gill1109 wrote: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):

minkwe wrote: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.