New clocked EPR Simulation with 100% detection.

[Heinera]

They are in fact saying that BobOutcome1 in (BobOutcome1 + BobOutcome2) is the same as BobOutcome1 in (BobOutcome1 - BobOutcome2) (aka, the same particle). Calculating (BobOutcome1 + BobOutcome2) from one particle and (BobOutcome1 - BobOutcome2) from a completely different particle is a mathematical error.

But they are of course not calculating (BobOutcome1 + BobOutcome2) and (BobOutcome1 - BobOutcome2) from completely different particles. BobOutcome1 in the first expression is the same as BobOutcome1 in the second expression, and ditto for BobOutcome2. So I'm still struggeling to get your point here.

Who do you mean by they?

So obviously, I referred to the same they as you did. Unfortunately, your sort of rambling reply did not make things any clearer, though. So I'm afraid I'm still struggling with your point, yes.

[minkwe]

"Rambling" in what way? What part of my reply don't you understand but actually want to understand?

Let us see, I said:

They are in fact saying that BobOutcome1 in (BobOutcome1 + BobOutcome2) is the same as BobOutcome1 in (BobOutcome1 - BobOutcome2) (aka, the same particle). Calculating (BobOutcome1 + BobOutcome2) from one particle and (BobOutcome1 - BobOutcome2) from a completely different particle is a mathematical error.

And you said:

But they are of course not calculating (BobOutcome1 + BobOutcome2) and (BobOutcome1 - BobOutcome2) from completely different particles.

If you were referring to the same they as I was, then who said they were calculating from completely different particles??? You assumed that I said that. Had you read the full post you would have recognized what I meant, and who it was that was calculating from different particles.

So obviously, I referred to the same they as you did.

No, you misunderstood what I meant.

So I'm afraid I'm still struggling with your point, yes.

Here is my point again:
1) Bell's theorem is based on the mistaken assumption that QM predictions for 4 disjoint sets of particles can be combined together in the same CHSH expression with an upper bound of 2.
2) Claimed experimental violation of the CHSH is based on the mistaken assumption that correlations measured from 4 disjoint sets of particles can be combined together in the same CHSH expression with an upper bound of 2.
3) The correct upperbound for 4 disjoint sets of particles and their averages is 4. This is the value QM and EPR-experiments should be compared with.
4) In cases where particles are destroyed during measurement, it is impossible to perform an experiment that will test the CHSH with an upper bound of 2.
5) It is a mathematical error to substitute correlations measured from/predicted for 4 disjoint sets of particles into an expression derived assuming only a single set.

Still struggling with any of the above ramblings? If so point out the one and I will expand on it.

[gill1109]

Which means: the theory can be augmented so that outcomes of all possible measurements are defined simultaneously.

This is another key misunderstanding on your part. If a mathematical theory is accurate and consistent, then all it's predictions are well defined at all times. The suggestion that the predictions of a mathematical theory can be defined at some times and not defined at other, simply because somebody decided to measure at a different angle, defies logic.

I think this is a key misunderstanding on your part.

I tried to explain, by looking in detail at your first computer simulation program https://github.com/minkwe/epr-simple, and thinking about running it with the number of pairs of particles to be generated equal to 1.

That program can be thought of as a mathematical model. It says: something classically random goes on at the source, leading to something called lambda, which is transmitted to the two measurement stations. At each station Alice and Bob choose a setting a and b, and get to see outcomes A(a, lambda) and B(b, lambda).

Do you deny that your computer programs could be used to calculate A(a, lambda) and B(b, lambda) for lots and lots of different values of a and b, but all with the same lambda?

This is what I mean by saying that your model of the EPR correlations is compatible with counterfactually definiteness. Basicly I am saying that it's a local hidden variables model! Do you deny that?

And how your program violates Bell-CHSH? By having ternary instead of binary outcomes. You'll notice that the detection rate is lower than the threshhold which has been established long ago by Jan-Ake Larsson and others for this kind of simulation experiment. One should use a generalized Bell inequality for a 2 x 2 x 3 experiment - two parties, two measurement settings each, three outcomes. There is just the so-called chained Bell inequality, and various "embeddings" of CHSH by merging pairs of outcomes so as to reduce to a 2 x 2 x 2. Aka Clauser-Horner.

[minkwe]

Do you deny that your computer programs could be used to calculate A(a, lambda) and B(b, lambda) for lots and lots of different values of a and b, but all with the same lambda?

I do not deny that my simulation can be changed so that the same particle is measured repeatedly at lots of different angles. Why would you think I would deny that, when I've told you repeatedly that:

You modified the simulation such that already measured particles were recovered (by saving random number) seeds, and remeasured at different angles. I already told you that was meaningless because the QM predictions you are using to discredit counterfactual definiteness are not calculated for such a scenario. AND the experimental results you are using to discredit counterfactual definiteness are not done in such a manner, nor can they ever be.

Again, the point which I believe you haven't understood is that in experiments, actual measurements on different sets of particles are being substituted into an inequality derived using counter-factual outcomes on a single set of particles. Do you deny this?

This is what I mean by saying that your model of the EPR correlations is compatible with counterfactually definiteness. Basicly I am saying that it's a local hidden variables model! Do you deny that?

Why would I deny that, when I've told you repeatedly that

Counterfactual definiteness simply means those statements continue to have the same truth values, irrespective of whether the conditional clause is contrary to actuality or not. To abandon counterfactual definiteness means as soon as it is no longer possible to perform the experiment, the prediction which was true in the past ceases to be true. This is a logical error. To say that QM is incompatible with counterfactual definiteness is a logical error.

Every theory or simulation that is logical and consistent is compatible with counter-factual definiteness including mine. Just because a theory is compatible with counterfactual definiteness does not mean is mathematically meaningful to substitute actual outcomes from a different set of particles for counterfactual outcomes within a single set of particles.

And how your program violates Bell-CHSH? By having ternary instead of binary outcomes. You'll notice that the detection rate is lower than the threshhold which has been established long ago by Jan-Ake Larsson and others for this kind of simulation experiment. One should use a generalized Bell inequality for a 2 x 2 x 3 experiment - two parties, two measurement settings each, three outcomes. There is just the so-called chained Bell inequality, and various "embeddings" of CHSH by merging pairs of outcomes so as to reduce to a 2 x 2 x 2. Aka Clauser-Horner.

Unfortunately, your analysis is just wrong. My simulations (both versions) appear to violate the CHSH because I'm calculating each term from 4 distinct sets of particles for which the upper bound is 4 not 2, so when you errorneously compare the correlations from my simulation with the single set version of the CHSH, you get an apparent violation. But this violation is fake because it requires faulty mathematics in order to achieve, ie substituting actual outcomes from a different set of particles into an inequality involving counter-factual outcomes within the same set of particles. If you modify the simulation as you have done, so all correlations are measured from the same set of particles, you will never violate the CHSH with an upper bound of 2, not even with a loophole. This is why I say this loophole business is just a distraction from the real issue.

Use a single set and you'll never violated the upper bound of 2. Use 4 different sets and you'll never violate an upper bound of 4, but you can easily violate the upper bound of 2. This is the point you haven't understood, which I was showing you in the previous thread but you were not interested (reproduced below):

We will proceed as follows:
* Generate pairs of particles as done previously.
* Instead of measuring at just "alice" and "bob", we will add two more "ghost" stations called "cindy" and "dave". We will send an exact copy of Alice's particle to Cindy and an exact copy of Bob's particle to Dave. This way we will have counterfactual results for Alice's particle at Cindy, and the same for Bob at Dave.
* We will do the data analysis in two steps. In the first step, we will ignore Cindy and Dave and simply use Alice and Bob as we have been doing until now. This scenario is equivalent to substituting actual results on different sets of particles for counterfactual results on a single set.
* The next step of data analysis will involve using all 4 outcomes for calculating the correlations. So that we use Alice and Bob to calculate C(a,b), Cindy and Bob to calculate C(a',b), Alice and Dave to calculate C(a,b') and Cindy and Dave to calculate C(a',b'). This step is equivalent to using counter-factual correlations just as is intended in the CHSH.
* We will then compare the results between the two scenarios and be able to answer our main question.

So here are quick results I've done using my python version for the above:

=== USING SEPARATE SETS =====.
===== Using only the ('alice', 'bob') data pair ===
E( 0.0, 22.5), AB=-0.93, QM=-0.92
E( 0.0, 67.5), AB=-0.40, QM=-0.38
E( 45.0, 22.5), AB=-0.93, QM=-0.92
E( 45.0, 67.5), AB=-0.93, QM=-0.92
CHSH: < 2.0, Sim: 2.391, QM: 2.389

===== Using only the ('alice', 'dave') data pair ===
E( 0.0, 22.5), AB=-0.93, QM=-0.92
E( 0.0, 67.5), AB=-0.40, QM=-0.38
E( 45.0, 22.5), AB=-0.93, QM=-0.92
E( 45.0, 67.5), AB=-0.93, QM=-0.92
CHSH: < 2.0, Sim: 2.390, QM: 2.389

===== Using only the ('cindy', 'bob') data pair ===
E( 0.0, 22.5), AB=-0.93, QM=-0.92
E( 0.0, 67.5), AB=-0.40, QM=-0.38
E( 45.0, 22.5), AB=-0.93, QM=-0.92
E( 45.0, 67.5), AB=-0.93, QM=-0.92
CHSH: < 2.0, Sim: 2.389, QM: 2.389

===== Using only the ('cindy', 'dave') data pair ===
E( 0.0, 22.5), AB=-0.93, QM=-0.92
E( 0.0, 67.5), AB=-0.41, QM=-0.38
E( 45.0, 22.5), AB=-0.93, QM=-0.92
E( 45.0, 67.5), AB=-0.93, QM=-0.92
CHSH: < 2.0, Sim: 2.386, QM: 2.389

==== USING ALL FOUR COUNTERFACTUAL ===
E(0, 22.5), AB=-0.90, QM=-0.92
E(0, 67.5), AB=-0.69, QM=-0.38
E(45, 22.5), AB=-0.90, QM=-0.92
E(45, 67.5), AB=-0.90, QM=-0.92
CHSH: < 2.0, Sim: 2.00, QM: 2.39


Just as I explained, using multiple sets, the CHSH is violated and QM is matched. Using a single set, the CHSH is not violated! See, the detection loophole is irrelevant!

Note, that the counterfactual portion is exactly the same simulation code with the same non-detection of some particles, the only difference is that each particle is measured at 2 angles each (impossible in practice), instead of one, so that all correlations can be calculated from the same set of particles. Yet, calculating from separate sets of particles, all the correlations match QM, while calculating from a single set (all actual outcomes, no counterfactual terms) the results obey the CHSH and does not match QM. Now you believe this shows that QM is not compatible with counterfactual definiteness, but you are wrong. The results confirm what we already know, that the QM predictions are for separate sets of particles not a single set.

This confirms my point I've been making to you repeatedly that you can not substitute actual outcomes from a different set of particles, for counterfactual outcomes within a single set of particles. Do you deny this?

Now this is going around in circles. I have explained very clearly what the issues are.

[Joy Christian]

...you can not substitute actual outcomes from a different set of particles, for counterfactual outcomes within a single set of particles.

This is at the heart of the Bell scandal of the past 50 years, at least from the experimental point of view.

A friend of mine asked me about a recent proposal to close the "free will" loophole. Here is how I replied:

"... several points. (1) Data is always good, so I am all for the experiment. (2) I am confident that eventually all the "loopholes" will be closed, even simultaneously, so that is good. (3) The real issues with all these experiments are not experimental, but conceptual. There is a fatal conceptual error in all of the experiments, and it cannot be fixed, ever, unless we can make repeated measurements on the same pair of particles. In the original EPR paper as well as in Bell's work there is this assumption of "counterfactual definiteness." What this means is that, "had we measured spin along this direction instead of that direction, we would have obtained this result instead of that result." Now the problem is that it is physically impossible to measure the spin in two different directions, even successively. Once the spin is measured, that particle is gone forever. So in the actual experiments they inevitably measure the spins of a different pair of particles (those next in line, so to speak). In conclusion, in my opinion the entire Bell's theorem saga is a scandal of epic proportions."

[gill1109]

Bell's theorem is a theorem about theories. Bell experiments are designed to test theories.

Both Michel and Joy are taking the Bohr Copenhagen track: it doesn't make sense to talk about outcomes of unperformed measurements. Well, in QM it doesn't, but in classical physics it did. In a local hidden variables theory, it does. In a computer simulation model of a LHV theory, it does.

Both Joy and Michel apparently *accept* Bell's theorem because they are happy to deny "realism" aka "counterfactual definiteness". More precisely, they are happy to accept that no theory can be built which fully reproduces QM predictions while it simultaneously admits realisations simultaneously of all A(a, lambda) ("a" varies, lambda fixed). They have no need of such a theory!

John Bell himself authorized this "track". It is one of the logically defensible positions to take.

It's my current position also: locality is alive and well, there is no grand conspiracy, but "realism" (in the narrow and technical sense just described) is dead and buried. Classical physics must be abandoned. Bohr won from Einstein.

[Joy Christian]

Both Michel and Joy are taking the Bohr Copenhagen track: it doesn't make sense to talk about outcomes of unperformed measurements.

... Both Joy and Michel apparently *accept* Bell's theorem because they are happy to deny "realism" aka "counterfactual definiteness".

Why are you twisting what I have written so clearly? What do you gain by twisting that which has been written so unambiguously? I have no time for Bohr or his Copenhagen interpretation. I am a strict adherent of Einstein's realist position. Anyone who has read anything I have written over the past three decades knows that.

I have absolutely no problem with counterfactual definiteness, and neither does Michel. Similarly, neither Michel nor I have any problem with talking about outcomes of unperformed measurements. We use counterfactual definiteness in physics as well as in daily life all the time. It is not possible to do physics without counterfactual definiteness. Even Bohr did not object to Einstein's implicit use of counterfactual definiteness in the EPR argument. Counterfactual definiteness is not an issue at all.

Let me point out your reading difficulty to you so you can perhaps read again correctly what Michael and I have actually written. Here is what Michel actually wrote:

...you can not substitute actual outcomes from a different set of particles, for counterfactual outcomes within a single set of particles.

Now where on earth do you see in this very clear sentence, written in your own native language, even a hint of a denial of realism or counterfactual definiteness?

[gill1109]

I have absolutely no problem with counterfactual definiteness, and neither does Michel. Similarly, neither Michel nor I have any problem with talking about outcomes of unperformed measurements. We use counterfactual definiteness in physics as well as in daily life all the time. It is not possible to do physics without counterfactual definiteness. Even Bohr did not object to Einstein's implicit use of counterfactual definiteness in the EPR argument. Counterfactual definiteness is not an issue at all.

Let me point out your reading difficulty to you so you can perhaps read again correctly what Michael and I have actually written. Here is what Michel actually wrote:

...you can not substitute actual outcomes from a different set of particles, for counterfactual outcomes within a single set of particles.

Now where on earth do you see in this very clear sentence, written in your own native language, even a hint of a denial of realism or counterfactual definiteness?

Joy, I am very glad to hear of your resounding support for counterfactual definiteness. Seems to me that if you believe in a local hidden variables theory underlying quantum mechanics, you are accepting counterfactual definiteness. However, just now you seemed to be saying something different.

Michel wrote many, many more sentences. He has repeatedly objected to my talking about the outcome of a different measurement on a given particle (different to the one which actually gets performed). (1) He claimed that the very words were meaningless. (2) He also claimed that it is factually impossible to do, in real experiments on quantum systems. (Though in my opinion it is very well possible for classical mechanics driven colourful exploding balls).

1) I hope the intended meaning of the words in the present content is now clear.

(2) In my opinion, the fact that it makes no sense to actually measure the polarization of one photon in two different directions at the same time, is totally besides the point. A local hidden variable theory makes both measurement outcomes well defined inside the mathematical theory in question, and if the experimenter also has the freedom to toss a coin to choose between the two directions of measurement, then relative to this theory one can say that the coin toss simply selects one of two independently existing polarisation measurement outcomes to get actually observed by the experimenter. From now on, the iron logic of Boole's inequality together with the statistical independence between the measurement choices outside the quantum systems and measurement devices, and the local hidden variables inside does the rest. (Plus of course Chernof's inequality: sample averages are with large probability close to theoretical mean values).

We have to wait for the sun to come up in Saskatoon in order to hear Michel's reaction.

[minkwe]

Why are you twisting what I have written so clearly? What do you gain by twisting that which has been written so unambiguously? I have no time for Bohr or his Copenhagen interpretation. I am a strict adherent of Einstein's realist position. Anyone who has read anything I have written over the past three decades knows that.

I have absolutely no problem with counterfactual definiteness, and neither does Michel. Similarly, neither Michel nor I have any problem with talking about outcomes of unperformed measurements. We use counterfactual definiteness in physics as well as in daily life all the time. It is not possible to do physics without counterfactual definiteness. Even Bohr did not object to Einstein's implicit use of counterfactual definiteness in the EPR argument. Counterfactual definiteness is not an issue at all.

Let me point out your reading difficulty to you so you can perhaps read again correctly what Michael and I have actually written. Here is what Michel actually wrote:

...you can not substitute actual outcomes from a different set of particles, for counterfactual outcomes within a single set of particles.

Now where on earth do you see in this very clear sentence, written in your own native language, even a hint of a denial of realism or counterfactual definiteness?

Thank you Joy! The point has been so clearly stated that it is actually a scandal that it continues to be twisted and misrepresented.

[gill1109]

...you can not substitute actual outcomes from a different set of particles, for counterfactual outcomes within a single set of particles.

Now where on earth do you see in this very clear sentence, written in your own native language, even a hint of a denial of realism or counterfactual definiteness?

Thank you Joy! The point has been so clearly stated that it is actually a scandal that it continues to be twisted and misrepresented.

I see more moving of goal-posts - earlier Michel vehemently attacked the notion of counterfactual definiteness, he more or less called it a contradiction in terms. Now suddenly Joy says it's fine, and Bohr thought so too, so suddenly Michel has no more objection any more.

But what is Joy talking about? Apparently someone said: "you can not substitute actual outcomes from a different set of particles, for counterfactual outcomes within a single set of particles". No you can't. And as far as I know, nobody ever proposed to do that! So whoever thought that someone else was doing that, has clearly totally misunderstood what was going on. (If this wasn't a deliberate "straw-man" trick).

[minkwe]

earlier Michel vehemently attacked the notion of counterfactual definiteness

This never happened. You must be living in an alternate universe. Have you been hanging around MWI'ers lately?

"you can not substitute actual outcomes from a different set of particles, for counterfactual outcomes within a single set of particles". No you can't. And as far as I know, nobody ever proposed to do that! So whoever thought that someone else was doing that, has clearly totally misunderstood what was going on.

Huh? Really?

The integrals on the right-hand side cannot easily be added when ΛAC′ =/= ΛAD′ , since we
are taking expectations over different ensembles ΛAC′ and ΛAD′ , with respect to different
probability measures.
The problem here is that the ensemble on which the correlations are evaluated changes
with the settings, while the original Bell inequality requires that they stay the same. In effect,
the Bell inequality only holds on the common part of the four different ensembles ΛAC′ , ΛAD′ ,
ΛBC′ , and ΛBD′ , i.e., for correlations of the form
E(AC′|ΛAC′ ∩ ΛAD′ ∩ ΛBC′ ∩ ΛBD′ ). (8)
Unfortunately our experimental data comes in the form
E(AC′|ΛAC′),

Consider now the following experimental set-up.
...
In each run, Alice and Bob are each sent one of a new pair of particles in the singlet state. While their particles are en route to them, they each toss a fair coin in order to choose one of their two measurement directions. In total 4N times, Alice observes either A = 1 or A' = 1 say, and Bob observes either B = 1 or B' = 1. At the end of the experiment, four "correlations" are calculated; these are simply the four sample means of the products AB, AB', A'B and A'B'. Each correlation is based on a different subset, of expected size N runs, and determined by the 8N fair coin tosses.

[gill1109]

Where does it say that actual outcomes from a different set of particles, are substituted for counterfactual outcomes within a single set of particles?

There is no substitution of any outcomes (factual or counterfactual) between different particles.

About your earlier strong opinions on counterfactuals, you seem to have not only changed your mind but also conveniently forgotten what you wrote some days ago. (You gave us some lectures about philosophy)

[gill1109]

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 a substitution of theoretical mean values by
empirically observed averages. And there is a "fair sampling" assumption,
aka no-conspiracy, or freedom. So statistical error has to be allowed for,
and 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.

[minkwe]

Where does it say that actual outcomes from a different set of particles, are substituted for counterfactual outcomes within a single set of particles?

Please can you explain how you demonstrate that QM violates the CHSH or do you now claim it doesn't?
Please can you explain how you demonstrate that EPR experiments violate the CHSH or do you now claim that they don't?

You haven't understood anything I've been saying OR you understand but just want to deceive others by deliberately creating confusion.

[minkwe]

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 a substitution of theoretical mean values by
empirically observed averages.

The theoretical mean values are calculated from a single set, the inequalities contain 4 correlations from a single set only one of which can be measured, the others therefore being counterfactual (counterfactual correlations from a single set), and the inequalities are only valid for a single set. You admit this in your LG paper:

The problem here is that the ensemble on which the correlations are evaluated changes
with the settings, while the original Bell inequality requires that they stay the same. In effect,
the Bell inequality only holds on the common part of the four different ensembles

The empirical values are calculated from outcomes measured from 4 disjoint sets (actual correlations from 4 different sets of particles). It is impossible to not have disjoint sets in the experiments, because a single particle pair can only be measured once. In other words, the common part of the 4 different ensembles in all EPR experiments is a null set, the sets of particles are disjoint! You do not deny this in your other paper:

In each run, Alice and Bob are each sent one of a new pair of particles in the singlet state. While their particles are en route to them, they each toss a fair coin in order to choose one of their two measurement directions. In total 4N times, Alice observes either A = 1 or A' = 1 say, and Bob observes either B = 1 or B' = 1. At the end of the experiment, four "correlations" are calculated; these are simply the four sample means of the products AB, AB', A'B and A'B'. Each correlation is based on a different subset, of expected size N runs, and determined by the 8N fair coin tosses.

The 4 QM correlations are predicted for an experimental situation with 4 disjoint sets of particles, just like in the experiment.

Your claim that nobody is doing that is obviously false. Everyone who claims that any experiment has violated the CHSH is doing that, you have. Any one who claims that QM violates the CHSH is doing that, you have. You do not know what you are talking about. Study what I'm saying carefully before you embarrass yourself further.

[gill1109]

Where does it say that actual outcomes from a different set of particles, are substituted for counterfactual outcomes within a single set of particles?

Please can you explain how you demonstrate that QM violates the CHSH or do you now claim it doesn't?
Please can you explain how you demonstrate that EPR experiments violate the CHSH or do you now claim that they don't?

You haven't understood anything I've been saying OR you understand but just want to deceive others by deliberately creating confusion.

Now at last you say something I do understand.

Indeed, I haven't understood anything you've been saying!

You clearly haven't understood anything I have been saying!

According to QM, EPR experiments might violate CHSH. Please read Bell (1965).

So far, no experiment has been done which both violated CHSH and was so stringently performed, that a local realist explanation could not be ruled out. But the top experimentalist groups are working towards this "holy grail" and people seem to think it will be done within five years.

[gill1109]

Your claim that nobody is doing that is obviously false. Everyone who claims that any experiment has violated the CHSH is doing that, you have. Any one who claims that QM violates the CHSH is doing that, you have. You do not know what you are talking about. Study what I'm saying carefully before you embarrass yourself further.

You are talking nonsense. I suggest you carefully read - in detail - sections 2 and 9 of my recent paper.

[gill1109]

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.

[minkwe]

Indeed, I haven't understood anything you've been saying!

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.

[gill1109]

Indeed, I haven't understood anything you've been saying!

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.

I already read Adenier, and I already read Hess and de Raedt. I understand them perfectly well.

Please read sections 2 and 9 of my paper, carefully.

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.