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How have you defined detection efficiency? There quite a few definitions out there. In experiments M is unmeasurable, and the number of non-detections is unmeasurable, so typically what you see reported as detection efficiency is P(D|S), D=both particles are detected, S= either particle is detected.

In Pearle's model the detection rate depends on the settings. This is an unpleasant feature of the model. As Zen says, in the real world you generally do not know the number of emissions but you might be prepared to assume that the rate is constant hence you can see if there are different rates of detection at different *differences* between the settings left and right. It has been proven that this defect of Pearle's model cannot be fixed by taking a different choice for the distribution of (his) r. In other words, no single choice achieves constant detection rate as a function of the pair of settings.

The Gisin-Gisin model does have this nice feature, but the detection rate is a whole lot lower. There are some open problems here, such as: what is the largest detection rate which be attained while reproducing exactly the singlet correlation and while keeping the pair detection rate independent of the setting pair?

Zen wrote:Looks like the joint theoretical efficiency of the Gisin-Gisin model is exactly 50%.

That's right.

Zen wrote:Hi Michel,

In this artificial Monte Carlo simulation environment, I've defined (joint) efficiency to be the number of "good" (accepted) states over the number of generated states. This is done for each simulated angle difference. In a real laboratory, if I'm using the same source, I would expect that running the experiment for two different angle differences for a sufficiently long time T would give me a ratio of detection counts in the same proportion as the corresponding ratio of the efficiencies predicted by, let's say, Pearle's model. Hence, absolute efficiencies may not be observable, but relative efficiencies are experimentally testable.

Good point, It should be possible then using existing data from Weih's experiment and similar experiments to calculate how the efficiency varies by angle difference. The only way the efficiency should vary by angle is if hidden variables are present. That to me seems like an easily doable test, instead of the unending focus on "loophole-free" experiments.

minkwe wrote:

Zen wrote:Hi Michel,es, corret.

In this artificial Monte Carlo simulation environment, I've defined (joint) efficiency to be the number of "good" (accepted) states over the number of generated states. This is done for each simulated angle difference. In a real laboratory, if I'm using the same source, I would expect that running the experiment for two different angle differences for a sufficiently long time T would give me a ratio of detection counts in the same proportion as the corresponding ratio of the efficiencies predicted by, let's say, Pearle's model. Hence, absolute efficiencies may not be observable, but relative efficiencies are experimentally testable.

Good point, It should be possible then using existing data from Weih's experiment and similar experiments to calculate how the efficiency varies by angle difference. The only way the efficiency should vary by angle is if hidden variables are present. That to me seems like an easily doable test, instead of the unending focus on "loophole-free" experiments.

If effiency varied by angle difference, that would be a clear indication of hidden varaibles, correct. But no notable experiment to date has seen such a relationship between angle difference and efficiency.

Heinera wrote:If effiency varied by angle difference, that would be a clear indication of hidden varaibles, correct. But no notable experiment to date has seen such a relationship between angle difference and efficiency.

Are you sure, that because they haven't looked. Check for example this analysis of Weihs data: http://arxiv.org/pdf/quant-ph/0606122.pdf, look at figure 1 where they report coincidences. Remembering that in experiments where they are doing post-selection, it is coincidence efficiency that is important. Look also at Figure 5.

Heinera wrote:If effiency varied by angle difference, that would be a clear indication of hidden variables, correct. But no notable experiment to date has seen such a relationship between angle difference and efficiency.

Caroline Thompson found this phenomenon in some of Aspect's experiments. Hidden variables? If there are systematic drifts in source and/or detector properties as the experiment proceeds. and if the settings are not being chosen again and again completely at random, then all kinds of correlations are introduced.

http://freespace.virgin.net/ch.thompson ... Record.htm

The experiment both needs to be performed, and the data analysed, in a way which rules out "loophole" interpretations of the correlations which are found. It's not actually difficult! There is no coicidence loophole if we determine paired events using a grid of fixed time windows. There is no detection loophole if we use the Clauser-Horne inequality, or the chained Bell inequality for a three outcome measurement, or Larsson's modified Bell inequality with a correction term for detection efficiency. There is no conspiracy loophole and no memory loophole and no time loophole if the settings are being chosen again and again completely at random.

There is no detection loophole if we use the Clauser-Horne inequality

Even the CH inequality is vulnerable to substitution of outcomes from actually measured particles for unmeasurable counter-factual outcomes. The CH inequality is also derived from a single set of particles. Had Bell studied Boole's work and understood it, he would never have proposed "Bell's theorem". It seems to me we need to start from a clean slate and unlearn many bad habits. Unfortunately that means many people will lose their jobs/grants in the "Bell enterprise", therefore it wont happen.

Bell in his first Bell-inequality paper in effect uses the Boole inequality "P(A or B or C) is less than or equal to P(A) + P(B) +P(C)".

CHSH and CH in effect use the Boole inequality use "P(A or B or C or D) is less than or equal to P(A) + P(B) +P(C) +P(D)."

I don't think one needs to study Boole's work in order to be able to use these inequalities. (Almost no one reads Boole nowadays). The point is to use them sensibly.

Bell is using them inside an "argument by contradiction". Assume locality + realism + no-conspiracy. Derive an inequality. Note that according to QM, that inequality can be violated. Deduce that locality or realism or no-conspiracy or quantum mechanics has to go.

Michel has told us that for him, counterfactual definiteness or realism is non-sensical, so he should have no problem with Bell. Niels Bohr had exactly the same opinion.

gill1109 wrote:Michel has told us that for him, counterfactual definiteness or realism is non-sensical

This is obviously false as anyone can see. If you were'nt deliberately trying to mislead, you'd have included a quote where I said that. That you will blatantly misrepresent my views despite my repeated explanation to you is unfortunate.

gill1109 wrote:Bell in his first Bell-inequality paper in effect uses the Boole inequality "P(A or B or C) is less than or equal to P(A) + P(B) +P(C)".

CHSH and CH in effect use the Boole inequality use "P(A or B or C or D) is less than or equal to P(A) + P(B) +P(C) +P(D)."

Had Bell read Boole's work, he would have noticed that Boole derived the same inequalities now called "Bell's inequalities", almost a century before Bell. Now you claim that Boole's inequalities are just "P(A or B or C) is less than or equal to P(A) + P(B) +P(C)". But that is because you too haven't read his work. I would encourage you to. You can find a detailed presentation in some of Pitowsky's work. Yes, that Pitowsky.

As concerns the inequality "P(A or B or C or D) is less than or equal to P(A) + P(B) +P(C) +P(D)."
I'm so happy you brought that up. Please could you write down the equality on which that inequality is based and I'll use it to show you from a different perspective what your error is. That is if you don't mind.

Yes I've read Boole. And I don't mind at all if you try to explain where you think I'm wrong. That can only lead to one or both of us learning something new.

To make things simple let's do the case of two events. A union B is the disjoint union of A and B setminus A. B is the disjoint union of B setminus A and A intersection B. Write down the two corresponding equalities (additivity of probability). By substituion find probability of A union B equals the sum of the probabilities of A and B, minus the probability of their intersection. Now use non-negativity of probability to get your inequality.

gill1109 wrote:To make things simple let's do the case of two events. A union B is the disjoint union of A and B setminus A. B is the disjoint union of B setminus A and A intersection B. Write down the two corresponding equalities (additivity of probability). By substituion find probability of A union B equals the sum of the probabilities of A and B, minus the probability of their intersection. Now use non-negativity of probability to get your inequality.

P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A ∩ B) >= 0 (by definition)
P(A U B) <= P(A) + P(B)

Is that what you mean?
Can this inequality ever be violated by anything, short of a mathematical error?
Do you agree that every inequality is a summary of an equality that must make sense for the inequality to make sense?
It will be interesting find out what the corresponding equality for "Bell's inequality" is, and to ask ourselves if it makes sense for all the scenarios we are apply the inequalities for.

For example, what if we make those events conditional on some condition (X), and we write:
P(A U B|X) = P(A|X) + P(B|X) - P(A ∩ B|X)
P(A ∩ B|X) >= 0 (by definition)
P(A U B|X) <= P(A|X) + P(B|X)

Is this inequality still valid? Will it still be valid if P(X) = 0?

Do you see the problem? Lots of questions, I know, but I don't expect you to answer them here so long as you answer them to yourself, I'm just attempting to guide your reasoning process.

X ~ All the measurements are performed on a single set of particles.

minkwe wrote:P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A ∩ B) >= 0 (by definition)
P(A U B) <= P(A) + P(B)
Is that what you mean?
Can this inequality ever be violated by anything, short of a mathematical error?
Do you agree that every inequality is a summary of an equality that must make sense for the inequality to make sense?
It will be interesting find out what the corresponding equality for "Bell's inequality" is, and to ask ourselves if it makes sense for all the scenarios we are apply the inequalities for.
For example, what if we make those events conditional on some condition (X), and we write:
P(A U B|X) = P(A|X) + P(B|X) - P(A ∩ B|X)
P(A ∩ B|X) >= 0 (by definition)
P(A U B|X) <= P(A|X) + P(B|X)
Is this inequality still valid? Will it still be valid if P(X) = 0?
Do you see the problem? Lots of questions, I know, but I don't expect you to answer them here so long as you answer them to yourself, I'm just attempting to guide your reasoning process.
X ~ All the measurements are performed on a single set of particles.

Interesting, apparently you think that the usual derivations of Bell's theorem involve conditioning on a zero probability event! I think you are badly mistaken. Take for example Theorem 1 in section 2 of my paper http://arxiv.org/abs/1207.5103. Do you see conditioning on a zero probability event here?

In section 9 I explain how we can apply this theorem to a computer simulation of a local hidden variables model such as your https://github.com/minkwe/epr-simple. There is no conditioning on zero probability events there, either.

It is of course trivial to extend this work to the case of ternary outcomes, like that of https://github.com/minkwe/epr-simple, in which situation we should use Clauser-Horne type inequalities (= CHSH after merging some outcomes on each side in order to reduce ternary to binary) and the CGLMP inequality (Collins-Gisin-Linden-Massar-Popescu, aka chained CHSH inequality, see http://arxiv.org/abs/1003.0616 and http://arxiv.org/abs/quant-ph/0612020).

Similarly we can apply the Larsson-Gill http://arxiv.org/abs/quant-ph/0312035 results on the coincidence loophole to a simulation like https://github.com/minkwe/epr-clocked.

It interesting to see a synchrotron scientist and adjunct professor in biochemistry trying to teach probability theory to a mathematical statistician. I sincerely admire your pluck and your fourthrightness.

gill1109 wrote:Interesting, apparently you think that the usual derivations of Bell's theorem involve conditioning on a zero probability event! I think you are badly mistaken.

Misdirection. Misrepresentation. You still do not get it. It is not the derivation that has zero probability but the situation you insist on applying the inequality so obtained on.It is not the set used in your LG paper that is null, it is the set in the actual experimental situation you insist on using your derived equations on. Your LG theory is valid, IF THE SET IS NOT NULL, UNFORTUNATELY IT IS NULL IN PRACTICE. Bell's inequality is valid IF THE CONDITIONING EVENT HAS NON-ZERO PROBABILITY, BUT IT DOES HAVE ZERO PROBABILITY IN PRACTICE.
Get it now, mathematical statistician?

There is no conditioning on zero probability events there, either.

The probability that all correlations are calculated from a single set of particles IN EPR EXPERIMENTS AND THE QM PREDICTIONS is zero. You do not deny this. Yet the mathematical statistician continues to use those same probabilities in an inequality which is DERIVED BY ASSUMING THAT THE PROBABILITIES ARE NOT CONDITIONED ON A ZERO PROBABILITY EVENT.

Similarly we can apply the Larsson-Gill http://arxiv.org/abs/quant-ph/0312035 results

The same theory which relies on a non-null set, failing to realize that in actual experiments, the set in question is in fact null, making the theory invalid for any performable experiments.

It interesting to see a synchrotron scientist and adjunct professor in biochemistry trying to teach probability theory to a mathematical statistician.

Apparently you believe science should be practiced like religion in which everyone bows to hierarchy based on titles such as "pope" or "mathematical statistician" who are are infallible. It must hurt that someone who you assume shouldn't know as much as you in your domain easily points out where the bodies are buried in your backyard, and you realize they are right. Its no excuse to resort to personal attacks though. So when you kept insisting in our private exchanges, wanting to know my background, this is what you were planning to use the information for? Having no coherent response to the clear arguments I've presented, your new argument is that I must be wrong because I'm a synchrotron scientist and an adjunct professor in biochemisty, and you must be correct because you are a mathematical statistician.

Funny that the same mathematical statistician thinks he is right about the foundations of quantum mechanics and a Nobel laureate theoretical physicist is wrong.

I think you can't read mathematics. You are writing absolute nonsense about Larsson - Gill. There is no conditioning.

We do assume that local hidden variables exist in a mathematical model which reproduces experimental results. For instance: they do exist in your computer simulations, which can be seen as a mathematical model for the experiments. We derive inequalities which would be true if a local hidden variables theory could be found which explains the experimental results. They apply to your computer experiments, as you can easily check for yourself. Local hidden variables guarantee that counterfactual outcomes of all possible measurements exist simultaneously, in a mathematical sense: in a given run with hidden variables lambda, the measurement outcome A(a, lambda) is defined for all settings a, not just for the single setting which Alice happened to choose in the particular run in question.

The point of the real world experiments is to find out if mathematical models of reality would also admit local hidden variables.

Joy thinks so. My former colleague Gerard 't Hooft thinks so. I don't know your opinion.

Gerard does not think that Bell was wrong. He believes that the conspiracy loophole applies in experiments at the Planck scale, which is the only thing that interests him. There are in fact no experiments at this level. No experimenters. No freedom to choose which experiment to do. Gerard 't Hooft is a super-determinist.

I suggest you take some time off to carefully study sections 2 and 9 of the recent paper by me which we talked about so often, http://arxiv.org/abs/1207.5103. They are about computer simulation models of synchronised Bell - CHSH experiments with binary outcomes only. Let me know immediately when there is something you don't understand.

gill1109 wrote: Local hidden variables guarantee that counterfactual outcomes of all possible measurements exist simultaneously, in a mathematical sense: in a given run with hidden variables lambda, the measurement outcome A(a, lambda) is defined for all settings a, not just for the single setting which Alice happened to choose in the particular run in question.

...

I suggest you take some time off to carefully study sections 2 and 9 of the recent paper by me

I suggest you take some time to carefully study what I've posted above. I don't think you understand any of it. Your response to it is incoherent.

minkwe wrote:

gill1109 wrote: Local hidden variables guarantee that counterfactual outcomes of all possible measurements exist simultaneously, in a mathematical sense: in a given run with hidden variables lambda, the measurement outcome A(a, lambda) is defined for all settings a, not just for the single setting which Alice happened to choose in the particular run in question.

...

I suggest you take some time off to carefully study sections 2 and 9 of the recent paper by me

I suggest you take some time to carefully study what I've posted above. I don't think you understand any of it. Your response to it is incoherent.

I have not been able to understand a thing of what you have been saying. I wasn't the only one, by the way.

To me it was completely incoherent, full of self-contradictions. You are a priori so certain that you are right and the rest of the world is wrong, that you don't even bother to look at the details of what other people are saying. You don't even know what they are saying. You are fighting straw men. You are fighting against the stupidest of ideas, which only exist in your imagination's picture of your opponents' minds.

Try to learn something from other people, instead of just fighting them all the time.

I suggest you concentrate on writing nice computer programs exploring the limits of the detection loophole, of the coincidence loophole, and of the conspiracy loophole. You are very good at this. They are splendid programs which beautifully illustrate everything I have been working on (as far as quantum foundations is concerned) during the last 15 years. (My main work nowadays is mainly in forensic statistics, and earlier I worked mainly in survival analysis and semiparametric models).

Michel, you wrote "We can not substitute actual outcomes from a different set of particles for counterfactual outcomes of a single set of particles."

Nobody is doing that. There is (1) a substitution of theoretical mean values by empirically observed averages. And there is (2) a "fair sampling" assumption, aka no-conspiracy, or freedom. So (1), statistical error has to be allowed for, and (2) we need to assume that the particle pairs on the basis of which one particular sample correlation was observed, are a random sample from all particle pairs. Or at least, a representative sample from all the particle pairs. Taking a random sample is a good way to guarantee that.

The fact of a local hidden variables theory ensures that we have counterfactual definiteness.

gill1109 wrote:I have not been able to understand a thing of what you have been saying. I wasn't the only one, by the way.

You admit that you have not understood it, yet at the same time you are so convinced that I am wrong. I rest my case. Come back when you have studied it carefully and understand it, because as you admit yourself, you do not understand what you are talking about. If you don't like reading what I have written, I suggest you study Adenier's paper (http://arxiv.org/pdf/quant-ph/0006014.pdf) very carefully instead and then come back when you understand it. If you do not like Adenier, I suggest you study Karl Hess and De Raedt's paper (http://arxiv.org/pdf/0901.2546.pdf) very carefully instead. If you dislike those authors, let me know and I will find others. It is not wise to pretend to be arguing against a position you do not yet understand. So first go and study those papers and when you understand them, come back and we can have a discussion about why you think they are wrong, because you currently have no clue about what we are talking about, as you admit yourself.