maybe you want to have another try at a different model?

[gill1109]

I don't understand the problem. A true mathematical theorem is a tautology.

I suggest we forget altogether about inequalities. Let's talk instead of the relation between theory and experiment (including computer experiments). I'm afraid that probability and statistics then enter. If people don't want to know about either, then they'll find it hard to contribute to a meaningful discussion.

[Heinera]

But this line is completely meaningless:

Code: Select all

print "JOINT (delta=1): S<=2, S=",  -(ca1*cb1).mean() + (ca1*cb2).mean() - (ca3*cb1).mean() - (ca3*cb2).mean()

You are just throwing together observations in a way that is nowhere to be found in the model.

[minkwe]

I don't understand the problem. A true mathematical theorem is a tautology.

I suggest we forget altogether about inequalities. Let's talk instead of the relation between theory and experiment (including computer experiments). I'm afraid that probability and statistics then enter. If people don't want to know about either, then they'll find it hard to contribute to a meaningful discussion.

Richard, if you want to understand finally what you've been missing, look closely at the above result and ask yourself, why the two outcomes in the last two statements are different.

[minkwe]

But this line is completely meaningless:

Code: Select all

print "JOINT (delta=1): S<=2, S=",  -(ca1*cb1).mean() + (ca1*cb2).mean() - (ca3*cb1).mean() - (ca3*cb2).mean()

You are just throwing together observations in a way that is nowhere to be found in the model.

Exactly, Heine! You are finally getting it. This is exactly what you are doing when you compare the CHSH with upper bound of 2 to any experiments or to QM!!!!!! Completely meaningless nonsense, that is why expressions of the form you are using have a different upper bound from 2, because unless you are calculating nonsense, you won't suggest that the upper bound should be 2. You just answered the question I asked Richard above.

[Heinera]

But this line is completely meaningless:

Code: Select all

print "JOINT (delta=1): S<=2, S=",  -(ca1*cb1).mean() + (ca1*cb2).mean() - (ca3*cb1).mean() - (ca3*cb2).mean()

You are just throwing together observations in a way that is nowhere to be found in the model.

Exactly, Heine! You are finally getting it. This is exactly what you are doing when you compare the CHSH with upper bound of 2 to any experiments or to QM!!!!!! Completely meaningless nonsense, that is why expressions of the form you are using have a different upper bound from 2, because unless you are calculating nonsense, you won't suggest that the upper bound should be 2. You just answered the question I asked Richard above.

Njaa, we are not excactly in agrement at the moment
(a) Do you agree that the NLHV model blew the CHSH inequality the way it was computed in the model?
(b) Would you venture to construct a LHV model that violates the same inequality, with the inequality computed in the same way as in my model? (and no data rejection, please)

After all, you argue that there is no difference between LHV models and other models regarding CHSH.

[minkwe]

Njaa, we are not excactly in agrement at the moment
(a) Do you agree that the NLHV model blew the CHSH inequality the way it was computed in the model?

Nope. The appropriate CHSH inequality for the model is S <= 4, you got S = 2.83, it blew it in the wrong direction. Now go read that thread I pointed you to if you do not understand this yet.

(b) Would you venture to construct a LHV model that violates the same inequality, with the inequality computed in the same way as in my model?

I already told you umpteen times that inequalities like the CHSH can not be violated by anything whatsoever, if you are doing a proper mathematical calculation as opposed to nonsense. However if you are allowed to compare apples with oranges (like you keep doing) I can easily write a LHV model which violates an inappropriate upper bound.

After all, you argue that there is no difference between LHV models and other models regarding CHSH.

Yep, I argue that if you are comparing oranges to oranges, and apples to apples, NOTHING WHATSOEVER can violate the appropriate bound.

[Heinera]

Someone is comparing apples to oranges, right:

Code: Select all

print "JOINT (delta=1): S<=2, S=",  -(ca1*cb1).mean() + (ca1*cb2).mean() - (ca3*cb1).mean() - (ca3*cb2).mean()

[minkwe]

Someone is comparing apples to oranges, right:

Code: Select all

print "JOINT (delta=1): S<=2, S=",  -(ca1*cb1).mean() + (ca1*cb2).mean() - (ca3*cb1).mean() - (ca3*cb2).mean()

Yep! That was the point. I'm glad you agree.

[Heinera]

(b) Would you venture to construct a LHV model that violates the same inequality, with the inequality computed in the same way as in my model?

I already told you umpteen times that inequalities like the CHSH can not be violated by anything whatsoever, if you are doing a proper mathematical calculation as opposed to nonsense. However if you are allowed to compare apples with oranges (like you keep doing) I can easily write a LHV model which violates an inappropriate upper bound.

If 2 is inappropriate enough for you, get going! Beat it! By a solid margin!

(no data rejection like the last time, please)

[minkwe]

If 2 is inappropriate enough for you, get going! Beat it! By a solid margin!

I already did but you were sleeping. Twice.

(no data rejection like the last time, please)

Why? Because you said so? Bell believers, like you think they can unilaterally make non-physical requirements and everyone is just supposed to toe the line under the threat of "loophole". I asked and you never answered where you got the idea that non-detection/data rejection was forbidden even though QM does not forbid it? What physical basis allows you to demand that? No answer.

I already asked you how you can know that a particle was emitted but never detected without using non-local information, and you never answered.

Until you can answer these questions, you will continue deluding yourself that QM/non-locality/non-realism violates a mathematical tautology.

http://vixra.org/pdf/1305.0129v1.pdf
Highly recommended paper

The inequalities (17) are purely mathematical. In particular, their proof depends in absolutely no way on anything else, except the mathematical properties of the set Z of positive and negative integers, set seen as a linearly ordered ring, [9].

As for the inequalities (16), they are a direct mathematical consequence of the inequalities (17), and thus again, their proof depends in absolutely no way on anything else, except the mathematical properties of the set R of real numbers, set seen as a linearly ordered eld, [9].

It is, therefore, bordering on the amusing tinted with the ridiculous, when any sort of so called "physical" meaning or arguments are enforced upon these inequalities - be it regarding their proof, or their connections with issues such as realism and locality in physics - and are so enforced due to a mixture of lack of understanding of rather elementary and quite obviously simple mathematics, to which is added an irresistible tendency among physicists to use their "infallible physical intuition" in absolutely every realm possible ...

In this regard, it is one of the major merits of DRHM to have pointed out clearly and repeatedly, even if in terms less hard than above, the essential and so far hardly known fact that the EBBI inequalities such as (17) simply cannot be violated either by classical, or by quantum physics. And they cannot be violated, precisely due to the fact that they only depend on mathematics, and of course, logic.

As a consequence, since as seen later, the EBBI contain as particular cases the Bell inequalities, these inequalities cannot be violated by classical or quantum physics. Therefore, the Bell inequalities turn out to be irrelevant to physics, be it classical or quantum, for that matter.

[gill1109]

Pythagoras theorem is completely irrelevant to physics. When we measure the sides of right angled triangles on the Earth, whether or not a^2 + b^2 >= c^2 has got absolutely nothing to do with whether the Earth is flat or round. The inequality a^2 + b^2 >= c^2 is false since the only the only inequalities which are always true are a^2 + b^2 >= 0, c^2 >= 0.

I see that http://vixra.org/pdf/1305.0129v1.pdf is by Elemér E Rosinger. He admires H. De Raedt, K. Hess and K. Michielsen, Extended Boole-Bell Inequalities Applicable to Quantum Theory", J. Comp. Theor. Nanosci. 8, pp. 1011-1039 (2011). One paper is a preprint in viXra; the other in a journal published by one of those new junk science publishing companies. http://www.aspbs.com/ctn/ Hans de Raedt is an associate editor of the journal.

Its impact factor is amusing

https://www.researchgate.net/journal/15 ... anoscience

In other words, two unreadable papers which no one is going to read.

[FrediFizzx]

And that has what to do with the actual truth? Did you read the paper? And if so, did you understand it?

[gill1109]

And that has what to do with the actual truth? Did you read the paper? And if so, did you understand it?

Good that you ask, Fred.

I read both these two papers carefully. I also know the authors, and I know other works by them. I meet de Raedt occasionally, invited him to be a keynote speaker at a conference I organized (he's really good at computational physics). I have a friendly correspondence, off and on, with both de Raedt and Rosinger.

In my opinion, the venues in which these two particulars papers are "published" (they are "self-publications" in fact) are both very appropriate.

Their fundamental error is exactly the same as that of Michel Fodje, and also the root of your misunderstandings. Do please carefully read chapters 13 and 16 of "Speakable and Unspeakable".

[Heinera]

(no data rejection like the last time, please)

Why? Because you said so? Bell believers, like you think they can unilaterally make non-physical requirements and everyone is just supposed to toe the line under the threat of "loophole". I asked and you never answered where you got the idea that non-detection/data rejection was forbidden even though QM does not forbid it? What physical basis allows you to demand that? No answer.

I already asked you how you can know that a particle was emitted but never detected without using non-local information, and you never answered.

If you think you got no answer, you haven't been paying attention. QM does not forbid non-detection, but it does not require it either. Your model does. You don't seem to understand that distinction. QM does not predict that the ratio of one sided detections must be above a certain threshold. Your model does. Whether you think that this has or has not yet been ruled out by any experiment performed so far is irrelevant. We are comparing predictions of two models here. Your model predicts something that QM doesn't.

[gill1109]

I already asked you how you can know that a particle was emitted but never detected without using non-local information, and you never answered.

This is exactly what Bell's chapters 13 and 16 focus on. Here is another simple solution. Turn down the intensity of the emissions very low. Agree in advance on time intervals 0=t0 < t1 < t2 < ...
During each time interval, there is just one setting in force at each detector. It is re-set at random from one interval to the next.
During one of those time intervals, there can obviously be 0, 1, 2 or more detections at Alice's detector. Keep just the first, if there is 1 or more.

So per time interval, on Alice's side, there is one setting in force, and the outcome is either +1, -1, or 0

Use a generalized Bell inequality for the 2x2x3 experiment (2 parties, 2 settings, 3 outcomes).

This is how the recent Colorado - Illinois - Geneva and the recent Vienna experiments have been analysed.

[minkwe]

QM does not forbid non-detection, but it does not require it either. Your model does. You don't seem to understand that distinction. QM does not predict that the ratio of one sided detections must be above a certain threshold. Your model does. Whether you think that this has or has not yet been ruled out by any experiment performed so far is irrelevant. We are comparing predictions of two models here. Your model predicts something that QM doesn't.

Heine, you too needs to review some logic. You can't compare a prediction of one model and a non-prediction of another model. Show me one prediction of QM which my model disagrees with or vice versa. Show me one experimental observation which agrees with QM and disagrees with my model.
In case you didn't know, the interest in hidden variable theories is precisely to complete QM. A more complete theory will always make more predictions that QM is unable to make. You can't then argue that since the more complete theory makes predictions which QM does not, it must be wrong!

[Heinera]

QM does not forbid non-detection, but it does not require it either. Your model does. You don't seem to understand that distinction. QM does not predict that the ratio of one sided detections must be above a certain threshold. Your model does. Whether you think that this has or has not yet been ruled out by any experiment performed so far is irrelevant. We are comparing predictions of two models here. Your model predicts something that QM doesn't.

Heine, you too needs to review some logic. You can't compare a prediction of one model and a non-prediction of another model. Show me one prediction of QM which my model disagrees with or vice versa. Show me one experimental observation which agrees with QM and disagrees with my model.

http://arxiv.org/abs/1212.0533
http://www.nature.com/nature/journal/v4 ... 791a0.html

But this thread is not about experiments. It is about the theoretical differences between LHV models and other models/theories.

Since Bell's theorem (which you seem to disagree with) is about loophole free models, show me a LHV model that reproduces the quantum correlations without data rejection.

[Heinera]

You should also read this section very carefully (from Richard's latest paper):

"In particular then, the program can be run with N = 1 and all four possible pairs of measurement settings, and the same initial random seed, and it will thereby generate successively four pairs (A,B), (A',B), (A,B'), (A,B'). If the programmer neiter cheated or made any errors, in other words, if the program is a correct implementation of a genuine LHV model, then both values of A are the same, and so are both values of A', both values of B, and both values of B'. We now have the first row of the Nx4 spreadsheet of Section 2 of this paper." (My emphasis.)

In other words, if the model is not a LHV model (e.g., a non-local model) both values are not generally the same, and there will be no table; no upper bound of 2.