Thoughts about Bell, Bohm, Christian, et al.

[minkwe]

For those who failed the exam, let us do a review the main points:

1. There is no "locality assumption" in Bell's derivation of his inequalities. None whatsoever, despite repeated noises about "locality".

- implies settings independence, not locality. It is possible to have , where represents a non-local hidden variable. Moreover, it is possible to have settings dependence even if the whole experimental setup is local and within each others light cones such that , as explained in this post
- Secondly, setting indepdendence is irrelevant for the derivation anyway because one could eliminate hidden variables (local or non-lcoal) completely and still proceed to derive the inequality, since the expectation value of the paired product can be calculated for any valid probability measure. This has been clearly explained in this post.



, Since
and after factorizing out , remembering that we get


The second term on the right is .

Therefore, any insistence that locality is required is simply poppycock, and a waste of time.

2. The counterfactual definiteness assumption invoked by Bell applies to QM as well. Bell himself uses it on page 1 to make a QM argument.

- 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..
- Bell's 2nd and 3rd sentence in paragraph 2 of page 1, applies CFD to quantum mechanics as follows: If Alice measures along "a" and obtained +1, then if Bob were to measure the sister particle along "a" he must obtain -1. Clearly, Bell believes and QM states that the measurement that was not performed has a single definite value. In fact, CFD applies to any theory that makes predictions. Any suggestion otherwise reflects lack of thinking ability, as it can easily shown that a prediction for an experiment which ends up not being done, is counterfactually definite. No theory is immune to this, including QM.

3. Bell's inequality relates one actual measurement, to two counterfactual measurements which could have been done but weren't.

- Bell invokes CFD in his derivation starting on Page 406 where he states that "it follows that c is another unit vector". Note, we have a pair of particles, one is measured along "a", the other is measured along "b". Bell says it follows that "c" is another unit vector, but we don't have any other particles to measure along "c". Therefore "c" is a counterfactual axis (what we could have measured but didn't). This is also revealed in the above derivation, by the use of the same index for all the summation terms, reflecting the fact that Bell is always looking at the outcomes for the same pair of particles along the three axes, one of which must be counterfactual. Futhermore, the factorization of outcomes from both terms in the summation/integral again reveals that it is always the same pair of particles measured at 3 axes, one of which must be counterfactual. Therefore, any terms in the final inequality which contain "c", MUST be counterfactual terms, ie .
- Therefore Bell's inequality is a relationship between one actual expectation value and two counterfactual expectation values .

4. Bell's inequality can not be derived if we do not assume counterfactual results, but instead use actual independent measurements .

- It does not apply to three actual expectation values because it can not be derived starting from those.
--> DEAD END. No way to derive P(b,c) on the RHS therefore no way to derive the inequality

Therefore, the following is also poppycock:

Starting from realism and Einstein locality, we can prove Bell's inequality.
Bell's inequality is violated.
Thus, "local realism" (Einstein-local realism would be more accurate) is falsified.

If locality is not required to obtain the inequalities, there is no reasonable way for a reasonable person to conclude that violations of the inequalities falsifies locality. [emphasis on reasonable] Thus poppycock.

[FrediFizzx]

"Bell's inequality" is equation (15) in his paper. "Bell's theorem" is a result of combining "Bell's inequality" with the predictions of Quantum Mechanics for and then concluding that since the results violate the inequality, one of assumptions required to obtain the inequality must be false.

Of course, Bell's theorem is the theorem that local realistic theories fulfill the Bell's inequalities. Considerations about QM are, of course, part of Bell's paper, but not of Bell's theorem.

From https://en.wikipedia.org/wiki/Bell's_theorem,

"Bell himself wrote: "If [a hidden variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This is what the theorem says." John Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, 1987, p. 65."

So you are wrong again.

[FrediFizzx]

If locality is not required to obtain the inequalities, there is no reasonable way for a reasonable person to conclude that violations of the inequalities falsifies locality. [emphasis on reasonable] Thus poppycock.

Didn't De Raedt, et al, show that Boole obtained the inequality from a purely mathematical standpoint?

[Schmelzer]

From https://en.wikipedia.org/wiki/Bell's_theorem,

"Bell himself wrote: "If [a hidden variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This is what the theorem says." John Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, 1987, p. 65."

So you are wrong again.

This is a nice informal summary of the consequences of Bell's theorem, given that everybody knows what QM predicts.
But the theorem is the part which proves the BI (15), thus, is about local realistic theories, and there is no reason to even mention that such an animal as QM exists for proving the theorem.

Therefore, any insistence that locality is required is simply poppycock, and a waste of time.
...
Bell's 2nd and 3rd sentence in paragraph 2 of page 1, applies CFD to quantum mechanics as follows: If Alice measures along "a" and obtained +1, then if Bob were to measure the sister particle along "a" he must obtain -1. Clearly, Bell believes and QM states that the measurement that was not performed has a single definite value. In fact, CFD applies to any theory that makes predictions.

Let's see what Bell writes:

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 just actually be predetermined.

So, Bell makes an assumption about locality, and, using this assumption, derives that the value is predetermined.

Then, you obviously did not get the point, of course Bell uses the CFD in his proof. But the result is about averages, and these averages can be measured without measuring P(a,b), P(a,c) and P(b,c) on the same particles. So, it is the proof which uses CFD, but the BI is not about them.

Any suggestion otherwise reflects lack of thinking ability, as it can easily shown that a prediction for an experiment which ends up not being done, is counterfactually definite. No theory is immune to this, including QM.

The Gurus of the new, revolutionary science obviously cannot argue without primitive insults, ok, I'm used to such things, modern democratic education leads to similar problems in all other domains too. You can, of course, show whatever you want about predictions, but QM does not predict the results (except in very special situations) but only probabilities.

[Schmelzer]

Didn't De Raedt, et al, show that Boole obtained the inequality from a purely mathematical standpoint?

I haven't read de Readt and Boole about this, but of course, it is quite trivial in a classical situation where you have no doubt that the third value c exists to prove the BI, without any reference to any locality.

As I have explained, the question which assumptions are "physically necessary" to prove the BI is nonsensical. And there is no question that one can invent assumptions so that one can prove the BI which do not use whatever you don't want to have used. The only reasonable question is if Bell has used locality, and this is obvious from the text.

[FrediFizzx]

From https://en.wikipedia.org/wiki/Bell's_theorem,

"Bell himself wrote: "If [a hidden variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This is what the theorem says." John Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, 1987, p. 65."

So you are wrong again.

This is a nice informal summary of the consequences of Bell's theorem, given that everybody knows what QM predicts.
But the theorem is the part which proves the BI (15), thus, is about local realistic theories, and there is no reason to even mention that such an animal as QM exists for proving the theorem.

Do you have a reference for your statement, "But the theorem is the part which proves the BI (15)..."? I gave a reference for mine. So Michel is right, you (and others) are confused as to what Bell's theorem actually is it would seem. I don't see how any definition of what the theorem is can be better than what Bell claims it to be.

[minkwe]

If locality is not required to obtain the inequalities, there is no reasonable way for a reasonable person to conclude that violations of the inequalities falsifies locality. [emphasis on reasonable] Thus poppycock.

Didn't De Raedt, et al, show that Boole obtained the inequality from a purely mathematical standpoint?

Indeed. It was Boole who discovered those inequalities not Bell, and from a purely mathematical standpoint, which means their violation points to mathematical error and not such physical concepts as locality.

You can find more details in :
J.Comp.Theor.Nanosci. 8, 1011 (2011)
http://arxiv.org/pdf/0901.2546v2
This is a huge, and very thorough paper.

The central result of this paper is that the necessary conditions and the proof of the inequalities of Boole for n-tuples of
two-valued data (see Section II) can be generalized to real non negative functions of two-valued variables (see Section III) and to quantum theory of two-valued dynamical variables (see Section IV). The resulting inequalities, that we refer to as extended Boole-Bell inequalities (EBBI) for reasons explained in the Introduction and in Section III, have the same form as those of Boole and Bell. Equally central is the fact that these EBBI express arithmetic relations between numbers that can never be violated by a mathematically correct treatment of the problem: These inequalities derive from the rules of arithmetic and the non negativity of some functions only. A violation of these inequalities is at odds with the commonly accepted rules of arithmetic or, in the case of quantum theory, with the commonly accepted postulates of quantum theory
...
A violation of the EBBI cannot be attributed to influences at a distance. The only possible way that a violation could arise is if grouping is performed in pairs (see Section VII A).

In the original EPRB thought experiment, one can measure pairs of data only, making it de-facto impossible to use Boole’s inequalities properly. This obstacle is removed in the extended EPRB thought experiment discussed in Section VI C. In this extended EPRB experiment, one can measure both pairs and triples and consequently, it is impossible for the data to violate Boole’s inequalities. This statement is generally true: It does not depend on whether the internal dynamics of the apparatuses induces some correlations among different triples or that there are influences at a distance. The fact that this experiment yields triples of two-valued numbers is sufficient to guarantee that Boole’s inequalities cannot be violated

And a different perspective in :
Quantum Matter, Volume 3, Number 6, December 2014, pp. 499-504(6)
https://hal.archives-ouvertes.fr/hal-00824124/document

It was shown in [1], cited in the sequel as DRHM, that upon a correct use of the respective statistical data, the celebrated Bell inequalities cannot be violated by quantum systems. This paper presents in more detail the surprisingly elementary, even if rather subtle related basic argument in DRHM
...

The inequalities (17) are purely mathematical. In particular, their proof depends in absolutely no way on anything else, except the mathematical
properties of the set Z of positive and negative integers, set seen as a linearly ordered ring, [9].
As for the inequalities (16), they are a direct mathematical consequence of the inequalities (17), and thus again, their proof depends in absolutely no way on anything else, except the mathematical properties of the set R of real numbers, set seen as a linearly ordered field, [9].
It is, therefore, bordering on the amusing tinted with the ridiculous, when any sort of so called “physical” meaning or arguments are enforced upon these inequalities - be it regarding their proof, or their connections with issues such as realism and locality in physics - and are so enforced due to a mixture of lack of understanding of rather elementary and quite obviously simple mathematics

For those who have been following along, note that the Bell inequalities require triples of outcomes for each event , one of which is counterfactual, in order to derive the inequality, while for all claimed violations by QM and experiments, they always use pairs of outcomes for each event: they measure one set of pairs to calculate , a different set of pairs to calculate to calculate , and yet a different set of pairs to calculate to calculate . This is the mathematical error De Raedt et al are talking about. And it is the same mathematical error as deriving an inequality using counterfactual expectations, and trying to test it using actually measured expectation values. It is as stupid as expecting that when if Alice measures along "a" and obtains +1 for event , When Bob measures along "a" for event he MUST observe -1, and vice versa. It really is that stupid.

[minkwe]

But the theorem is the part which proves the BI (15)

I see that there are still some who do not know what "Bell's theorem" is.

Bell's theorem states that since the predictions of Quantum Mechanics violate Bell's inequalities, it is impossible to find a local theory which reproduces those predictions of quantum mechanics.

To prove Bell's theorem, first the inequalities are derived, claiming that only local theories can give those inequalities. Then, the expectation values are calculated from QM, and substituted into the inequalities, and a violation is obtained. Then, it is claimed that since local theories imply the inequalities, and QM violates the inequalities, therefore local theories and QM are incompatible.

However, we now know that even though the inequalities are valid, and Bell claimed to be invoking locality, no concept of locality carries forward into his equations. Simply invoking "locality" in the text is not enough if what is encoded in the equations, is completely devoid of a locality assumption as we have seen. Besides, we have seen that locality is not required at all to derive the inequalities. And basic logic tells us, if it is not required, then the negation of the inequalities has absolutely no impact on locality.

[Schmelzer]

This is a nice informal summary of the consequences of Bell's theorem, given that everybody knows what QM predicts.
But the theorem is the part which proves the BI (15), thus, is about local realistic theories, and there is no reason to even mention that such an animal as QM exists for proving the theorem.

Do you have a reference for your statement, "But the theorem is the part which proves the BI (15)..."?

What about common sense?

The BI are (15), and the theorem is what proves them. Simple common sense.

Anyway, it is irrelevant what you name "Bell's theorem". But I can explain you why I think it is reasonable not to incorporate QM into the theorem. The very point of the theorem is that the BIs can be falsified by observation. And that after this one does not have to believe that QM is true to conclude that Einstein-causal realism is dead.

The Wiki page you have posted makes, BTW, the usual error to present the proof as if CFD was assumed instead of derived from the EPR argument.

[FrediFizzx]

This is a nice informal summary of the consequences of Bell's theorem, given that everybody knows what QM predicts.
But the theorem is the part which proves the BI (15), thus, is about local realistic theories, and there is no reason to even mention that such an animal as QM exists for proving the theorem.

Do you have a reference for your statement, "But the theorem is the part which proves the BI (15)..."?

What about common sense?

The BI are (15), and the theorem is what proves them. Simple common sense. Anyway, it is irrelevant what you name "Bell's theorem".

Michel already has shown that you are wrong about that. Correct, Bell's theorem and the inequality (15) are indeed irrelevant for physics. Pretty much common sense.

[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.