Emilio Santos joins the dark side

[lugita15]

That is why I argue that in Bell's inequality |P(a,b) - P(a,c)| <= P(b,c) + 1, the terms P(a,b), P(a,c), P(b,c) can not all be measured simultaneously, therefore a genuine experimental test of Bell's inequality is impossible.

In words:

P(a,b) = What they would have obtained had they measured along a and b
P(b,c) = What they would have obtained had they measured along b and c instead
P(a,c) = What they would have obtained had they measured along a and c instead

Now you combine those and obtain an inequality -- good. Unfortunately it is impossible to test this experimentally because in any experiment that is doable, measuring anyone of them makes the others impossible to measure. So the experimentalists perform three different things on three different ensembles and fool themselves into thinking they are measuring the terms in Bell's inequallity.

OK, let me ask you this. Sometimes the polarizations are measured along a and b, and sometimes the polarizations are not measured along a and b. In either case, as you have agreed, the question "what would have been obtained had they measured the polarizations along a and b?" has a definite answer - although of course we may not always be able to find out the answer in the cases where we do not measure along a and b.

Now consider the following two questions:
1. "What is the fraction of cases where the polarization measurements of the two particles would have yielded the same result had they measured along a and b?"
2. "In the subset of cases in which we measure along a and b, what is the fraction of cases where the polarization measurements of the two particles would have yielded the same result had they measured along a and b."

In some sense, the answer to question 1 is unknowable, because when we DON'T measure along a and b, we can't know what would have happened if we HAD measured along A and B. On the other hand, the answer to question 2 can be easily determined - we just look at all the cases in which the measurements were performed along a and b, and compute the percentage of these cases where the two measurements yielded the same result.

A crucial step in Bell's proof (and Herbert's proof) involves assuming that the answer to question 2 is the same as the answer to question 1 - in other words, assuming that the subset of cases in which we actually measure along a and b is a "representative sample" of the total set of cases. Is that the step in the logic that you dispute? If so, I can try to mount a defense for that step.

 

[billschnieder]

Now consider the following two questions:
1. "What is the fraction of cases where the polarization measurements of the two particles would have yielded the same result had they measured along a and b?"
2. "In the subset of cases in which we measure along a and b, what is the fraction of cases where the polarization measurements of the two particles would have yielded the same result had they measured along a and b."

First of all, in Bell's treatment we are talking about the expectation value of the paired product A()*B(), not "fractions of cases where things match". Secondly are you referring to an experiment or a prediction. You have to be very clear. Once you start asking about "fraction of cases" you are talking about relative frequences which are in the domain of analyzing experimental results and the questions do not make any sense. However if you are asking what the expectation value for the paired product would be for measuring along a and b. Such a prediction has a definite answer even if it is no longer possible to measure along a and b. The terms in Bell's inequality correspond to such predictions.

So I would phrase those questions differently:

(1) What do we predict the expectation value of the paired product to be if we measure along a and b
(2) In an experiment in which we measure along a and b, what do we observe for the expectation value of the paired product.

This way it is clear that we are dealing in (1) with a prediction which might never be realized, and in (2) we are dealing with values that actually exist since the measurement was performed. Mixing the two without regard leads you to paradoxes.

In some sense, the answer to question 1 is unknowable, because when we DON'T measure along a and b, we can't know what would have happened if we HAD measured along A and B.

I disagree with the premise of this statement. We can predict it with certainty but we can not measure it. If the prediction is true, and we know the prediction, then it is knowable. Of course you can not know something which is false. You can not know that "the particles were measured along A and B and obtained results J" if the particles were in fact not measured along A and B. But you can know that "IF the particles were measured along A and B we would have obtained results J". Note what is being known is different.

On the other hand, the answer to question 2 can be easily determined - we just look at all the cases in which the measurements were performed along a and b, and compute the percentage of these cases where the two measurements yielded the same result.

A crucial step in Bell's proof (and Herbert's proof) involves assuming that the answer to question 2 is the same as the answer to question 1 - in other words, assuming that the subset of cases in which we actually measure along a and b is a "representative sample" of the total set of cases. Is that the step in the logic that you dispute? If so, I can try to mount a defense for that step.

It is absolutely wrong to suggest that Bell's proof depends on the two being the same. Herberts might but not Bell's. If you like, we can go through the derivation step-by-step to hash this out. The terms in Bell's inequalities deal ONLY with questions of the type (1). Experiments provide answers ONLY to questions of the type (2). It is only after experiments have been performed that experiments make the assumption that (1) and (2) are always the same and substitute terms obtain according to (2) into inequalities based on (1).

The part I dispute is that it is not correct to use type (2) answers from three different experiments and substitute them into an inequality obtained using type (1) questions. Simply because not all type (1) question can be simultaneously realized in an experiment and Bell's inequality which explicitly uses simultaneously unrealizable type (1) terms can never be tested in any experiment.

In short, an inequality which involves *mutually exclusive possibilities* can never be tested experimentally even if we can contemplate it and spend decades discussing it.

 

[lugita15]

First of all, in Bell's treatment we are talking about the expectation value of the paired product A()*B(), not "fractions of cases where things match".

OK then, I'm talking about Herbert's treatment "quantumtantra.com/bell2.html" .

Secondly are you referring to an experiment or a prediction. You have to be very clear. Once you start asking about "fraction of cases" you are talking about relative frequences which are in the domain of analyzing experimental results and the questions do not make any sense.

I'm talking about a hypothetical, idealized experiment, as described by Herbert. And when I say "fraction of cases", all I mean is probability.

However if you are asking what the expectation value for the paired product would be for measuring along a and b. Such a prediction has a definite answer even if it is no longer possible to measure along a and b. The terms in Bell's inequality correspond to such predictions.

OK, I haven't really examined Bell's paper in detail, but at least the Bell inequality in Herbert's proof involves probabilities, not expectation values.

So I would phrase those questions differently:

(1) What do we predict the expectation value of the paired product to be if we measure along a and b
(2) In an experiment in which we measure along a and b, what do we observe for the expectation value of the paired product.

This way it is clear that we are dealing in (1) with a prediction which might never be realized, and in (2) we are dealing with values that actually exist since the measurement was performed. Mixing the two without regard leads you to paradoxes.

Yes, confusing one question for the other leads to confusion, but I hope you agree that both questions are well-defined questions with well-defined answers.

I disagree with the premise of this statement. We can predict it with certainty but we can not measure it. If the prediction is true, and we know the prediction, then it is knowable. Of course you can not know something which is false. You can not know that "the particles were measured along A and B and obtained results J" if the particles were in fact not measured along A and B. But you can know that "IF the particles were measured along A and B we would have obtained results J". Note what is being known is different.

Yes, I'm aware of all this. I didn't mean to say that it was absolutely unknowable, because of course if you had a correct local hidden variable theory it would be able to give you the answer. I just meant that the direct polarization measurements don't give us an answer to this question.

It is absolutely wrong to suggest that Bell's proof depends on the two being the same. Herberts might but not Bell's. If you like, we can go through the derivation step-by-step to hash this out.

OK, then if you don't mind let's stick to Herbert. It's simpler and more intuitive, so we don't need to get bogged down in Bell's formal details.

The terms in Bell's inequalities deal ONLY with questions of the type (1). Experiments provide answers ONLY to questions of the type (2). It is only after experiments have been performed that experiments make the assumption that (1) and (2) are always the same and substitute terms obtain according to (2) into inequalities based on (1).

Right, and I was asking you whether you think that that is a correct assumption to make. I was guessing you think that it's an incorrect assumption, and based on the next quote it looks like I was right.

The part I dispute is that it is not correct to use type (2) answers from three different experiments and substitute them into an inequality obtained using type (1) questions.

OK, that's what I thought you would say.

So since you think that substituting the measurable type (2) answers for the unmeasurable type (1) answers is wrong, you must believe that the question "what behavior would result if they measured along a and b" has different answers based on whether or not they actually measure along a and b. Do I have this part right?

 

[ThomasT]

I'm enjoying this thread. Wrt Norsen, whether or not one agrees with his conclusion that nature is nonlocal, I think he has some interesting insights ... though, with DrC (and billschneider and G.W.), I think that he's wrong in concluding that nature is nonlocal. It's an open question imho.

The inputs of billschneider, DrC et al. have been most helpful.

 

[billschnieder]

OK then, I'm talking about Herbert's treatment "quantumtantra.com/bell2.html" . I'm talking about a hypothetical, idealized experiment, as described by Herbert. And when I say "fraction of cases", all I mean is probability. OK, I haven't really examined Bell's paper in detail, but at least the Bell inequality in Herbert's proof involves probabilities, not expectation values.

The reason I avoid wasting time on proofs like Herberts is because they make other errors not present in Bell's treatment for which counter arguments do not necessarily clarify the real issues surrounding Bell's theorem. For example in the on-going thread about Herbet's proof, zonde has already pointed out one of the errors which invalidate his proof. And it is apparently an error you keep making whenever you talk of "fraction of cases" etc, as illustrated by the following simple example:

*I* design a source to produce exactly 100 and only 100 particles with a certain hidden property F. I do not tell you the number of particles I'm producing, nor do I tell you anything about the hidden property. *You* point yor instrument at my source and find that your detector reveals two possible outcomes "red" or "blue". After your experiment you tabulate your results. It turns out you detected 10 events 5 of them blue and 5 of them red.

Now let me ask you:
- Based only on what you know from your results, what is the fraction of cases in which you observed "red"?
- Based on the actual situation as described, what is the fraction of cases in which you observed "red"?
- Assuming it is possible to repeat the experiment, (ie regenerate the source and re-fire) and we repeated this experiment a near infinite amount of times. Will you ever be able to make those two questions yield the same answer withou knowing the hidden properties?

The error with Herberts proof is the one illustrated above which zonde has already responded to in the appropriate thread. What we are addressing here is different.

So since you think that substituting the measurable type (2) answers for the unmeasurable type (1) answers is wrong,

No! I think it is wrong to substitute *three different actually measured* type (2) answers into an inequality which involves *simultaneously unmeasurable* type (1) answers.

you must believe that the question "what behavior would result if they measured along a and b" has different answers based on whether or not they actually measure along a and b. Do I have this part right?

No! There are some problems with your logic here, to dispell it, let me quote from another post I made previously about this issue:

--
The statements:

*If A is true then X is false.*
*If A is false then X is true.*

Have only one truth value (true or false). They can not be valid at one time and invalid at another time. They can not be true at one time and false at another time. They are statements about the logical relationship between the truth values of two entities (A and X). They are not statements about X only, or about A only. The above statements are completely different statements from the ones.

*X is false*, *A is true*, *X is true*, *A is false*

The statements will have the same truth value (true or false) regardless of whether or not A is true and whether or not X is true.

see: https://www.physicsforums.com/showpost.php?p=3326791&postcount=180
--

Similarly the answer to the question:
(1) What do we predict the expectation value of the paired product to be if we measure along a and b.
Will not change just because we chose to measure along A and B instead of a and b.

 

[billschnieder]

I thought I should point out also this example which rlduncan posted a while back which also clearly illustrates the issue:
https://www.physicsforums.com/showpost.php?p=3288873&postcount=1

Three coins are tossed simultaneously by three individuals. For simplicity, let's them be a, b, and c and each coin is tossed eight times.

Example 1:
a =HTTTHTHH
b=TTHHTHHH,

b=TTHHTHHH
c=HTHTTTHH,

a=HTTTHTHH
c=HTHTTTHH,
Bell’s Theorem, nab(HH) + nbc(HH) ≥ nac(HH) or 2+3 ≥ 3 (True)

Example 2:
a1=HTTHTHHH
b1=THHTTHTT,

b2=HTHHTHHT
c1=TTTTHHTH,

a2=THHTHTTH
c2=HHHTHTTT,
Bell’s Theorem, nab(HH) + nbc(HH) ≥ nac(HH) or 1+1 ≥ 3 (False)

There is a one-to-one mapping of the three sequences in Example 1 for ab, bc, and ac. In the EPRB experiments only one angle can be measured at a time. As a result there are six sequences necessary which give different runs of photons and a1 sequence is not the same as a2, etc and the one-to-one mapping is lost; and violation of Bell’s theorem may occur as demonstrated in Example 2. This may be the case for the EPRB experiments.