Scholarpedia article on Bell's Theorem

[ttn]

It's exactly this kind of inconsistencies that I noticed in the first place in your article: you recognize that it's hard to pin down "what Einstein thought" on this issue, and still you don't see anything confusing/misleading about labeling a view that he did not consistently have with his name. I find that counter-productive - and as I showed, it's completely unnecessary.

I don't recall your "showing" much of anything. You made a very brief comment about how the parts of the article you read made it seem like we didn't understand what we were talking about. I don't know what parts of the article you read, I don't know what "inconsistencies" you're talking about, etc. For example, did you read the last section, on "nonlocality and relativity"? I had been assuming so, but now I'm no longer sure. So, basically, I'm just saying that your worries about the article are far less clear than I think you take them to be. I'm interested in hearing them, but you have to actually explain more clearly what they are.

There we go again - Einstein said around 1920 that according GR an ether exists, but earlier he had a "shut up and calculate" attitude! Now, what is your "Einsteinian relativity"?

It's just what we say it is, the view in which the "notion of a really-existing but unobservable 'ether' rest frame is dispensed with and all uniform states of motion are regarded as equivalent". If your quibble is that it's not so clear that this really represents Einstein's view in some particular decade, yes, that's true, I agree. (Incidentally, when Einstein meant by "ether" in the 20s was not exactly the same as this Lorentzian idea that there's a privileged but unobservable frame -- all he meant, really, was that the GR metric tensor should be thought of as "real" such that there is "some stuff there" in "otherwise empty space". But probably we needn't get into that here.) But still, come on. It's pretty clear that back in 1905 this was Einstein's view, at least it is the view he took in the relativity paper, and it is (as I suggested before) the view of every physicist who takes himself to believe in "Einstein's theory of special relativity". (The way normal physicists hold this is: "Einstein showed in 1905 that we don't *need* an ether". And that's entirely correct!) So calling the view "Einsteinian" is hardly inappropriate, unjustifiable, or misleading.

if you want to present a quality article, you scrap this kind of debatable things which you don't need at all,

If giving the name "Einsteinian" to the view that there is no ether is the most controversial/debatable thing in the article, I'd say we did a pretty good job!

and simple say for example that with "fundamental relativity" the article refers to a block universe model.

Well that is *not* what we think "fundamental relativity" means, so that's why we didn't "simply" put it that way. Indeed, I don't think any of the authors would claim to know how to formulate precisely what "fundamental relativity" means! That's what we say at the very end, and it's why we think the question of whether nonlocality is or is not compatible with "fundamental relativity" is very much an open question.

Now I'm starting to think it's *your* views on relativity that are based on a too-quick skimming of too-few books.

 

[harrylin]

For example, did you read the last section, on "nonlocality and relativity"?

That's the only part I read so far...

If giving the name "Einsteinian" to the view that there is no ether is the most controversial/debatable thing in the article, I'd say we did a pretty good job!

No regretfully it was merely the last point that we discussed...

[..]
Well that is *not* what we think "fundamental relativity" means, so that's why we didn't "simply" put it that way. Indeed, I don't think any of the authors would claim to know how to formulate precisely what "fundamental relativity" means! [..]

You introduced a term in an encyclopedia article of which you can't define the meaning?
Most authors probably mean with "truly" (or fundamentally) relativistic, that no influence (incl. undetectable quantum collapse kind of influences) can propagate faster than light; in particular it's incompatible with the block universe concept of Spacetime.

Now I'm starting to think it's *your* views on relativity that are based on a too-quick skimming of too-few books.

Funny!

Anyway I do plan to read your discussion of Bell's Theorem itself, although I'm not an expert in that topic. At least I could point out if something is unclear.

Cheers,
Harald

 

[harrylin]

I now started reading from the start and I have read and discussed already enough about Bell's Theorem to notice that your introduction is, as you phrase it, "dogmatizing" (in Wikipedia terms, a particular "point of view" that is not universally accepted). I think that some others already made similar remarks, but now I understand why. Probably you would have written the same about Von Neumann's theorem before it was disproved. That is not what I expect of a good encyclopedia article; consequently I find the introduction of the Wikipedia article at the moment superior. More later!

 

[DrChinese]

I am in the happy position of getting to basically agree with Dr Chinese. Of course you can violate a Bell type inequality by just making up lists of how the data might have come out. The point is that such data will imply a violation of one of the assumptions that went into the inequality, or of the relevant QM predictions. So it's not a refutation of Bell's proof; it's a demonstration of it!

The right approach would be instead the following (basically the Dr C challenge): make lists of how you think each particle in each pair will "answer" (H/T) when "asked" any of the (3 or 4) possible "questions". Then I'll go down the list, one pair at a time, and decide randomly for each pair which 2 questions I want to ask. (Here, by "random", I basically just mean that I have to decide which questions to ask before I look at what you've written down for that pair -- also that I won't ask you, who already know what you've written down for each pair, for advice on which questions to ask... I'll instead let which questions I ask be determined by something totally unrelated to you and the lists you made, e.g., I'll roll a die or look at the 5th digit in the current price of porkbellies or ...) We'll keep track of what the outcomes will be and then calculate at the end all 3 or all 4 of the correlation coefficients. (Note that this procedure is in effect a way a implementing the "no conspiracies" assumption.) I assume you understand perfectly well that if we played *that* game, the correlations would respect the inequality. Which of course proves that in *your* game, the way you violate the inequality is because you get to decide what outcomes to assign to each particle pair *after you already know what questions are being asked*.

What I don't understand is why you and Bill don't just openly acknowledge this painfully obvious fact: your beef is with the "no conspiracy" assumption. (Or perhaps also to some extent, and despite your protestations to the contrary, with locality!) All the stuff about "cyclic dependency" is just a red herring shaped hot air balloon.

Woo hoo!

I know billschnieder must know better. Not really sure why he plays these games, such a waste of time. Why not start from a position we all can agree, and move from there to identify relevant differences?

 

[ttn]

I now started reading from the start and I have read and discussed already enough about Bell's Theorem to notice that your introduction is, as you phrase it, "dogmatizing" (in Wikipedia terms, a particular "point of view" that is not universally accepted). I think that some others already made similar remarks, but now I understand why. Probably you would have written the same about Von Neumann's theorem before it was disproved. That is not what I expect of a good encyclopedia article; consequently I find the introduction of the Wikipedia article at the moment superior. More later!

Well, now it's my turn to quibble about terminology. If "dogma" means "anything different from what the herd endlessly repeats", then yes, our article is "dogmatic". On the other hand, if "dogma" means "something that has no good evidence or arguments behind it, and which gets repeated over and over again only out of sheer unthinking inertia" then it is (roughly) everybody else (certainly including wikipedia) that is "dogmatic". But this ground has already been well-covered in this thread; I'll be happy to read any comments you have about the article, but I won't engage in further discussion trying to defend the article against charges that it is "biased" or "dogmatic" or whatever. It is what it is, and if you don't like it, don't recommend it to your friends; perhaps even if you don't like it, you can still appreciate that it's a good thing that there now exists a thorough and careful treatment of Bell's theorem from this particular POV.

As to von Neumann, I think it's fair to say that if anybody had scrutinized his theorem as carefully as we scrutinize, in our article, the reasoning involved in Bell's theorem, the theorem would have been "disproved" much earlier. (Of course, really it's not the theorem that was disproved -- just its significance vis a vis "hidden variables".) That is, if your point was that our article is "dogmatic" in the first sense I described above -- we are just unthinkingly and uncarefully and unskeptically repeating a view we heard from Bell or whoever -- I think that is quite wrong, and I think it'll become obvious as you read further that it's quite wrong.

 

[billschnieder]

But suppose the flips turn out instead like this:

a=TTH
b=THT
c=HTH

So nab(HH)=0, nbc(HH)=0, and nac(HH)=1. The inequality is violated. So... why should I believe the inequality in the first place? Did Bill type the wrong thing? Did I understand it wrong?

When a big alleged "knock down concrete example refutation" starts off with an obvious error like this, you maybe shouldn't be surprised that people don't bother to respond, tend to stop listening to your arguments, and don't even bother to look at subsequent "knock down concrete example refutations".

Not withstanding the fact that you were unable to read that the coins were tossed 8 times not 3 times, the above example has an error which can easily be rectified, ie, it uses matches instead of mismatches. So let's see how you weave yourself out of the rectified version which continues to make the exact same central point you have dodged all along.

Here it is:

3 coins (a,b,c), where nAB represents number of MISMATCHES between the outcomes of a and b.

Inequality: nAB + nAC >= nBC
a= THHHTHTH
b= HHHTTTHH
c= TTTHHHHT
4 + 5 >= 7 : Obeyed (ONLY 3 lists of outcomes)

a1= HTHTTHHT
b1= HHTTTTHT

a2= TTHHTTHT
c2= THHHTTTT

b3= HTHHTTHH
c3= THTTTHTT
3 + 2 >= 7 Disobeyed (6 lists of outcomes)

Use any number of coin tosses you like for this one, not just the 8 used in the example. As is clearly obvious, you are trying to find the slightest thing to avoid addressing the central issue. Good luck.

I am in the happy position of getting to basically agree with Dr Chinese. Of course you can violate a Bell type inequality by just making up lists of how the data might have come out. The point is that such data will imply a violation of one of the assumptions that went into the inequality, or of the relevant QM predictions. So it's not a refutation of Bell's proof; it's a demonstration of it!

Despite repeated explanations, you still think Bell's proof is being refuted, it is not. It is the equivalence between experiments and Bell's proof that is being refuted. 2 + 2 = 4 is a perfectly valid expression; it does not mean 2inches + 2cm =/= 4 inches is a valid expression. Just because somebody questions the latter does not mean the former is not correct. And just because the former is correct does not mean it corresponds to the case in which 2inches were measured in one experiment and 2cm in another. This is basic logic.

The right approach would be instead the following (basically the Dr C challenge): make lists of how you think each particle in each pair will "answer" (H/T) when "asked" any of the (3 or 4) possible "questions". Then I'll go down the list, one pair at a time, and decide randomly for each pair which 2 questions I want to ask. (Here, by "random", I basically just mean that I have to decide which questions to ask before I look at what you've written down for that pair -- also that I won't ask you, who already know what you've written down for each pair, for advice on which questions to ask... I'll instead let which questions I ask be determined by something totally unrelated to you and the lists you made, e.g., I'll roll a die or look at the 5th digit in the current price of porkbellies or ...) We'll keep track of what the outcomes will be and then calculate at the end all 3 or all 4 of the correlation coefficients. (Note that this procedure is in effect a way a implementing the "no conspiracies" assumption.) I assume you understand perfectly well that if we played *that* game, the correlations would respect the inequality. Which of course proves that in *your* game, the way you violate the inequality is because you get to decide what outcomes to assign to each particle pair *after you already know what questions are being asked*.

Sorry, that game was already played and DrC lost.
See:
https://www.physicsforums.com/showthread.php?t=499002&page=5
https://www.physicsforums.com/showpost.php?p=3350656&postcount=115

If you want we can play it again to prove to you that you and DrC are both wrong.

 

[DrChinese]

Sorry, that game was already played and DrC lost.
See:
https://www.physicsforums.com/showthread.php?t=499002&page=5
https://www.physicsforums.com/showpost.php?p=3350656&postcount=115

If you want we can play it again to prove to you that you and DrC are both wrong.

Laughable. You simply declared yourself the winner. Which is not a bad strategy sometimes, especially when you have a losing hand. Notice that the average was still the classical .33 in the sample, and the result would rarely result in a violation if you were to select each data element randomly. (You did all 10 the same way - and the sample was hand picked by you to have this specific attribute when coupled with your selection technique.)

This is not the DrC challenge, and it is not the ttn challenge. Certainly you know this bill, why are you wasting our time? Do you think you will pull the wool over our eyes with a fast one?

 

[ttn]

Not withstanding the fact that you were unable to read that the coins were tossed 8 times not 3 times,

I thought you might say that. But I thought even for you it would be obvious that I could add, e.g., strings of 5 Ts to the end of each list.

But you are right that that was not the real issue. You say I only quibbled about your mis-statement of the setup to avoid addressing the real issue. That's not true. I quibbled about your mis-statement of the setup just for the sheer fun of it. But I know perfectly well what you should have said, and I already addressed the real issue (which you intended to raise with the example) in my other comments above. There is no need to continue going around in these circles. Your beef, as I said before, is with the "no conspiracy" assumption. In particular, you think it doesn't apply to the real experiments. I think that's crazy. We've both made our positions clear.

 

[rlduncan]

Not withstanding the fact that you were unable to read that the coins were tossed 8 times not 3 times, the above example has an error which can easily be rectified, ie, it uses matches instead of mismatches. So let's see how you weave yourself out of the rectified version which continues to make the exact same central point you have dodged all along.

Here it is:

3 coins (a,b,c), where nAB represents number of MISMATCHES between the outcomes of a and b.

Inequality: nAB + nAC >= nBC
a= THHHTHTH
b= HHHTTTHH
c= TTTHHHHT
4 + 5 >= 7 : Obeyed (ONLY 3 lists of outcomes)

a1= HTHTTHHT
b1= HHTTTTHT

a2= TTHHTTHT
c2= THHHTTTT

b3= HTHHTTHH
c3= THTTTHTT
3 + 2 >= 7 Disobeyed (6 lists of outcomes)

Use any number of coin tosses you like for this one, not just the 8 used in the example. As is clearly obvious, you are trying to find the slightest thing to avoid addressing the central issue. Good luck.

Thanks Bill. The error in the inequality was mine and apologize for it. I should have written it as: nab(HT) + nbc(HT) ≥ nac(HT). This inequality is derivable and impossible to violate using three lists.

However, if you use 6 lists as in the EPR experiments (because only one angle can be measure at a time) then a1≠a2, b1≠b3, and c2≠c3 then violations may occur. This type of violation must be ruled out, before any meaningful conclusions can be drawn from the EPR experiments.

 

[DrChinese]

This type of violation must be ruled out, before any meaningful conclusions can be drawn from the EPR experiments.

Nope. Please note that Bell tests are considered meaningful, are well cited and included in the standard physics domain. You are personally free to accept or reject anything you like.

 

[ttn]

This type of violation must be ruled out, before any meaningful conclusions can be drawn from the EPR experiments.

Let me ask you a question I asked earlier but got no serious reply to. In the context of some other experiment, like a randomized drug trial, do you have this same opinion? So, somebody flips a coin to decide which patients get the real drug and which get the placebo. Then everybody takes their pills for a while and you look to see who got better and who didn't. Do you think that, in this kind of situation, you need to "rule out" the possibility that the coin flips might have been somehow correlated with the prior healthiness of the patients, such that in effect the "drug" and "placebo" groups represent biased samples? Or do you think it is reasonable to assume, in this kind of case, that there are no correlations there, such that you can more or less interpret the statistics naively? (I mean, by "interpret them naively", for example, that if 90% of the people taking the drug got better, and 90% of the people taking the placebo got worse, you'd conclude that the drug was *making* them get better.)

Let me pose some specific questions:

1. Do you agree that a "no conspiracy" assumption is made in this kind of case, just like it is made in the Bell experiment kind of case?

2. Assuming yes to #1, are you as skeptical about the applicability of the "no conspiracy" assumption to this drug trial kind of case, as you are to the Bell kind of case?

3. If no to #2, why not? What's the difference?

4. If yes to #2, do you agree that such skepticism can never be answered, such that you're left unable to accept that anything is ever actually established by scientific experiments?

 

[lugita15]

However, if you use 6 lists as in the EPR experiments (because only one angle can be measure at a time) then a1≠a2, b1≠b3, and c2≠c3 then violations may occur. This type of violation must be ruled out, before any meaningful conclusions can be drawn from the EPR experiments.

Om so rlduncan, do you disagree with the EPR argument that if we have perfect correlation whenever we set the polarizers to identical angle settings, then even when we DON'T set the polarizers to identical angle settings, it is still true that we would have gotten perfect correlation if we HAD set the the polarizers to equal angle settings, and thus assuming locality the two particles must have agreed in advance which angles to go through and which ones not to go through?

O FRABJOUS DAY! A THOUSAND POSTS!

 

[rlduncan]

Nope. Please note that Bell tests are considered meaningful, are well cited and included in the standard physics domain. You are personally free to accept or reject anything you like.

I understand what you are saying. However, in the context of our discussions with the available knowledge about the origin of these types of inequalities is not very convincing. I am here to learn. Give me a reference where these violations have been considered and ruled out. Show how randomly selecting the one angle to measure insures that these violations are screened off. I would like to know.

P.S. I am reminded of the following quote:

"History shows clearly that the advances of science have always been frustrated by the tyrannical influences of certain preconceived notions which were turned into unassailable dogmas. For that reason alone, every serious scientist should periodically make a profound reexamination of his basic principles".

—Louis de Broglie

 

[DrChinese]

"History shows clearly that the advances of science have always been frustrated by the tyrannical influences of certain preconceived notions which were turned into unassailable dogmas. For that reason alone, every serious scientist should periodically make a profound reexamination of his basic principles".

—Louis de Broglie

A great quote which you are free to apply to yourself as you desire.

You and several others seem to miss some key points here. PhysicsForums is not intended as a spot to debate your original or nonstandard ideas, which clearly describes your assertion. The key idea here is to share useful knowledge, answer normal questions, etc.

The fact is, your premise (that something needs to be ruled out) is one you seem to feel is important somehow. You will need to first convince me or someone that it is relevant. There are a lot of things that are not relevant as well, and I don't plan to debate each one. But I will say this:

You may have heard of the fair sampling assumption. This is accepted as applying to many Bell tests. Although this assumption has already been shown to be unnecessary, I have no issue with it. So if this gives you the qualifier you need for rejecting Bell tests, well, go right ahead and reject 'em. But that does not mean that I and others need to, since we can live with the fair sampling assumption. Science involves sampling, and issues about this have been discussed at length by those in the area. I would suggest you read some of those. Of course, since Bell tests are routinely performed with frequent random switching of angle settings, this is hardly much of a stretch.

 

[rlduncan]

Let me ask you a question I asked earlier but got no serious reply to. In the context of some other experiment, like a randomized drug trial, do you have this same opinion? So, somebody flips a coin to decide which patients get the real drug and which get the placebo. Then everybody takes their pills for a while and you look to see who got better and who didn't. Do you think that, in this kind of situation, you need to "rule out" the possibility that the coin flips might have been somehow correlated with the prior healthiness of the patients, such that in effect the "drug" and "placebo" groups represent biased samples? Or do you think it is reasonable to assume, in this kind of case, that there are no correlations there, such that you can more or less interpret the statistics naively? (I mean, by "interpret them naively", for example, that if 90% of the people taking the drug got better, and 90% of the people taking the placebo got worse, you'd conclude that the drug was *making* them get better.)

Let me pose some specific questions:

1. Do you agree that a "no conspiracy" assumption is made in this kind of case, just like it is made in the Bell experiment kind of case?

2. Assuming yes to #1, are you as skeptical about the applicability of the "no conspiracy" assumption to this drug trial kind of case, as you are to the Bell kind of case?

3. If no to #2, why not? What's the difference?

4. If yes to #2, do you agree that such skepticism can never be answered, such that you're left unable to accept that anything is ever actually established by scientific experiments?

You did not answer my questions given in Post #145. Can we start there.

 

[mattt]

I guess some people here never use any medicine, after all there could have been a "cosmic conspiracy" in the double-blind, triple-blind randomized trials that may invalidate the results.

So for them, all experimental science (that relies heavily on randomized sampling, double-blind trials...) is invalid.

How funny...

 

[ttn]

Why not start with the coin toss experiment and explain how it is possible this simple experiment can violate a Bell-type inequality?

I did. It violates "no conspiracies".

Notice the similarity to the EPR experiments.

Noted.

Am I to conclude that nature is nonlocal because the inequality was violated?

Which violation? Are you talking about the coin toss example? In that example you or someone just makes up the "data", so obviously nothing about nature can be inferred. In the real Bell experiments, we have excellent reason (though not anything like direct empirical proof, which would be impossible) to accept the "no conspiracies" assumption. And so there it does indeed follow from the violation of Bell's inequality that locality (the only other thing assumed in the derivation of the inequality) is false.

If yes, then why do we need to use entangled photons?

I don't get the question. If you use un-entangled photons, then QM predicts (and experiments will confirm) that the inequality is respected. So, use entangled photons because otherwise you won't find the shocking and wonderful result that the inequality is violated. If you meant "why do entangled photons violate locality?", that's of course a harder question. Different theories will tell different stories here. But what all the theories will have in common (unless they are "superdeterministic", i.e., unless they are cooked up to violate "no conspiracies"!) is that they will involve nonlocality. That's what the theorem shows. Or... if what you meant is "why should I go to the trouble of using entangled photons, when I can just as well violate the inequality by flipping coins independently?" -- which I suspect is what you actually meant -- the point is that, actually, you can't violate the inequality that way... at least, not without cheating, i.e., not without violating the "no conspiracy" or "locality" assumptions. That is, your coin flips will certainly no longer violate the inequality if we play the game "modified Dr C challenge" style as I suggested before.

 

[ttn]

I guess some people here never use any medicine, after all there could have been a "cosmic conspiracy" in the double-blind, triple-blind randomized trials that may invalidate the results.

So for them, all experimental science (that relies heavily on randomized sampling, double-blind trials...) is invalid.

How funny...

Exactly. Of course, the truth is that they do use medicine and are just inconsistent. That's what I've been trying to get them to see. It's nice to know that somebody got the point, if not them!

 

[rlduncan]

Which violation? Are you talking about the coin toss example? In that example you or someone just makes up the "data", so obviously nothing about nature can be inferred. In the real Bell experiments, we have excellent reason (though not anything like direct empirical proof, which would be impossible) to accept the "no conspiracies" assumption. And so there it does indeed follow from the violation of Bell's inequality that locality (the only other thing assumed in the derivation of the inequality) is false. I don't get the question. If you use un-entangled photons, then QM predicts (and experiments will confirm) that the inequality is respected. So, use entangled photons because otherwise you won't find the shocking and wonderful result that the inequality is violated. If you meant "why do entangled photons violate locality?", that's of course a harder question. Different theories will tell different stories here. But what all the theories will have in common (unless they are "superdeterministic", i.e., unless they are cooked up to violate "no conspiracies"!) is that they will involve nonlocality. That's what the theorem shows. Or... if what you meant is "why should I go to the trouble of using entangled photons, when I can just as well violate the inequality by flipping coins independently?" -- which I suspect is what you actually meant -- the point is that, actually, you can't violate the inequality that way... at least, not without cheating, i.e., not without violating the "no conspiracy" or "locality" assumptions. That is, your coin flips will certainly no longer violate the inequality if we play the game "modified Dr C challenge" style as I suggested before.

First, someone just makes up the data! You have got to be kidding. Per the first coin toss example flip three coins: a,b,c. You record the sequence of heads and tails. You will never violate the inequality: nab(HT) + nbc(HT) ≥ nac(HT). Do you know this?

Repeat the second example several times and you will find a violation. It is disingenuous to say the data will only violate the inequality if you “cherry pick” the sequence of head and tails. If you have more than three data lists for a,b,c then a violation will ultimately occur. There is no way to avoid it. Don't take my word for it. Perform the experiments. Once you find a violation. Explain to me how you cheated the inequality to give a false result.

Surely you must know when flipping a coin via the first example all the data is collected simultaneouly. You can't do the same in the EPR experiments. It is impossible to do without multiple tossings (runs). In these experiments only one angle can be measured at a time. Hence, the problem in substitution of terms into the inequality which leads to a violation. All of this has been stated very clearly by billschnieder.

 

[ttn]

First, someone just makes up the data! You have got to be kidding. Per the first coin toss example flip three coins: a,b,c. You record the sequence of heads and tails. You will never violate the inequality: nab(HT) + nbc(HT) ≥ nac(HT). Do you know this?

Repeat the second example several times and you will find a violation. It is disingenuous to say the data will only violate the inequality if you “cherry pick” the sequence of head and tails. If you have more than three data lists for a,b,c then a violation will ultimately occur. There is no way to avoid it. Don't take my word for it. Perform the experiments. Once you find a violation. Explain to me how you cheated the inequality to give a false result.

Surely you must know when flipping a coin via the first example all the data is collected simultaneouly. You can't do the same in the EPR experiments. It is impossible to do without multiple tossings (runs). In these experiments only one angle can measured at a time. Hence, the problem in substitution of terms into the inequality which leads to a violation. All of this has been stated very clearly by billschnieder.

The "cherry picking" pertains, obviously, not to what you're calling "the first coin toss example", but rather the second. The claim is that you can violate the inequality without "cherry picking". But that simply is not true. The whole way you come at this is confused. Here's how you should do it. Make a bunch of data like you describe for "the first coin toss example". Now, starting at the first row, decide *randomly*, for each row, whether to look at (a,b), (a,c), or (b,c). Go through, say, a million rows, and keep track of

fab = nab(HT)/nab

(i.e., the fraction of time that one happened to pick (a,b) and saw a disagreement), etc.

Do you agree that, with overwhelmingly large probability, you will see these f values respecting the inequality

fab + fbc ≥ fac

?

I'm sure you'll say yes, of course. So then it should be obvious that the only way you can possibly get a violation of the inequality in your "second coin toss experiment" (which is of course no different except that now you are pre-arranging the data into different columns depending on what is measured) is by having the choice of which pair to look at (ab, ac, or bc) NOT BE RANDOM. That is, you need to "cherry pick". Or more precisely, you violate the "no conspiracy" assumption. As I've said now at least a million times.

So isn't the situation just what I've said repeatedly? You think that the "no conspiracy" assumption is NOT REASONABLE for the Bell experiments. That is, you think the particle pairs somehow "know in advance" which measurements will be performed on them later, and/or that what the experimenters *think* (erroneously) are "random settings" for each particle pair, are actually being determined by something that is in a kind of pre-established harmony with whatever is determining the particle states, such that in effect it's impossible to get an unbiased sample. That's what you think. What I don't understand is why you don't just admit, yes, this is what you think. It's actually not so terrible or crazy. You don't have to be embarrassed to admit it. Actually, it's a perfectly respectable position -- the idea that there is a conspiracy is crazy, but then the idea that there is superluminal causation all over the place is crazy too, and it's hardly obvious which one is more crazy. None of the available options are all that comfortable! Indeed, Bell even gave a happy respectable name to your position: super-determinism. And if determinism is good, how awesome is *super* - determinism? I mean, seriously, just admit that this is what you think and then we can agree to disagree. Sheesh.

 

[billschnieder]

P.S. I am reminded of the following quote:

"History shows clearly that the advances of science have always been frustrated by the tyrannical influences of certain preconceived notions which were turned into unassailable dogmas. For that reason alone, every serious scientist should periodically make a profound reexamination of his basic principles".

—Louis de Broglie

Hi rlduncan,
Your quote above reminded me of the following quote:

In any field, the Establishment is not seeking the truth, because it is composed of those who, having found part of it yesterday, believe that they are in possession of all of it today. Progress requires the introduction, not just of new mathematics which is always tolerated by the Establishment; but new conceptual ideas which are necessarily different from those held by the Establishment (for, if the ideas of the Establishment were sufficient to lead to further progress, that progress would have been made).

Therefore, to anyone who has new ideas of a currently unconventional kind, I want to give this advice, in the strongest possible terms: Do not allow yourself to be discouraged or deflected from your course by negative criticisms; particularly those that were invented for the sole purpose of discouraging you unless they exhibit some clear and specific error of reasoning or conflict with experiment. Unless they can do this, your critics are almost certainly wrong, but to reply by trying to show exactly where and why they are wrong would be wasted effort which would not convince your critics and would only keep you from the far more important, constructive things that you might have accomplished in the same time. Let others deal with them; if you allow your enemies to direct your work, then they have won after all.

Although the arguments of your critics are almost certainly wrong, they will retain just enough plausibility in the minds of some to maintain a place for them in the realm of controversy; that is just a fact of life that you must accept as the price of doing creative work. Take comfort in the historical record, which shows that no creative person has ever been able to escape this; the more fundamental the new idea, the more bitter the controversy it will stir up. Newton, Darwin, Boltzmann, Pasteur, Einstein, Wegener were all embroiled in this. Newton wrote in 1676: "I see a man must either resolve to put out nothing new, or become a slave to defend it." Throughout his lifetime, Alfred Wegener received nothing but attacks on his ideas; yet he was right and today those ideas are the foundation of geophysics. We revere the names of James Clerk Maxwell and J. Willard Gibbs; yet their work was never fully appreciated in their lifetimes, and even today it is still, like that of Darwin, under attack by persons who, after a Century, have not yet comprehended their message Atkins, 1986.

- E T Jaynes

 

[billschnieder]

The "cherry picking" pertains, obviously, not to what you're calling "the first coin toss example", but rather the second. The claim is that you can violate the inequality without "cherry picking". But that simply is not true. The whole way you come at this is confused. Here's how you should do it. Make a bunch of data like you describe for "the first coin toss example". Now, starting at the first row, decide *randomly*, for each row, whether to look at (a,b), (a,c), or (b,c). Go through, say, a million rows, and keep track of

fab = nab(HT)/nab

(i.e., the fraction of time that one happened to pick (a,b) and saw a disagreement), etc.

Do you agree that, with overwhelmingly large probability, you will see these f values respecting the inequality

fab + fbc ≥ fac

First of all, the inequality is dealing the total numbers of mismatches not averages as you state it, so you are just dodging there. Secondly, it appears you missed post #125 https://www.physicsforums.com/showpost.php?p=3856772&postcount=125

Where I actually listed all the posibilities for the 6 lists obtained in Bell test experiments and showed that violations of Bell's inequality were obtained 25% of the time. It doesn't matter if you sample 1million or 1 billion times, you will still see a violation 25% of the time. Maybe you think 75% is overwhelmingly large enough for you to declare that the inequality is obeyed but for anyone with any training in basic math, ONE counter example is enough to reject a mathematical theorem -- ONE.

 

[ttn]

First of all, the inequality is dealing the total numbers of mismatches not averages as you state it, so you are just dodging there. Secondly, it appears you missed post #125 https://www.physicsforums.com/showpost.php?p=3856772&postcount=125

Where I actually listed all the posibilities for the 6 lists obtained in Bell test experiments and showed that violations of Bell's inequality were obtained 25% of the time. It doesn't matter if you sample 1million or 1 billion times, you will still see a violation 25% of the time. Maybe you think 75% is overwhelmingly large enough for you to declare that the inequality is obeyed but for anyone with any training in basic math, ONE counter example is enough to reject a mathematical theorem -- ONE.

OK, I give up with these guys. :zzz:

 

[ThomasT]

OK, I give up with these guys. :zzz:

I don't really understand their arguments. But then, I don't really understand yours (for nonlocality in nature) either.

I'm still digesting your article. It might be that it's just too technical for me to fully comprehend/understand. Anyway, once I felt that I actually understood Bell's theorem, and came to agree that at least Bell-LR models of quantum entanglement were definitively ruled out, then the consideration became the relationship between Bell's theorem and reality. That is, should I conclude from experimental BI violations that nature is nonlocal?

Wrt that question, the focus is on the locality assumption/condition as it's encoded into an LR model of entanglement, and the effective cause(s) of experimental BI violation.

If you haven't become too tired of this, then might you simplify and synopsize (preferably in ordinary language) how/why the formalized Bell locality condition/assumption can only be violated due to the fact that nature is nonlocal, and not due to some other, more mundane, reason (such as a more or less trivial incompatibility between the formalization of the locality assumption, and the design and execution of Bell tests)?

 

[billschnieder]

I don't really understand their arguments.

Hi TT, What is it about my argument you do not understand?

 

[ThomasT]

Hi TT, What is it about my argument you do not understand?

Hi Bill, ok, first, what is your argument? Are you saying that Bell's math is wrong? Or are you saying that concluding that nature is nonlocal from Bell's math (and experimental violations of BIs) is unwarranted? If the latter, then we're sort of on the same page. But maybe not really, because it seems that you're approaching the consideration in a different way than I am.

Which is not to say that there aren't multiple legitimate ways of approaching the question. It's just that I don't think I fully understand your approach.

My current hypothesis is that Bell's locality assumption/condition isn't, strictly speaking, as it's encoded in LR models of entanglement, exclusively and uniquely a locality assumption. Which, if true, entails that BI violations don't necessarily inform wrt the underlying reality.

 

[billschnieder]

Hi Bill, ok, first, what is your argument? Are you saying that Bell's math is wrong?

This is what I said back in post #104:

And just to be clear, I do not believe there is an error in the proof. The are two errors:

1 - Thinking that the terms from QM could be meaningfully plugged into the LHS of the CHSH.
2 - Thinking that the terms from Experiments could be meaningfully plugged into the LHS of the CHSH.

Now if Bell proponents insist that Bell's math is attempting to model exactly the way the experiments are performed, then one could argue that the math will be the wrong model of the experiment unless addition assumptions are made. ie that a1=a2, b1=b3, c2=c3, and also that ρ(λ) = ρ(a,b,λ). In that case, I would argue that these assumptions are unreasonable.

So the argument goes like this:

1) Bell's math as derived is essentially correct mathematically, but does not correspond to the QM or experimental situation
2) Even if we grant (for argument sake) that the math corresponds to QM and the experimental situation, you will need to make the unreasonable assumptions that a1=a2, b1=b3, c2=c3, and ρ(λ) = ρ(a,b,λ)

Therefore no matter how you look at it, you can not draw any conclusion from violation of Bell's math by QM and Experiments about the real physical situation happening in the experiments.

Or are you saying that concluding that nature is nonlocal from Bell's math (and experimental violations of BIs) is unwarranted? If the latter, then we're sort of on the same page.

I think we are on the same page.

 

[ThomasT]

This is what I said back in post #104:

And just to be clear, I do not believe there is an error in the proof. The are two errors:

1 - Thinking that the terms from QM could be meaningfully plugged into the LHS of the CHSH.
2 - Thinking that the terms from Experiments could be meaningfully plugged into the LHS of the CHSH.

Now if Bell proponents insist that Bell's math is attempting to model exactly the way the experiments are performed, then one could argue that the math will be the wrong model of the experiment unless addition assumptions are made. ie that a1=a2, b1=b3, c2=c3, and also that ρ(λ) = ρ(a,b,λ). In that case, I would argue that these assumptions are unreasonable.

So the argument goes like this:

1) Bell's math as derived is essentially correct mathematically, but does not correspond to the QM or experimental situation
2) Even if we grant (for argument sake) that the math corresponds to QM and the experimental situation, you will need to make the unreasonable assumptions that a1=a2, b1=b3, c2=c3, and ρ(λ) = ρ(a,b,λ)

Therefore no matter how you look at it, you can not draw any conclusion from violation of Bell's math by QM and Experiments about the real physical situation happening in the experiments.

I think we are on the same page.

Maybe, maybe not. Why is the assumption that ρ(λ) = ρ(a,b,λ) unreasonable? It seems reasonable to me. Also, a, b and c are just polarizer settings, aren't they? So, why is it unreasonable to say that a1 (the polarizer setting in one run) is the same as a2 (the same polarizer setting in another run) ... and the same for b and c?

My focus is currently on the locality condition. Is it, necessarily, a locality condition? Jarrett apparently doesn't think so. And until Dr. Norsen tells me why I shouldn't agree with Jarrett's parsing and conclusion, then that's how I'm thinking about this. In other words, there is an effective cause wrt BI violations, and it has to do with the formal explication of the locality (independence) assumption, wrt which BIs are effectively violated due to a disparagement between the LR formalism and the design and execution of optical Bell tests vis the encoding of the locality assumption/condition, and therefore it can't be concluded from experimental BI violations that nature is nonlocal. In other words, wrt the question of whether or not nature is nonlocal, Bell test results are ambiguous because of the ambiguity of the encoded locality assumption/condition.

 

[lugita15]

If you haven't become too tired of this, then might you simplify and synopsize (preferably in ordinary language) how/why the formalized Bell locality condition/assumption can only be violated due to the fact that nature is nonlocal, and not due to some other, more mundane, reason (such as a more or less trivial incompatibility between the formalization of the locality assumption, and the design and execution of Bell tests)?

ThomasT, I've been trying to do this for you for a while now, with my restatement of Herbert's proof. What step do you disagree with now? I have said that the only remotely nontrivial step in the argument is the step from 1 to 2. You have disagreed with step 3, but as I explained it follows directly from step 2 and the transitive property of equality. So we're back to step 2, and the only criticism you've leveled against it is that its wording is too anthropomorphic, but I responded that you can easily replace "the particles agree in advance what angles to go through and not go through" with "it is determined in advance what angles the two particles will go through or not go through". With that rewording, do you still disagree in the logic from step 1 to step 2? (You may want to reply back in the other thread, to keep this thread uncluttered).

 

[Delta Kilo]

Now if Bell proponents insist that Bell's math is attempting to model exactly the way the experiments are performed, then one could argue that the math will be the wrong model of the experiment unless addition assumptions are made.

But the proof is not supposed to "model exactly the way the experiments are performed". It is a black box. If you agree with assumptions, you have to accept the conclusions. You cannot argue against it because some intermediate step in derivation does not have a clear physical meaning. Yes, there is a step in Bell's proof where there is a product of A(a,λ)A(b,λ)A(c,λ) under the integral, so what? It is just an intermediate step, it does not have to have physical meaning. Specifically, it does not introduce any new physical assumptions. The only assumptions are those used to formulate initial steps of the derivation.

Second, some people apparently confuse the requirement of 'having the same ρ(λ)' with 'having the same λ' when carrying out measurements C(a,b), C(a,c), C(b,c). Bell requires the former, but not the latter.

Third, some people confuse expectation value E[X] = \sum \rho_i X_i and arithmetic mean \overline{X}=\frac{1}{N}\sum X_i. Bell's inequality applies only to the former and not the latter. Which means you do NOT apply Bell's inequality to individual measurement outcomes. Instead, you use experimental data to estimate expectation values, and you plug those expectation values (along with their estimated standard deviations) into Bell's inequality.

PS: We've been through that several times before.

 

[ThomasT]

ThomasT, I've been trying to do this for you for a while now, with my restatement of Herbert's proof. What step do you disagree with now? I have said that the only remotely nontrivial step in the argument is the step from 1 to 2. You have disagreed with step 3, but as I explained it follows directly from step 2 and the transitive property of equality. So we're back to step 2, and the only criticism you've leveled against it is that its wording is too anthropomorphic, but I responded that you can easily replace "the particles agree in advance what angles to go through and not go through" with "it is determined in advance what angles the two particles will go through or not go through". With that rewording, do you still disagree in the logic from step 1 to step 2? (You may want to reply back in the other thread, to keep this thread uncluttered).

Hi lugita. How do you go from step 2 to step 3? Honestly, I don't understand how Herbert concludes that nature is nonlocal. In one sentence he's saying that it's assumed that events at A and B are independent. And then he proceeds to calculate the expected results in a way that I can't connect to his assumption of locality (independence). Same for your restatement of Herbert's proof.

Not insignificantly, Herbert makes the statement that no local reality can explain the facts of optical Bell tests, and therefore reality must be nonlocal.

But that statement is misleading. It should be phrased that no Bell-LR model of quantum entanglement (not "no local reality") can correctly predict the results of optical Bell tests.

 

[ThomasT]

If you agree with assumptions, you have to accept the conclusions.

This is the crux of the matter, imo. The assumption of locality is, as Bell and Dr. Norsen have indicated, the crucial assumption. This assumption is encoded/formalized in a certain way. It's been shown by Jarrett and others that this formalization is ambiguous wrt the assumption of locality, that is, this form also contradicts the design and execution of optical Bell tests in a way that might have nothing to do with whether nature is local or nonlocal.

 

[lugita15]

Hi lugita. How do you go from step 2 to step 3? Honestly, I don't understand how Herbert concludes that nature is nonlocal. In one sentence he's saying that it's assumed that events at A and B are independent. And then he proceeds to calculate the expected results in a way that I can't connect to his assumption of locality (independence). Same for your restatement of Herbert's proof.

Not insignificantly, Herbert makes the statement that no local reality can explain the facts of optical Bell tests, and therefore reality must be nonlocal.

But that statement is misleading. It should be phrased that no Bell-LR model of quantum entanglement (not "no local reality") can correctly predict the results of optical Bell tests.

I've replied back in the other thread here, so that we don't clutter this thread that's supposed to be about ttn's article.

 

[harrylin]

Well, now it's my turn to quibble about terminology. If "dogma" means "anything different from what the herd endlessly repeats", then yes, our article is "dogmatic". [..]

Exactly - and I expect better from a good encyclopedia than proclaiming the POV of the herd, instead I require a fair and neutral presentation of POV's. But perhaps you hold that we already have Wikipedia for that purpose.

[..] you can still appreciate that it's a good thing that there now exists a thorough and careful treatment of Bell's theorem from this particular POV.

Certainly! Each encyclopedia (even each article) has its strong and weak points, and it suffices to be aware of them - for example Wikipedia is generally a mess, but happily it exists.

As to von Neumann, I think it's fair to say that if anybody had scrutinized his theorem as carefully as we scrutinize, in our article, the reasoning involved in Bell's theorem, the theorem would have been "disproved" much earlier. (Of course, really it's not the theorem that was disproved -- just its significance vis a vis "hidden variables".) [..].

I interpret that as a clear overestimation of your group's abilities; which fits with the impression that I already got from the introduction.
Anyway, it looks like a nice overview from that point of view, and I'll read on!

 

[ttn]

My focus is currently on the locality condition. Is it, necessarily, a locality condition? Jarrett apparently doesn't think so. And until Dr. Norsen tells me why I shouldn't agree with Jarrett's parsing and conclusion, then that's how I'm thinking about this.

http://arxiv.org/abs/0808.2178

 

[mattt]

First of all, the inequality is dealing the total numbers of mismatches not averages

This must be a joke, right?

 

[mattt]

In the CHSH-Bell Inequality Theorem:

In a experiment, at both ends each team may choose to measure a,b,c or d to each particle that is coming. The measured result of each measure is +1 or -1.

At the end, they may have recorded, let's say, 1000000 of measured pairs (1,-1), (1,1), (1,1), (-1,-1), (-1,1), (1,-1), (1,-1), (-1,1),...

It may be the case that 105000 of the 1000000 measured pairs correspond to the setting (a,b), other 99000 to the setting (a,c), other 85000 to the setting (d,b), other 450000 to the setting (d,c), and the 261000 remaining measured pairs correspond to the other possible settings ( (a,a), (b,a), (b,b), (c,a), (c,c)...).

If the 105000 measured pairs that correspond to the setting (a,b) are (1,-1), (-1,1), (1,-1), (1,1), (-1,-1),... then C(a,b)=(1(-1)+(-1)1+1(-1)+1*1+(-1)(-1)+...)/105000

And the same with the other terms C(a,c), C(d,b), C(d,c).

 

[DrChinese]

Where I actually listed all the posibilities for the 6 lists obtained in Bell test experiments and showed that violations of Bell's inequality were obtained 25% of the time. It doesn't matter if you sample 1million or 1 billion times, you will still see a violation 25% of the time. Maybe you think 75% is overwhelmingly large enough for you to declare that the inequality is obeyed but for anyone with any training in basic math, ONE counter example is enough to reject a mathematical theorem -- ONE.

That is unbelievable, even coming from you. You think there is something special about arbitrarily calling a trial one where n=10? Guess what, if you make n=1, then every trial that is a match is counter-evidence by your bizarre standards.

Similarly, you would probably reject the idea that the chance of heads after a coin flip is 50%. Any result would disprove it!

 

[rlduncan]

You and several others seem to miss some key points here. PhysicsForums is not intended as a spot to debate your original or nonstandard ideas, which clearly describes your assertion. The key idea here is to share useful knowledge, answer normal questions, etc.

I understand your concern and I have tried not to incorporate my own ideas or theories in the postings.

The examples of experiments and ideas presented in this thread are not original to me. I must give credit to others, particularly the inventor of Boolean logic, George Boole. And of course the published works of others pertaining to his ideas in which references have provided in this thread.

I would not consider Boole’s ideas to be nonstandard but the standard! This discussion via the computer is possible because of his concepts.

Best regards

 

[DrChinese]

I understand your concern and I have tried not to incorporate my own ideas or theories in the postings.

The examples of experiments and ideas presented in this thread are not original to me. I must give credit to others, particularly the inventor of Boolean logic, George Boole. And of course the published works of others pertaining to his ideas in which references have provided in this thread.

I would not consider Boole’s ideas to be nonstandard but the standard! This discussion via the computer is possible because of his concepts.

Best regards

I like Aristotle, Newton and Bohr too. But referencing those whose shoulders we stand on is not an acceptable substitute for today's generally accepted science. You can't really talk about the Bohr model when something better has come along. And If Boole had known of Bell, I am certain he would tip his hat.

Similarly for published references. A lot of things have been published, that does not make it a suitable reference here.

So please, stay with the program here. Identify as such points you are making which are not standard so other readers will understand the difference between your non-standard opinion and that which is generally accepted. I believe you clearly know the difference. Even billschnieder does, he often points out that he is right and everyone else is wrong.

 

[billschnieder]

Why is the assumption that ρ(λ) = ρ(a,b,λ) unreasonable? It seems reasonable to me. Also, a, b and c are just polarizer settings, aren't they?

ρ(λ) = ρ(a,b,λ) is unreasonable because it implies that the distribution of λ which corresponds to the measured outcomes does not depend on the angular settings on either arm of the setup (Alice or Bob). But this can not be true where coincidence counting is done.

To be clear, imagine that every pair of outcomes (Ai, Bi) obtained, corresponds to a specific λi value, ie A(ai,λi) = Ai = ±1, B(bi,λi) = Bi = ±1.

To say that ρ(λ) = ρ(a,b,λ), implies that if you would take all the λs corresponding to all the measured outcomes, their distribution will be exactly the same irrespective of whether we measured at angles (a,b) or (b,c) or (a,c). With coincidence counting and what we know classically about Malus law, this is unreasonable.

To be clear even further, it is equivalent to saying that for the setup of a single stream of particles and 2 polarizers A,B in sequence set at angles a, b, the distribution of hidden polarization parameter λ of the photons that pass through both polarizers is independent of the angles at which both are set, ie ρ(λ) = ρ(a,b,λ)

You do not need conspiracy to realize that the assumption is unreasonable in classical case of two polarizers in sequence. Coincidence counting for two separate arms does effectively the same thing because it only allows photons to be considered on one side if they passed through the other side.

 

[billschnieder]

Also, a, b and c are just polarizer settings, aren't they? So, why is it unreasonable to say that a1 (the polarizer setting in one run) is the same as a2 (the same polarizer setting in another run) ... and the same for b and c?

a1 is complete context for run1 when the angle "a" was set. a2 is the complete context for run2 when angle "a" was set. "a1" is (angle setting "a" + everything else that makes run 1 different from run 2, including time, the complete microscopic state of the device etc.). When Bell's inequality is written as

|<ab> - <ac>| <= 1 + <bc>

"a" in that expression does not represent the angle, it is a label for the list of outcomes. Similarly, "a1" in this case represents the list of outcomes when the angle was set to "a" under context 1 (run 1), and "a2" is the list of outcomes when the angle was set to "a2" for run 2. The above inequality is not valid unless the list of outcomes labeled "a1" is identical to the list of outcomes labeled "a1". In other words, the six lists of outcomes a1,a2,b1,b3,c2,c3 MUST be sortable such that we end up with just three lists a,b,c (ie, a1=a2, b1=b3,c2=c3). Note we are talking about lists of outcomes here.

My focus is currently on the locality condition.

I think it is peripheral. How else will you explain Boole's derivation, he made no locality assumption. There has been a lot of misunderstanding and confusion caused by mixing up functions with probabilities. Some people think that Bell was trying to calculate a joint probability in his equation (2) of his original paper, but he was not. He wrote:

P(a,b) = ∫A(a,λ)B(b,λ)ρ(λ)

Some have misunderstood this to be a joint probability equation which it is not. First of all A(a,λ), B(b,λ) can take up negative values contrary to probabilities. What Bell was calculating was an expectation value for the paired product of the outcome at Alice and Bob. So there is no locality here. The separability of the expectation value is simply due to the fact that a paired product is necessarily separable.

As I showed in post #123, you can derive the same inequality if you start with 3 dichotomous variables and calculate their paired products, or 3 list containing values ±1, without any additional assumption. So any "Blah blah bla" that gives you paired products of 3 dichotomous variables can be used to fool you into thinking the "Blah blah bla" is important for the inequality. It is not.

Earlier in the thread (post #101), I got ttn to admit that λ could be non-local hidden variables and you will still obtain the inequalities.

 

[billschnieder]

In the CHSH-Bell Inequality Theorem:

In a experiment, at both ends each team may choose to measure a,b,c or d to each particle that is coming. The measured result of each measure is +1 or -1.

At the end, they may have recorded, let's say, 1000000 of measured pairs (1,-1), (1,1), (1,1), (-1,-1), (-1,1), (1,-1), (1,-1), (-1,1),...

It may be the case that 105000 of the 1000000 measured pairs correspond to the setting (a,b), other 99000 to the setting (a,c), other 85000 to the setting (d,b), other 450000 to the setting (d,c), and the 261000 remaining measured pairs correspond to the other possible settings ( (a,a), (b,a), (b,b), (c,a), (c,c)...).

If the 105000 measured pairs that correspond to the setting (a,b) are (1,-1), (-1,1), (1,-1), (1,1), (-1,-1),... then C(a,b)=(1(-1)+(-1)1+1(-1)+1*1+(-1)(-1)+...)/105000

And the same with the other terms C(a,c), C(d,b), C(d,c).

But this is not how C(a,b), C(a,c), C(d,b) and C(d,c) are defined within the inequality. They are defined such that the ABSOLUTELY CRUCIAL integration variable λ, is identical for all the terms. In other words, if you take all the individual lambda values from all cases in which the setting pair was (a,b) and all the individual lambda values from all the cases in which the setting pair was (b,c) etc, they will be identical from setting pair to setting pair. ONLY under such conditions can the inequality be derived and ONLY under this scenario are the terms you measured equivalent to the terms in CHSH inequality.

Now I ask you, is it a reasonable assumption to say that the distribution of lambda values for MEASURED pairs is IDENTICAL from setting pair to setting pair.

 

[ThomasT]

ρ(λ) = ρ(a,b,λ) is unreasonable because it implies that the distribution of λ which corresponds to the measured outcomes does not depend on the angular settings on either arm of the setup (Alice or Bob). But this can not be true where coincidence counting is done.

To be clear, imagine that every pair of outcomes (Ai, Bi) obtained, corresponds to a specific λi value, ie A(ai,λi) = Ai = ±1, B(bi,λi) = Bi = ±1.

To say that ρ(λ) = ρ(a,b,λ), implies that if you would take all the λs corresponding to all the measured outcomes, their distribution will be exactly the same irrespective of whether we measured at angles (a,b) or (b,c) or (a,c). With coincidence counting and what we know classically about Malus law, this is unreasonable.

To be clear even further, it is equivalent to saying that for the setup of a single stream of particles and 2 polarizers A,B in sequence set at angles a, b, the distribution of hidden polarization parameter λ of the photons that pass through both polarizers is independent of the angles at which both are set, ie ρ(λ) = ρ(a,b,λ)

You do not need conspiracy to realize that the assumption is unreasonable in classical case of two polarizers in sequence. Coincidence counting for two separate arms does effectively the same thing because it only allows photons to be considered on one side if they passed through the other side.

Ok. Thanks for explaining Bill. I understand and agree with the above.

I'll be reading ttn's paper, http://arxiv.org/abs/0808.2178 , to see if I understand and agree with how he deals with Jarrett's analysis.

But first, I'll deal with your post #192.

 

[billschnieder]

But the proof is not supposed to "model exactly the way the experiments are performed". It is a black box. If you agree with assumptions, you have to accept the conclusions. You cannot argue against it because some intermediate step in derivation does not have a clear physical meaning. Yes, there is a step in Bell's proof where there is a product of A(a,λ)A(b,λ)A(c,λ) under the integral, so what? It is just an intermediate step, it does not have to have physical meaning. Specifically, it does not introduce any new physical assumptions. The only assumptions are those used to formulate initial steps of the derivation.

Second, some people apparently confuse the requirement of 'having the same ρ(λ)' with 'having the same λ' when carrying out measurements C(a,b), C(a,c), C(b,c). Bell requires the former, but not the latter.

Third, some people confuse expectation value E[X] = \sum \rho_i X_i and arithmetic mean \overline{X}=\frac{1}{N}\sum X_i. Bell's inequality applies only to the former and not the latter. Which means you do NOT apply Bell's inequality to individual measurement outcomes. Instead, you use experimental data to estimate expectation values, and you plug those expectation values (along with their estimated standard deviations) into Bell's inequality.

PS: We've been through that several times before.

It seems like you are responding to me but there is nothing in your post that is actually a response to anything I've actually said.

 

[billschnieder]

First of all, the inequality is dealing the total numbers of mismatches not averages

This must be a joke, right?

Eh NO! Did you read the context of the statement? Or have you gone non-contextual on me

In case you were not paying attention, in was in the context of the coin toss example:

3 coins (a,b,c), where nAB represents number of MISMATCHES between the outcomes of a and b.

Inequality: nAB + nAC >= nBC
a= THHHTHTH
b= HHHTTTHH
c= TTTHHHHT
4 + 5 >= 7 : Obeyed (ONLY 3 lists of outcomes)

a1= HTHTTHHT
b1= HHTTTTHT

a2= TTHHTTHT
c2= THHHTTTT

b3= HTHHTTHH
c3= THTTTHTT
3 + 2 >= 7 Disobeyed (6 lists of outcomes)

ttn's response was to change the inequality to a different one between averages. Which was a non-response because he was effectively saying: "I have no explanation why the inequality you provided is violated, but look here I have a different one that is always obeyed".

 

[ThomasT]

a1 is complete context for run1 when the angle "a" was set. a2 is the complete context for run2 when angle "a" was set. "a1" is (angle setting "a" + everything else that makes run 1 different from run 2, including time, the complete microscopic state of the device etc.). When Bell's inequality is written as

|<ab> - <ac>| <= 1 + <bc>

"a" in that expression does not represent the angle, it is a label for the list of outcomes. Similarly, "a1" in this case represents the list of outcomes when the angle was set to "a" under context 1 (run 1), and "a2" is the list of outcomes when the angle was set to "a2" for run 2. The above inequality is not valid unless the list of outcomes labeled "a1" is identical to the list of outcomes labeled "a1". In other words, the six lists of outcomes a1,a2,b1,b3,c2,c3 MUST be sortable such that we end up with just three lists a,b,c (ie, a1=a2, b1=b3,c2=c3). Note we are talking about lists of outcomes here.


I think it is peripheral. How else will you explain Boole's derivation, he made no locality assumption. There has been a lot of misunderstanding and confusion caused by mixing up functions with probabilities. Some people think that Bell was trying to calculate a joint probability in his equation (2) of his original paper, but he was not. He wrote:

P(a,b) = ∫A(a,λ)B(b,λ)ρ(λ)

Some have misunderstood this to be a joint probability equation which it is not. First of all A(a,λ), B(b,λ) can take up negative values contrary to probabilities. What Bell was calculating was an expectation value for the paired product of the outcome at Alice and Bob. So there is no locality here. The separability of the expectation value is simply due to the fact that a paired product is necessarily separable.

As I showed in post #123, you can derive the same inequality if you start with 3 dichotomous variables and calculate their paired products, or 3 list containing values ±1, without any additional assumption. So any "Blah blah bla" that gives you paired products of 3 dichotomous variables can be used to fool you into thinking the "Blah blah bla" is important for the inequality. It is not.

Earlier in the thread (post #101), I got ttn to admit that λ could be non-local hidden variables and you will still obtain the inequalities.

Ok, thanks Bill. I actually think I understand your argument now. It seems to make sense. I'm going to have to reread this and other threads to understand exactly why some people are objecting to it.

 

[billschnieder]

Ok, thanks Bill. I actually think I understand your argument now. It seems to make sense. I'm going to have to reread this and other threads to understand exactly why some people are objecting to it.

Thank you for your patience. Glad to help anytime.

 

[ttn]

Congrats to Thomas for figuring out exactly how to probe Bill to get him to confess openly what I've been saying all along he thinks:

ρ(λ) = ρ(a,b,λ) is unreasonable because it implies that the distribution of λ which corresponds to the measured outcomes does not depend on the angular settings on either arm of the setup (Alice or Bob).

In short, he thinks the "no conspiracy" assumption is unreasonable.

Note also the highly illuminating reasons given:

With coincidence counting and what we know classically about Malus law, this is unreasonable.

To be clear even further, it is equivalent to saying that for the setup of a single stream of particles and 2 polarizers A,B in sequence set at angles a, b, the distribution of hidden polarization parameter λ of the photons that pass through both polarizers is independent of the angles at which both are set, ie ρ(λ) = ρ(a,b,λ)

It is equivalent to that, if (in both cases) the λ refers to the state of the particles *before any measurements are made on them*. That, of course, is precisely what λ means in all the derivations. But why in the world should ρ(λ) -- the distribution of states of an ensemble of particles that have just been shot toward some polarizers -- depend on the orientation of the polarizers? The answer is: there's no reason it should depend on that, not in the Bell type case and not in the Malus type case Bill has in mind here.

My guess is that Bill is wrongly thinking of λ as referring to the state of the particles after some or all of the polarization measurements have been made. If that's what you think λ means, then -- no doubt -- ρ(λ) should probably depend on the polarizer orientations! But ... that's simply not what λ refers to.

You do not need conspiracy to realize that the assumption is unreasonable in classical case of two polarizers in sequence.

No, the assumption is completely reasonable in this "classical case". It only seems unreasonable if you misunderstand what is being claimed -- in particular, if you misunderstand ρ(λ) to mean the distribution of particle states *after the measurements*. But if you correctly understand ρ(λ) to mean the distribution of particle states *prior to any measurements* -- i.e., the distribution of particle states *emitted by the particle source* -- it starts to seem pretty darn reasonable that this should be the same, no matter what somebody is going to decide (later and independently) to measure.

Coincidence counting for two separate arms does effectively the same thing because it only allows photons to be considered on one side if they passed through the other side.

Note another misunderstanding here. The modern experiments use 2-channel polarizers. It isn't true that a pair only gets counted if both particles "pass" their polarizers. Yes, there are detection efficiency issues in the experiments, but basically each photon is subjected to a measurement in which one detector clicks if the photon is "horizontal" (relative to the axis a) and a different detector clicks if the photon is instead "vertical" (relative to a). That is, each photon is detected either way. The alternative to "passing through the polarizer" is not getting absorbed and hence never seen and hence never counted, but is rather getting counted instead by the other detector.

Not that this particular issue is all that relevant to the main discussion here, except insofar as it shows another way in which Bill doesn't know what he's talking about.

 

[mattt]

Travis, I think now I have a problem with your "CHSH-Bell Inequality Theorem".

The mathematical theorem is correct, i.e. the mathematical proof is correct (in my opinion at least).

The problem I think I have now is with respect to the mathematical setup (the \lambda distribution meaning) and the factorizability condition (4) (concretely about how it is supposed to codify a necessary condition for locality).

Imagine I have a theory that predict the outcomes of the experiment the following mathematical way (kind of a hidden variable stochastic theory) :

My theory says that the process that produces the pairs of particles doesn't produce exactly the same "kind of pair" everytime, but there are "different groups" of pairs (following a probability distribution), and my theory says that pairs from the same group will have the exact same (stochastic) outcomes prediction for the experiment (but pairs from different "groups" will have different (stochastic) outcomes prediction for the experiment).

Mathematically:

The Probability Space (\Lambda, P) will account for the different "groups" of pairs.

Then, for each \lambda=\lambda_0, \alpha_1=a, \alpha_2=b, my theory says that the outcomes will follow a distribution we will call P_{a,b}(A_1,A_2|\lambda_0)

Imagine one of these distributions prediction outcomes is the following one:

P_{a,b}(A_1=1,A_2=1|\lambda_0)=0.9

P_{a,b}(A_1=1,A_2=-1|\lambda_0)=0.04

P_{a,b}(A_1=-1,A_2=1|\lambda_0)=0.03

P_{a,b}(A_1=-1,A_2=-1|\lambda_0)=0.03


This "theory" does NOT satisfy your factorizability condition (4), but now I don't see why someone who believes in "locality" would call this "theory" non-local.

ETA: if someone does not understand, I will put it into words:

This "theory" says that the source produce "different types of pairs" and the theory says that if we only pay attention to pairs of one type (called \lambda_0 ) then, if the setting is a,b then 90% of the outcomes (of pairs from exactly this group) will be (1,1), 4% will be (1,-1), 3% will be (-1,1) and 3% will be (-1,-1).

Of course this "theory" has to give another stochastic/probabilistic prediction for any other setting and any other "type/group" of pairs.

The thing is that this "theory" does not satisfy Travis's "necessary condition for locality" (4) and what I ask is if everybody would call this "theory" non-local (taking into account the meaning of "locality" anyone of you may have).