Some people do not understand Counterfactual Definiteness

[gill1109]

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Gill's argument above was dismissed by Einstein when Bell was hardly seven years old. The additivity of expectation values simply does not hold for any hidden variable theories.
The Bell-test experiments are verifying Einstein's observation and ruling out the additivity of expectation values. This is the sad end of Bell's theorem. Sadly, it was a nonstarter.

Sorry, Joy, this argument by myself is *not* the argument that was dismissed by Einstein long, long ago. You are doing an "argumentum ad verecundiam" (argument by authority). That's a sign of weakness on your part. Especially since you don't reproduce Einstein's words and reasoning. You have not shown that there is anything wrong with *my* argument.
The Bell-test experiments confirm quantum mechanics and moreover generate results which cannot be explained by local realism. They certainly do not rule out additivity of expectation values. On the contrary, as my argument shows, the fact that they confirm quantum mechanics confirms the additivity of expectation values in quantum mechanics even of non-commuting observables.

Look at Einstein's argument which you yourself kindly reproduced on another thread. "Einstein then said that there is no reason why this premise should hold in a state not acknowledged by quantum mechanics if R, S etc. are not simultaneously measurable". Einstein admits that it does hold under a quantum mechanical state. It holds when we prepare a state in a state rho, one of the states acknowledged by quantum mechanics.

Sorry, Joy, you have to read the small print.

[Joy Christian]

.
Gill's argument above was dismissed by Einstein when Bell was hardly seven years old. The additivity of expectation values simply does not hold for any hidden variable theories.
The Bell-test experiments are verifying Einstein's observation and ruling out the additivity of expectation values. This is the sad end of Bell's theorem. Sadly, it was a nonstarter.

Sorry, Joy, this argument by myself is *not* the argument that was dismissed by Einstein long, long ago. You are doing an "argumentum ad verecundiam" (argument by authority). That's a sign of weakness on your part. Especially since you don't reproduce Einstein's words and reasoning. You have not shown that there is anything wrong with *my* argument.
The Bell-test experiments confirm quantum mechanics and moreover generate results which cannot be explained by local realism. They certainly do not rule out additivity of expectation values. On the contrary, as my argument shows, the fact that they confirm quantum mechanics confirms the additivity of expectation values in quantum mechanics even of non-commuting observables.

Look at Einstein's argument which you yourself kindly reproduced on another thread. "Einstein then said that there is no reason why this premise should hold in a state not acknowledged by quantum mechanics if R, S etc. are not simultaneously measurable". Einstein admits that it does hold under a quantum mechanical state. It holds when we prepare a state in a state rho, one of the states acknowledged by quantum mechanics.

Sorry, Joy, you have to read the small print.

You are entitled to your dogmatic slumber. Sleep well.

PS: It is best to leave this thread about CFD for Michel to finish. I have started a new thread about my claim that Bell-test experiments do not rule out local realism but Bell's implicit assumption of the additivity of expectation values in the proof of his theorem: viewtopic.php?f=6&t=474#p12968.
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[minkwe]

So, the first obligation of the proponents of Bell's theorem is to acknowledge that the additivity of expectation values is one of the implicit assumptions on which Bell's theorem depends.

Additivity of expectation values is not an issue in Bell's inequality.

I disagree. If you think the additivity of expectation values is not an assumption over and above Bell's other assumptions, then you should be able to derive it from the other assumptions.

I will give a silly example to explain why additivity of expectation values is not an issue in Bell's inequality. Let us assume that Alice and Bob each have a fair coin that they toss jointly and find either +1 or -1 as head and tails. They toss the coin many times and take note of their results say for Alice and . Define .

To evaluate we can choose two different methods, we can evaluate mean values first and then sum or we sum and then evaluate the mean



Passing from the second term to the third one does not involve a physical assumption. If there is an assumption here is that arithmetic laws are valid. That is exactly what is assumed in Bell's derivation when the terms are put under the same integral.

There is no problem here as in the case of von Neumann's theorem where it would mean that the sum of eigenvalues is the eigenvalue of the operators sum. Here there are no operators, that is a quantum mechanical issue the which does not correspond to a classical model.

The Bell inequality asks, what is the prediction of the classical model? Then, and independently the quantum mechanical prediction is calculated.

Bell-Kochen-Specker theorem is different, there the issue arises that we can not simply assume that eigenvalues of the sum is the equal to the sum of eigenvalues

Your example above is very silly and completely irrelevant. If you want a relevant coin-toss example, there is already one presented earlier in this thread that is directly comparable to the current situation. See viewtopic.php?f=6&t=463&sid=29c51abcfdaa1f3f63b69ff0e55744d6#p12485

[Justo]

Your example above is very silly and completely irrelevant. If you want a relevant coin-toss example, there is already one presented earlier in this thread that is directly comparable to the current situation. See viewtopic.php?f=6&t=463&sid=29c51abcfdaa1f3f63b69ff0e55744d6#p12485

I agree it is silly, however, it is relevant. You said earlier

The contradiction is present even on the left-hand side of 14a.

P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)"

The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.

You misinterpret the meanings of P(a,b) and P(a,c). They represent the results obtained through two different series of many experiments. P(a,b) represents the mean of a series of experiments realized with settings (a,b). P(a,c) represents the mean of a different series of experiments performed with settings (a,c).
Of course, in a given experiment you either use (a,b) or (a,c) but not both.

It is good that you already realized that your interpretation is meaningless. Now you have to make a little more effort to consider and realize that the rest of the scientific community is not so incredibly stupid to believe that such an interpretation could be correct.

[Justo]

Your example above is very silly and completely irrelevant. If you want a relevant coin-toss example, there is already one presented earlier in this thread that is directly comparable to the current situation. See viewtopic.php?f=6&t=463&sid=29c51abcfdaa1f3f63b69ff0e55744d6#p12485

Also, I agree your coin example is relevant. However, it reveals that maybe you do not understand the statistical meaning of probabilities. In your example your say that P(T) + P(H) = 1 is violated in your experiment. That would mean that the frequentist interpretation of probabilities is incorrect.
I am prepared to admit that I might be wrong. What makes a person a c****pot is not that he may be mistaken but that he is incapable of accepting that he is mistaken.

I will accept that your coin example is correct and that I am mistaken if Richard Gill decides whether your coin example is correct supposing that the experiment is done with the same coin, i.e., if the machine returns the coin unaltered after each trial.

Richar Gill is recognized as a statistical mathematician and I respect that, although he is not my friend and I disagree with him about the interpretation of the Bell inequality.

[gill1109]

I consider Justo to be my friend, I even think that he and I agree on many things! But anyway, I have many friends with whom I disagree about many things. I love argueing.

Minkwe wrote ‘The contradiction is present even on the left-hand side of 14a. P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)". The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.’

Sorry, this is nonsense. P(a, b) is a number. P(a, c) is another number. One is not prohibited from computing the difference between two numbers. Further assumptions were made. A correct mathematical argument allowed one *under those assumptions* to deduce something about the difference between those numbers. If you don’t like the answer, then the problem lies with the assumptions.

[minkwe]

Your example above is very silly and completely irrelevant. If you want a relevant coin-toss example, there is already one presented earlier in this thread that is directly comparable to the current situation. See viewtopic.php?f=6&t=463&sid=29c51abcfdaa1f3f63b69ff0e55744d6#p12485

Also, I agree your coin example is relevant. However, it reveals that maybe you do not understand the statistical meaning of probabilities. In your example your say that P(T) + P(H) = 1 is violated in your experiment. That would mean that the frequentist interpretation of probabilities is incorrect.
I am prepared to admit that I might be wrong. What makes a person a c****pot is not that he may be mistaken but that he is incapable of accepting that he is mistaken.

I will accept that your coin example is correct and that I am mistaken if Richard Gill decides whether your coin example is correct supposing that the experiment is done with the same coin, i.e., if the machine returns the coin unaltered after each trial.

Richar Gill is recognized as a statistical mathematician and I respect that, although he is not my friend and I disagree with him about the interpretation of the Bell inequality.

Then you probably do not understand the example. Please read it again, more carefully this time.

[gill1109]

Your example above is very silly and completely irrelevant. If you want a relevant coin-toss example, there is already one presented earlier in this thread that is directly comparable to the current situation. See viewtopic.php?f=6&t=463&sid=29c51abcfdaa1f3f63b69ff0e55744d6#p12485

Also, I agree your coin example is relevant. However, it reveals that maybe you do not understand the statistical meaning of probabilities. In your example your say that P(T) + P(H) = 1 is violated in your experiment. That would mean that the frequentist interpretation of probabilities is incorrect.
I am prepared to admit that I might be wrong. What makes a person a c****pot is not that he may be mistaken but that he is incapable of accepting that he is mistaken.

I will accept that your coin example is correct and that I am mistaken if Richard Gill decides whether your coin example is correct supposing that the experiment is done with the same coin, i.e., if the machine returns the coin unaltered after each trial.

Richar Gill is recognized as a statistical mathematician and I respect that, although he is not my friend and I disagree with him about the interpretation of the Bell inequality.

Then you probably do not understand the example. Please read it again, more carefully this time.

In your example, Michel, there are two experiments. One with the machine preset in one way, the other with the machine preset a different way. There is no reason whatsoever for the probabilities of outcomes with preset "H" to have anything whatever to do with the probabilities of outcomes with preset "T".

However, there are sound *physical* reasons why a carefully performed Bell-type experiment could be such that the probability distributions of joint outcomes with any pair of joint settings should be related to one another in the way specified by Bell (existence of functions A and B and probability measure rho such that, etc, etc). The reasons are because of the concept of local realism, which many physicists of Einstein's generation would have found perfectly natural; and for which moreover the QM model of the singlet state (EPR-B experiment) gives support; together with the constraints in timing and spatial configuration which Bell described in his Bertlmann's socks paper, and which could at last be actually implemented in 2015.

[minkwe]

In your example, Michel, there are two experiments. One with the machine preset in one way, the other with the machine preset a different way. There is no reason whatsoever for the probabilities of outcomes with preset "H" to have anything whatever to do with the probabilities of outcomes with preset "T".

Let us do some substation and see where your argument leads.

In the Bell Test Experiments, there are three experiments. One with the machine preset in one way, the others with the machine preset a different way. There is no reason whatsoever for the probabilities of outcomes with preset "(a,b)" to have anything whatever to do with the probabilities of outcomes with preset "(a,c)" or (b,c).

Using your line of argumentation, I could also argue that it's mathematics. I can place one number next to another number and add them up, what's the beef? There are also sound physical reasons why a carefully performed coin-toss experiment would allow those probabilities to be related to one another (existence of local functions h(.) and t(.) and rho(.) such that, etc, etc.

I hope you see the irony in your arguments about and vacuousness of your response. Focusing on the existence or lack thereof of a relationship between probabilities is missing the point. Contrary to your claim, there is in fact a relationship between those probabilities in the coin-toss machine. The point is that the correct relationship is P(H) + P(T) = 1.5 not P(H) + P(T) = 1. And the mistake made was to think it was the latter. This is exactly the same situation for Bell.

[gill1109]

In your example, Michel, there are two experiments. One with the machine preset in one way, the other with the machine preset a different way. There is no reason whatsoever for the probabilities of outcomes with preset "H" to have anything whatever to do with the probabilities of outcomes with preset "T".

Let us do some substation and see where your argument leads.

In the Bell Test Experiments, there are three experiments. One with the machine preset in one way, the others with the machine preset a different way. There is no reason whatsoever for the probabilities of outcomes with preset "(a,b)" to have anything whatever to do with the probabilities of outcomes with preset "(a,c)" or (b,c).

Using your line of argumentation, I could also argue that it's mathematics. I can place one number next to another number and add them up, what's the beef? There are also sound physical reasons why a carefully performed coin-toss experiment would allow those probabilities to be related to one another (existence of local functions h(.) and t(.) and rho(.) such that, etc, etc.

I hope you see the irony in your arguments about and vacuousness of your response. Focusing on the existence or lack thereof of a relationship between probabilities is missing the point. Contrary to your claim, there is in fact a relationship between those probabilities in the coin-toss machine. The point is that the correct relationship is P(H) + P(T) = 1.5 not P(H) + P(T) = 1. And the mistake made was to think it was the latter. This is exactly the same situation for Bell.

My arguments are not vacuous. I referred you to Bell’s arguments for his mathematical characterisation of local realism. I have written them up in my own words in recent publications.

If there are physical reasons why, in your example, it could be known in advance that P(H) + P(T) = 1.5, then a good statistician will know how to experimentally test them, or, assuming they are correct, use them to get a better statistical estimate of the two probabilities.

It’s a good example. The parallel can be taken further. The irony is that you haven’t apparently taken any notice of the physical reasoning, Einstein’s reasoning, which leads to the constraints on those correlations.

[gill1109]

PS of course, Michel, I could simply blame you for creating the confusion by your inadequate notation. If you had written P(H|”H”) and P(T|”T”), we wouldn’t be having this conversation. That’s a Counterfactual.

[minkwe]

PS of course, Michel, I could simply blame you for creating the confusion by your inadequate notation. If you had written P(H|”H”) and P(T|”T”), we wouldn’t be having this conversation. That’s a Counterfactual.

There is no confusion, the example is very clear. You are grasping.

[minkwe]

If there are physical reasons why, in your example, it could be known in advance that P(H) + P(T) = 1.5, then a good statistician will know how to experimentally test them, or, assuming they are correct, use them to get a better statistical estimate of the two probabilities.

You are missing the point completely. Please read it again. It's not about which relationship is correct. It's about the difference between counterfactual probabilities, and measured probabilities for the same experiment.

The parallel can be taken further. The irony is that you haven’t apparently taken any notice of the physical reasoning, Einstein’s reasoning, which leads to the constraints on those correlations.

Nope, again you aren't actually making a substantive point here, just handwaving.

1. You admit that Bell combines actual and counterfactual expectations in deriving a relationship although you refused to point out the counterfactual terms in equation 14.
2. You admit that the counterfactual relationship in my coin toss example is different from the empirical relationship.You think I should use different notation for both, I agree just like I also think you should use different notation for eq. 4 and 6 in your paper. That's the point of the example!
3. You haven't explained why you assume that the counterfactual relationship in Bell's theorem MUST be the same as the empirical one (same notation). You made vague mention of Einstein, and local functions not realizing that my coin toss machine is local realistic and governed by local functions also. All physical reasoning and assumptions that come before Bell's equation 14 is irrelevant to the point of the example. We are squarely focused on the introduction of counterfactual expectations in equation 14 and its implication. This is why I don't think you have understood the point at all, since you keep going back to Einstein and functions.

[Justo]

minkwe,
The correct probabilistic equation is P(H) + P(T) = 1. Let us say that for our coin P(H)=0.8. In the frequentist interpretation of probability, this means that if we perform N=100 trials we would obtain approximately N_H=80 heads, and in the limit


What probability theory tells us is that if perform another experiment and count tails instead of heads we will find that


To test whether this is true we must perform two different series of experiments, in one you count heads, and in the other, you count tails.
Interpreting counterfactually P(H) + P(T)= 1 is meaningless because it implies incompatible experiments. You either obtain H or T but you cannot obtain both. That is exactly the same reason for which the counterfactual interpretation of the Bell inequality is meaningless. Joy Christian is correct when he criticized that interpretation of the Bell inequality. However, he is wrong when ascribes that interpretation to John Bell.

[gill1109]

If there are physical reasons why, in your example, it could be known in advance that P(H) + P(T) = 1.5, then a good statistician will know how to experimentally test them, or, assuming they are correct, use them to get a better statistical estimate of the two probabilities.

You are missing the point completely. Please read it again. It's not about which relationship is correct. It's about the difference between counterfactual probabilities, and measured probabilities for the same experiment.

The parallel can be taken further. The irony is that you haven’t apparently taken any notice of the physical reasoning, Einstein’s reasoning, which leads to the constraints on those correlations.

Nope, again you aren't actually making a substantive point here, just handwaving.

1. You admit that Bell combines actual and counterfactual expectations in deriving a relationship although you refused to point out the counterfactual terms in equation 14.
2. You admit that the counterfactual relationship in my coin toss example is different from the empirical relationship.You think I should use different notation for both, I agree just like I also think you should use different notation for eq. 4 and 6 in your paper. That's the point of the example!
3. You haven't explained why you assume that the counterfactual relationship in Bell's theorem MUST be the same as the empirical one (same notation). You made vague mention of Einstein, and local functions not realizing that my coin toss machine is local realistic and governed by local functions also. All physical reasoning and assumptions that come before Bell's equation 14 is irrelevant to the point of the example. We are squarely focused on the introduction of counterfactual expectations in equation 14 and its implication. This is why I don't think you have understood the point at all, since you keep going back to Einstein and functions.

I did not handwave. I referred you to a published paper by a famous physicist who is extremely eloquent and has a nice sense of humour too. Please read it first. If you don’t understand, come and ask again, and I’ll refer you to my own most recent attempts to say the same thing in different words. In particular, I can point you to particular passages in https://arxiv.org/abs/2103.00225 (published in IEEE Access) and in https://arxiv.org/abs/2012.00719 (in preparation).

Could you please say which equations in whose papers you are talking about? Equations 4 and 6 in which paper of mine? Bell’s 14 in Bell (1964)? I see nothing “counterfactual” in Bell 1964. There is a physical assumption leading to a mathematical model. There are some mathematical derivations within the model, which lead to some conclusions concerning objects which physicists talk a lot about (“correlations”). The conclusions are not satisfied in certain experiments where, on the other hand, predictions of quantum mechanics are satisfied. So the physical assumption made by Bell is false.

I think you agree with that, too. Your own simulation experiments do not simulate Bell’s model. You agree that Bell’s model is wrong.

[Joy Christian]

https://arxiv.org/abs/2103.00225 (published in IEEE Access)...

Gill is lying again. The junk preprint he has linked is not published in IEEE Access. It has nothing to do with my 3-sphere model and it is unlikely to be published anywhere in current form.

Note also that Gill's junk preprint also makes his false and now discredited priority claim about the simulation codes presented in my paper https://ieeexplore.ieee.org/document/8836453.
.

[minkwe]

Could you please say which equations in whose papers you are talking about? Equations 4 and 6 in which paper of mine?

https://arxiv.org/pdf/1207.5103.pdf

[minkwe]

Justo, have you actually read the post talking about the coin-tossing machine example? It doesn't look like you have because you don't appear to understand it at all:

minkwe,
The correct probabilistic equation is P(H) + P(T) = 1.

Correct probability equation for what? Please be specific. It is easy to conflate different things when you are not being specific so please explain exactly what situation you are talking about. Or better just read the example more carefully to understand it.

Let us say that for our coin P(H)=0.8.

This doesn't make sense in the context of my example. This is why I don't think you understand it. There is no P(H) for a coin in my example, there is P(H) for the outcome of a coin-reading machine experiment. Nevertheless, let us continue with your train of thought.

In the frequentist interpretation of probability, this means that if we perform N=100 trials we would obtain approximately N_H=80 heads, and in the limit

Yes, so what. The frequentist interpretation applies just as well to my coin-reading machine example.

What probability theory tells us is that if perform another experiment and count tails instead of heads we will find that

This is false and this is the point of the example that you have not gotten. Probability Theory DOES NOT tell you that. That's why I asked you to explain for exactly what scenario you claim "The correct probabilistic equation is P(H) + P(T) = 1". Please explain the basis for claiming that . The frequentist interpretation of probability applies to my coin reading machine but the correct probability equation for my coin-reading machine experiment is not P(H) + P(T) = 1. It is P(H) + P(T) = 1.5. According to the frequentist interpretation of probability for my coin reading machine:



You are making the exact same mistake that the mathematician in my example made. That is why you end up suggesting that my example violates probability theory. So perhaps after this example, you will finally understand the problem with such reasoning. I would encourage you to engage with that example a bit more seriously than you apparently have so far.

[Justo]

Justo, have you actually read the post talking about the coin-tossing machine example? It doesn't look like you have because you don't appear to understand it at all:

minkwe,
The correct probabilistic equation is P(H) + P(T) = 1.

Correct probability equation for what? Please be specific. It is easy to conflate different things when you are not being specific so please explain exactly what situation you are talking about. Or better just read the example more carefully to understand it.

When we are talking about coin tosses and write P(H) + P(T) = 1, there is only one natural interpretation: P(H)="probability of obtaining Heads" and P(T)="probability of obtaining Tails", when the coin is tossed.

Let us say that for our coin P(H)=0.8.

This doesn't make sense in the context of my example. This is why I don't think you understand it. There is no P(H) for a coin in my example, there is P(H) for the outcome of a coin-reading machine experiment. Nevertheless, let us continue with your train of thought.

I believe it is you who is not being specific here, at least if your reading machine does something else than just "reading". When you set the machine to "H" I understood that your machine just tells you when "H" comes up without influencing the result. If your machine does not influence the result, then we have that , otherwise we would have
I think the only way your equation makes sense if we accept that they represent conditional probabilities. That is why Richard Gill told you

PS of course, Michel, I could simply blame you for creating the confusion by your inadequate notation. If you had written P(H|”H”) and P(T|”T”), we wouldn’t be having this conversation. That’s a Counterfactual.

Maybe I just do not understand the meaning of probabilities or your example is too much for me. Either way it is ok for me.

[minkwe]

Justo, please do yourself a favor and take 5 minutes to read my description of the example again. You are clearly not engaging with it, but with some other erroneous misinterpretation.
Here it is again step by step:
1.Say a smart mathematician knows a thing or two about coins and probability theory, so he confidently derives and writes down an equality relationship that holds for all coins based on the assumptions that (1) coins have 2 sides, (2) Probabilities of mutually exclusive possibilities must add up to exactly 1. This relationship applies to all coins, no matter how biased

, where (H=head or T=tail).

Do you have any issues with this part

2. He's not an experimentalist, thus to test this relationship in the lab, contacts his friend who has designed a coin-reading machine. The machine works by accepting one of two settings (H=head or T=tail). A coin is tossed into an opening above the machine, causing a bell to ring if the coin comes up the same side as the setting.

Together, they perform an experiment, with the machine set to H. After 50 tosses, they get 40 rings. . They repeat the experiment with the setting at T and after 50 tosses, they get 35 rings. .

What about this part, Amy objections?