Thoughts about Bell, Bohm, Christian, et al.

[minkwe]

There is one more piece of evidence which should put the final nail in the coffin. For those of you who remember my simulation epr-simple (https://github.com/minkwe/epr-simple/), which is an event-by-event simulation that violates the CHSH while reproducing the QM correlations. Now there are a lot of things detractors would like to focus on about that simulation but there is a hidden gem, which I had revealed on these forums (viewtopic.php?f=6&t=21&start=20) a while back and nobody was really interested. A few things to remember before I reveal it again:

1. Everything we just discussed about Bell's inequalities, applies to the CHSH inequality. The only difference being that instead of a single counterfactual axis "c", we now have two counterfactual axes "c" and "d".
2. Therefore the inequality

contains one actual term , and three counterfactual terms , while the expectation values calculated from QM, and measured in experiments , all represent actual values, none of which is counterfactual, meaning each measured on a distinct independent set of particle pairs.
3. It is impossible to measure the same set of particle pairs more than once, it is impossible to measure counterfactual expectation values. But in a simulation, it can easily be done because we can always reproduce the exact same conditions (by saving and restoring random number seeds) and simply cloning the particle pairs into any number of identical pairs we like at any number of "counterfactual" axes we like.
4. In the original "epr-simple", just like in actual experiments and QM, each of the expectation values were calculated from a different set of particle pairs, with no counterfactuals.

You can probably guess where I'm going with this then: What will happen if we took epr-simple, and instead of calculating the actual Expectation values for 4 different sets of particle pairs, let us calculate all 4 expectation values from the same set of particles, such that one of them correspond to the actual one, and the other 3 correspond to the counterfactual ones. No other modification will be done to the simulation. Here is how we will do it:

* 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 the original simulation without any counterfactual results.
* The next step of data analysis will involve using all 4 outcomes for calculating the correlations. Such that we use Alice and Bob to calculate E(a,b), Cindy and Bob to calculate E(c,b), Alice and Dave to calculate E(a,d) and Cindy and Dave to calculate E(c,d). This is equivalent to the way the inequality was derived with one actual and 3 counterfactual correlations. Since Cindy and Dave are counterfactual stations, only E(a,b) is actual, the rest are counterfactual.

Here are the results. The QM values are included for comparison:

===== Using only the ('alice', 'bob') data pair (No counterfactual)===
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 (No counterfactual)===
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 (No counterfactual)===
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 (No counterfactual) ===
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 (1-Actual 3-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

Notice anything?
In terms of De Raedt's argument, we notice that there is a violation whenever we use 4 sets of pairs , but you will also notice that if we use a single set of quadruples , the inequality is not be violated.

Aside: For those not familiar with epr-simple, who may be confused by me saying we have 4 sets of pairs when we use just a pair of stations such as (Alice, Bob), or (Cindy, Dave), etc, remember that when using just two stations, like in real experiments, with two particles arriving at a time, and settings being changed randomly, at the end of the experiment, we have to split a set of outcomes into the set which were measured at settings , and same for , and , the 4 sets of particle pairs are disjoint. However, in the case when we use all 4 stations with two extra ghost particles, we measure each particle pair simultaneously at 4 settings, the exact same set of particles is measured at setting pairs , thus we have just a single set of quadruples of outcomes .

It should be clear by now that the reason for the violation is the absence of counterfactual terms. Not that CFD as a concept is wrong, but simply due to the fact that there are no counterfactual terms in the experiments being used to claim violation. Duh.

[minkwe]

Given everything I have explained so far, I believe I have backed up my initial claim that:

... the Bell proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it. It’s not just flawed, it’s silly. If you look at the assumptions it made, it does not hold up for a moment. It’s the work of a mathematician, and he makes assumptions that have a mathematical symmetry to them. When you translate them into terms of physical disposition, they’re nonsense. You may quote me on that: the proof of Bell is not merely false but foolish.

If after understanding the arguments presented here, anybody still believes Bell's theorem is true, I would like to examine what is in their coffee.

[Schmelzer]

There is one more piece of evidence which should put the final nail in the coffin. For those of you who remember my simulation epr-simple (https://github.com/minkwe/epr-simple/), which is an event-by-event simulation that violates the CHSH while reproducing the QM correlations.

What will happen if we took epr-simple, and instead of calculating the actual Expectation values for 4 different sets of particle pairs, let us calculate all 4 expectation values from the same set of particles, such that one of them correspond to the actual one, and the other 3 correspond to the counterfactual ones. No other modification will be done to the simulation.

Code: Select all

A(a,λ) = sign(-1ⁿ cos n(a − e)) if |cos n(a − e)| > p, 0 otherwise
B(b,λ) = sign(-1ⁿ cos n(b − e')) if |cos n(b − e')| > p, 0 otherwise


If `|C| > p` the particle goes through. Every particle which goes through the filter is detected by one of the two channels.

As usual 0 values which depend on a, b, and define it the detector works - a classical detector loophole. So, in itself the violations are not interesting at all.

Notice anything?
In terms of De Raedt's argument, we notice that there is a violation whenever we use 4 sets of pairs , but you will also notice that if we use a single set of quadruples , the inequality is not be violated.

Nothing strange, if one applies the criteria which exclude "bad" choices of a,b, to all four directions a,b,c,d, at the same time, the original independence of the choice between a, b, c, d is recovered. Once this is what one needs to prove the inequalities, no wonder that the inequality works.

[minkwe]

Now there are a lot of things detractors would like to focus on about that simulation

Just like I suspected, the detractors will jump on "detection loophole", and miss completely the whole point of my previous post .

Code: Select all

A(a,λ) = sign(-1ⁿ cos n(a − e)) if |cos n(a − e)| > p, 0 otherwise
B(b,λ) = sign(-1ⁿ cos n(b − e')) if |cos n(b − e')| > p, 0 otherwise


As usual 0 values which depend on a, b, and define it the detector works - a classical detector loophole. So, in itself the violations are not interesting at all.

Anyone who would look at those equations, and see "0 values which depend on a, b" can not read mathematics.

Nothing strange, if one applies the criteria which exclude "bad" choices of a,b, to all four directions a,b,c,d, at the same time, the original independence of the choice between a, b, c, d is recovered.

Huh? There are no "good" or "bad" choices in epr-simple, there are no "all four directions "a,b,c,d" except for the ghost case with Cindy and Dave added. Again you don't know what you are talking about. Two particles leave the source one heads towards Alice, where outcome

Code: Select all

A(a,λ) = sign(-1ⁿ cos n(a − e)) if |cos n(a − e)| > p, 0 otherwise

is calculated.
The other heads towards Bob, were outcome

Code: Select all

B(b,λ) = sign(-1ⁿ cos n(b − e')) if |cos n(b − e')| > p, 0 otherwise

is calculated.

The inequalities require counterfactual outcomes to derive. They can never be violated by counterfactual expectation values, ever, with or without loopholes. The loophole business is another misguided franchise, and we can go through them one by one too if you like. In short, there is just one loophole to rule them all, and it is a mathematical one, ie the use of actual expectation values, where counterfactual ones should be used. This loophole is fatal. It is impossible to close for a performable experiment.

[Heinera]

3. It is impossible to measure the same set of particle pairs more than once, it is impossible to measure counterfactual expectation values. But in a simulation, it can easily be done because we can always reproduce the exact same conditions (by saving and restoring random number seeds) and simply cloning the particle pairs into any number of identical pairs we like at any number of "counterfactual" axes we like.

Good. So I take it that we now agree that in a simulation of a LHV model, the calculated correlations can on average (i.e. with statistical significance) never beat the inequality in Bell's paper?

[FrediFizzx]

3. It is impossible to measure the same set of particle pairs more than once, it is impossible to measure counterfactual expectation values. But in a simulation, it can easily be done because we can always reproduce the exact same conditions (by saving and restoring random number seeds) and simply cloning the particle pairs into any number of identical pairs we like at any number of "counterfactual" axes we like.

Good. So I take it that we now agree that in a simulation of a LHV model, the calculated correlations can on average never beat the relevant Bell inequality?

What is the point? Michel has once again shown Bell's theorem and inequality are irrelevant for physics. QM can't even "beat" the relevant Bell inequality. You really need to go back and carefully study what he has posted here.

[Schmelzer]

Just like I suspected, the detractors will jump on "detection loophole", and miss completely the whole point of my previous post .

Code: Select all

A(a,λ) = sign(-1ⁿ cos n(a − e)) if |cos n(a − e)| > p, 0 otherwise
B(b,λ) = sign(-1ⁿ cos n(b − e')) if |cos n(b − e')| > p, 0 otherwise


As usual 0 values which depend on a, b, and define it the detector works - a classical detector loophole. So, in itself the violations are not interesting at all.

Anyone who would look at those equations, and see "0 values which depend on a, b" can not read mathematics.

I see that if the value is zero depends on |cos n(a − e)| > p or not, resp. |cos n(b − e')| > p or not, thus, on a and b.

Huh? There are no "good" or "bad" choices in epr-simple, there are no "all four directions "a,b,c,d" except for the ghost case with Cindy and Dave added. Again you don't know what you are talking about. Two particles leave the source one heads towards Alice, where outcome

Code: Select all

A(a,λ) = sign(-1ⁿ cos n(a − e)) if |cos n(a − e)| > p, 0 otherwise

is calculated.
The other heads towards Bob, were outcome

Code: Select all

B(b,λ) = sign(-1ⁿ cos n(b − e')) if |cos n(b − e')| > p, 0 otherwise

is calculated.

Yes, and if this or the other value gives 0, the particle goes not through. This is the "bad choice", and opens the detection loophole. Once you know that this simulation simply uses the detection loophole, why you propose it here to argue that

... the Bell proof, if you actually come to grips with it, falls apart in your hands!

??? Given that it uses a well-known loophole, it gives exactly nothing against Bell's theorem.

The inequalities require counterfactual outcomes to derive.

And the existence of counterfactual outcomes is derived using the EPR argument in the first part. So, of course, a triviality.

They can never be violated by counterfactual expectation values, ever, with or without loopholes.

If you mean that if you use all four values for the evaluation, of course.

The loophole business is another misguided franchise, and we can go through them one by one too if you like. In short, there is just one loophole to rule them all, and it is a mathematical one, ie the use of actual expectation values, where counterfactual ones should be used. This loophole is fatal. It is impossible to close for a performable experiment.

But, given that the CFD is derived, one can use them to prove the inequalities, and, then, use the expectation values obtained independently to find violations. This, of course, allows for various loopholes. Your example uses the detection loophole. And this is well-known and acknowledged.

[FrediFizzx]

Just like I suspected, the detractors will jump on "detection loophole", and miss completely the whole point of my previous post .

Code: Select all

A(a,λ) = sign(-1ⁿ cos n(a − e)) if |cos n(a − e)| > p, 0 otherwise
B(b,λ) = sign(-1ⁿ cos n(b − e')) if |cos n(b − e')| > p, 0 otherwise


As usual 0 values which depend on a, b, and define it the detector works - a classical detector loophole. So, in itself the violations are not interesting at all.

Anyone who would look at those equations, and see "0 values which depend on a, b" can not read mathematics.

I see that if the value is zero depends on |cos n(a − e)| > p or not, resp. |cos n(b − e')| > p or not, thus, on a and b.

Huh? There are no "good" or "bad" choices in epr-simple, there are no "all four directions "a,b,c,d" except for the ghost case with Cindy and Dave added. Again you don't know what you are talking about. Two particles leave the source one heads towards Alice, where outcome

Code: Select all

A(a,λ) = sign(-1ⁿ cos n(a − e)) if |cos n(a − e)| > p, 0 otherwise

is calculated.
The other heads towards Bob, were outcome

Code: Select all

B(b,λ) = sign(-1ⁿ cos n(b − e')) if |cos n(b − e')| > p, 0 otherwise

is calculated.

Yes, and if this or the other value gives 0, the particle goes not through. This is the "bad choice", and opens the detection loophole. Once you know that this simulation simply uses the detection loophole, why you propose it here to argue that

... the Bell proof, if you actually come to grips with it, falls apart in your hands!

??? Given that it uses a well-known loophole, it gives exactly nothing against Bell's theorem.

The inequalities require counterfactual outcomes to derive.

And the existence of counterfactual outcomes is derived using the EPR argument in the first part. So, of course, a triviality.

They can never be violated by counterfactual expectation values, ever, with or without loopholes.

If you mean that if you use all four values for the evaluation, of course.

The loophole business is another misguided franchise, and we can go through them one by one too if you like. In short, there is just one loophole to rule them all, and it is a mathematical one, ie the use of actual expectation values, where counterfactual ones should be used. This loophole is fatal. It is impossible to close for a performable experiment.

But, given that the CFD is derived, one can use them to prove the inequalities, and, then, use the expectation values obtained independently to find violations. This, of course, allows for various loopholes. Your example uses the detection loophole. And this is well-known and acknowledged.

What is the point? The point is that it doesn't really matter. Michel has once again shown Bell's theorem and inequality are irrelevant for physics. QM can't even "beat" the relevant Bell inequality. You really need to go back and carefully study what he has posted here.

[Heinera]

What is the point? The point is that it doesn't really matter. Michel has once again shown Bell's theorem and inequality are irrelevant for physics

Relevance, like beauty, is in the eye of the beholder. But weren't we discussing correctness and not relevance here?

[FrediFizzx]

What is the point? The point is that it doesn't really matter. Michel has once again shown Bell's theorem and inequality are irrelevant for physics

Relevance, like beauty, is in the eye of the beholder. But weren't we discussing correctness and not relevance here?

Gibberish. We are discussing everything about how flawed Bell's theorem is.

[minkwe]

I see that if the value is zero depends on |cos n(a − e)| > p or not, resp. |cos n(b − e')| > p or not, thus, on a and b.
...
Yes, and if this or the other value gives 0, the particle goes not through. This is the "bad choice", and opens the detection loophole. Once you know that this simulation simply uses the detection loophole, why you propose it here to argue that

Seriously! I need to add you back to my ignore list, you apparently cannot read simple equations. Whether a particle is detected or not, is a completely local calculation. Please look at the equations again for your own sanity. There is no comparing of zeros in order to tell if a particle is detected or not.

And the existence of counterfactual outcomes is derived using the EPR argument in the first part,

But, given that the CFD is derived, one can use them to prove the inequalities, and, then, use the expectation values obtained independently to find violations. This, of course, allows for various loopholes. Your example uses the detection loophole. And this is well-known and acknowledged.

Are you joking? Counterfactural outcomes is "derived"? Do you know how nonsensical that sounds?

Please proceed to derive it let us see. I bet you will reveal in the process that either you do not understand what CFD means, nor that you do not understand the EPR argument. We shall see.

[minkwe]

3. It is impossible to measure the same set of particle pairs more than once, it is impossible to measure counterfactual expectation values. But in a simulation, it can easily be done because we can always reproduce the exact same conditions (by saving and restoring random number seeds) and simply cloning the particle pairs into any number of identical pairs we like at any number of "counterfactual" axes we like.

Good. So I take it that we now agree that in a simulation of a LHV model, the calculated correlations can on average (i.e. with statistical significance) never beat the inequality in Bell's paper?

Heine,
You too can't read?

===== Using only the ('alice', 'bob') data pair (No counterfactual)===
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 <- Violation

===== Using only the ('alice', 'dave') data pair (No counterfactual)===
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 <- Violation

===== Using only the ('cindy', 'bob') data pair (No counterfactual)===
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 <- Violation

===== Using only the ('cindy', 'dave') data pair (No counterfactual) ===
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 <- Violation

==== USING ALL FOUR (1-Actual 3-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 <- No Violation

Last case with 1-Actual and 3-Counterfactual expectations can never violate the CHSH, not even by an error margin of 1x10^-50. The other cases violate the inequality soundly by huge margins. They are all exactly the same simulation model.

Do you know what the difference is between them, Heine? This is a test. You should be able to pass it with flying colors after the last couple of days.

[Schmelzer]

Whether a particle is detected or not, is a completely local calculation. Please look at the equations again for your own sanity. There is no comparing of zeros in order to tell if a particle is detected or not.

No problem - for the detection loophole local calculation if a particle is "nice" or "bad" is sufficient. In mathematics, if are allowed to have 0 values, which make the experiment invalid, then to proof Bell's inequalities is impossible.

And the existence of counterfactual outcomes is derived using the EPR argument in the first part,

Are you joking? Counterfactural outcomes is "derived"? Do you know how nonsensical that sounds?
Please proceed to derive it let us see.

Not the outcomes themself, but their existence:

With the example advocated by Bohm and Aharonov, the EPR argument is the following. [...] Now we make the hypothesis, and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of , by previously measuring the same component of  , it follows that the result of any such measurement must actually be predetermined. [...] this predetermination implies the possibility of a more complete specification of the state. [...]

and this more complete specification of the state is (1), which, I hope, even in your understanding of CFD contains CFD.

I bet you will reveal in the process that either you do not understand what CFD means, nor that you do not understand the EPR argument. We shall see.

No problem, I'm already used to the fact that if there are no viable couterarguments, one will use "you do not understand"-claims, of course, without an explanation of the essential differences and why they matter in this context.

That there are big differences between your "understanding" of CFD and what the mainstream names CFD is quite obvious. Bell's understanding of "predetermined" is close to mainstream CFD, nor your CFD. Nonetheless, CFD is the closest thing in the language you use to Bell's "predetermined", and the difference does not seem to matter very much in this particular context.

[Schmelzer]

Last case with 1-Actual and 3-Counterfactual expectations can never violate the CHSH, not even by an error margin of 1x10^-50. The other cases violate the inequality soundly by huge margins. They are all exactly the same simulation model.

Do you know what the difference is between them, Heine? This is a test.

The simulation model uses the detection loophole, thus, allows the functions to have the result 0, in which case the experiment is simply rejected (if one names this "the detector has not worked" or differently does not matter).

The point of this detector loophole is that the rejection defined by depends on a, Thus, this can be used to select "nice" results for the pair (a,b) which are different from the "nice" results for the other pairs (a,c), (b,c), (b,d).

But in the last case, the symmetry is recovered, because what is choosen is for all n=a,b,c,d.

[minkwe]

and this more complete specification of the state is (1), which, I hope, even in your understanding of CFD contains CFD.

Stop hoping and show exactly what you mean.

That there are big differences between your "understanding" of CFD and what the mainstream names CFD is quite obvious.

Talk is cheap, why don't you explain why the following definitions are not mainstream enough for you, and after you have done that, it should be easy for you to show your claimed "obvious" difference between my definition of CFD, which you must state, and the mainstream definition, which you must also state clearly. Can you do that, or will you hide behind big empty claims?

- Counterfactual Definiteness is defined as: Wikipedia: In quantum mechanics, Counterfactual definiteness (CFD) is the ability to speak meaningfully of the definiteness of the results of measurements that have not been performed (i.e. the ability to assume the existence of objects, and properties of objects, even when they have not been measured).
Gill (http://arxiv.org/pdf/1207.5103v6.pdf): Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.
http://arxiv.org/pdf/1007.4281.pdf: the assumption that a measurement that was not performed had a single definite result..

But, given that the CFD is derived, one can use them to prove the inequalities

I'm waiting for the *derivation* of the CFD. And after you've shown the "derivation", you should also answer this question:

Is it or is it not true that:According to QM if Alice measures along "a" and obtains +1, and Bell measures along "b", Bell' would have obtained -1 had he also measured along "a" and vice versa.

[Schmelzer]

I'm waiting for the *derivation* of CFD.

See the Bell quote in http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=75&p=4413#p4411.

And after you've shown the "derivation", you should also answer this question:
Is it or is it not true that [b]According to QM if Alice measures along "a" and obtains +1, and Bell measures along "b", Bell' would have obtained -1 had he also measured along "a" and vice versa.

If Alice measures first, and obtains +1, and Bob later, then, yes, he would obtain -1.

If Bob measures first, the answer is less clear. By analogy, if, say, Alice and Bob have an agreement to say the opposite, once the other has already made a statement, but are free to make an own choice if they are first, the fact that Alice has chosen 1 being first tells nothing about what Bob would have chosen being first. Analogically, the fact what Alice has measured, given she has measured first, does not tell us anything about what would have happened if Bob would have measured first.

If one understands the question differently - we know, as a fact, that Alice has measured 1 given that Bob has measured a, then, of course, we can conclude that Bob has obtained -1. But this scenario is not exactly what you have asked about.

Whatever, even if you would have the complete description of what has happened in the whole history according to dBB theory, which contains much more information than QM (it is, last but not least, a deterministic hidden variable theory of QM), and the measured directions are a and b, nothing in this complete description defines the outcome which would have appeared if another c would have been measured, or what would have been the result if the first one who makes the measurement (say Bob) decides to measure the other value (a) instead.

and this more complete specification of the state is (1), which, I hope, even in your understanding of CFD contains CFD.

Stop hoping and show exactly what you mean.

What I mean is described nicely by Bell.

That there are big differences between your "understanding" of CFD and what the mainstream names CFD is quite obvious.

Talk is cheap, why don't you explain why the following definitions are not mainstream enough for you, and after you have done that, it should be easy for you to show your claimed "obvious" difference between my definition of CFD, which you must state, and the mainstream definition, which you must also state clearly. Can you do that, or will you hide behind big empty claims?

I don't have to do that much to support a little side remark. I have never seen a mainstream physicist thinking that CFD holds in QM, you seem to think this, that's sufficient to conclude that there must be a difference.

[minkwe]

According to QM if Alice measures along "a" and obtains +1, and Bob measures along "b", Bell' would have obtained -1 had he also measured along "a" and vice versa.

You conveniently avoided the question. Is the above statement true or false?

If Alice measures first, and obtains +1, and Bob later, then, yes, he would obtain -1.

Alice and Bob have already measured. You know that Alice measured along "a". You do not know what axis Bob measured along. Alice obtained +1. Is it or is it not true that According to QM, if Bob's measurement axis was along "a" he MUST have obtained -1.

That there are big differences between your "understanding" of CFD and what the mainstream names CFD is quite obvious.

Talk is cheap, why don't you explain why the following definitions are not mainstream enough for you, and after you have done that, it should be easy for you to show your claimed "obvious" difference between my definition of CFD, which you must state, and the mainstream definition, which you must also state clearly. Can you do that, or will you hide behind big empty claims?

- Counterfactual Definiteness is defined as: Wikipedia: In quantum mechanics, Counterfactual definiteness (CFD) is the ability to speak meaningfully of the definiteness of the results of measurements that have not been performed (i.e. the ability to assume the existence of objects, and properties of objects, even when they have not been measured).
Gill (http://arxiv.org/pdf/1207.5103v6.pdf): Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.
http://arxiv.org/pdf/1007.4281.pdf: the assumption that a measurement that was not performed had a single definite result..

I have never seen a mainstream physicist thinking that CFD holds in QM

Any blind man can claim, "I have never seen the sun, therefore it does not exist" Why don't you provide the mainstream of definition of "CFD" that you have actually seen.

[minkwe]

Whether a particle is detected or not, is a completely local calculation. Please look at the equations again for your own sanity. There is no comparing of zeros in order to tell if a particle is detected or not.

No problem - for the detection loophole local calculation if a particle is "nice" or "bad" is sufficient. In mathematics, if are allowed to have 0 values, which make the experiment invalid, then to proof Bell's inequalities is impossible.

Again there is no "nice", or "bad" in epr-simple, that you keep using those words reveals severe misunderstandings. A 0 value means the particle was not detected. What exactly is "bad" about that? What physical principle allows you to claim that all particles must be detected? Does QM say all particles must be detected?

allows the functions to have the result 0, in which case the experiment is simply rejected (if one names this "the detector has not worked" or differently does not matter).

Please think before you write, what rejection are you talking about in experiments expectation value is calculated as


see equation (1) of this Wikipedia page https://en.wikipedia.org/wiki/Bell_test_experiments

Now please tell me how exactly where you claim experiments are being rejected based on the 0 outcomes in that calculation. What exactly do you claim is rejected here that would have been different otherwise?

depends on a, Thus, this can be used to select "nice" results for the pair (a,b) which are different from the "nice" results for the other pairs (a,c), (b,c), (b,d).

Huh? The outcomes (a,b) are always different from the outcomes (a,c) with or without zero outcomes! The outcomes (a,b) always depend on both "a", and "b". The outcomes (a,c), (b,c), (b,d) are always different from each other, whether you have zero outcomes or not. Again, think before you write: I can replace your statement with:

depends on a, Thus, this can be used to select "nice" results for the pair (a,b) which are different from the "nice" results for the other pairs (a,c), (b,c), (b,d).

You are not making any sense, because you do not know what you are talking about.

[minkwe]

I'm waiting for the *derivation* of CFD.

See the Bell quote in http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=75&p=4413#p4411.

With the example advocated by Bohm and Aharonov, the EPR argument is the following. [...] Now we make the hypothesis, and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of , by previously measuring the same component of  , it follows that the result of any such measurement must actually be predetermined. [...] this predetermination implies the possibility of a more complete specification of the state. [...]

Where exactly in that passage is CFD defined or derived. You seem to think the paragraph represents a "derivation" of CFD, even though Bell himself does not claim that. Please start by presenting a "mainstream" definition of CFD, then explain exactly where in that paragraph CFD is derived.

[Schmelzer]

With the example advocated by Bohm and Aharonov, the EPR argument is the following. [...] Now we make the hypothesis, and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of , by previously measuring the same component of  , it follows that the result of any such measurement must actually be predetermined. [...] this predetermination implies the possibility of a more complete specification of the state. [...]

Where exactly in that passage is CFD defined or derived.

Bell names it differently (and I think more adequate) "predetermined". Whatever, some details follow about what this means, resulting in the formulas (1) and (2). And if one accepts that if (1) and (2) holds, then CFD holds for this particular experimental situation, then it means CFD has been derived using the EPR argument. If nor, I have misunderstood your understanding of CFD, but in this case I would not care about your understanding of CFD anymore, because the second part of Bell's proof needs only (1) and (2), and, in case this does not contain your CFD, your CFD is not necessary for the proof and your irrelevant hobby.

Feel free to find loopholes in this derivation of predetermination, (1) and (2), and replace the "has been derived" by "falsely claims to have derived" if you like, then we can argue about this. But common sense tells me that the use of words like "follows" and "implies" describe something what at least the author considers as a derivation.

If Alice measures first, and obtains +1, and Bob later, then, yes, he would obtain -1.

Alice and Bob have already measured. You know that Alice measured along "a". You do not know what axis Bob measured along. Alice obtained +1. Is it or is it not true that According to QM, if Bob's measurement axis was along "a" he MUST have obtained -1.

True.

why don't you explain why the following definitions are not mainstream enough for you

Why should I? They are.

I have never seen a mainstream physicist thinking that CFD holds in QM

Any blind man can claim, "I have never seen the sun, therefore it does not exist" Why don't you provide the mainstream of definition of "CFD" that you have actually seen.

No necessity. I see a difference in the conclusions - the mainstream says that there is no CFD in QM, you seem to think there is. It's not my job to find out where exactly you err, that's your problem. Maybe you misunderstand the definition, whatever else, I don't really care. I see the difference, have mentioned it to avoid misunderstandings (say, I say something about mainstream CFD, you interpret it as about your CFD), that's all.

Again there is no "nice", or "bad" in epr-simple, that you keep using those words reveals severe misunderstandings. A 0 value means the particle was not detected. What exactly is "bad" about that? What physical principle allows you to claim that all particles must be detected? Does QM say all particles must be detected?

Bell's proof requires that all particles must be detected, without this assumption the theorem cannot be proved. That's the detector efficiency loophole.

Please think before you write, what rejection are you talking about in experiments expectation value is calculated as

Of course, about the outcomes with a 0 value, which means "A 0 value means the particle was not detected".

Now please tell me how exactly where you claim experiments are being rejected based on the 0 outcomes in that calculation. What exactly do you claim is rejected here that would have been different otherwise?

Experiments where the particle was not detected are, of course, not in this sum. Thus, the corresponding initial values have been rejected.

depends on a, Thus, this can be used to select "nice" results for the pair (a,b) which are different from the "nice" results for the other pairs (a,c), (b,c), (b,d).

Huh? The outcomes (a,b) are always different from the outcomes (a,c) with or without zero outcomes! The outcomes (a,b) always depend on both "a", and "b". The outcomes (a,c), (b,c), (b,d) are always different from each other, whether you have zero outcomes or not.

The sum is over those a, b, which have values , . If you sum over those which have, additionally, also , resp. for B, you get a sum over a different subset of experiments, and even if the experimental outcomes themself are the same for all choicse in above sums, the sums will be different.