Scholarpedia article on Bell's Theorem

[ttn]

I said I wasn't going to argue with Bill anymore, but for the sake of anybody else reading, I wanted to be sure the following was clear:

Now let us break down what this implies about what you believe:

- You believe contrary to Malus law that the angular difference between the two sides, does not affect the rate of coincidence detection.

That is just out of the blue. Of course it's true that the angular difference between the two sides does affect the rate of coincidence detection. (Incidentally, this is *not* "Malus law". Malus' law is about the probability for light to pass through two successive polarizers with some relative angle between them. The EPR-Bell setup involves two hunks of light, with each hunk going in opposite directions, and with each hunk being subjected to only a single polarization measurement.) Why Bill thinks something I've said commits me to denying this, is a mystery (but not such a big surprise) to me.

- You believe that every property of the complete system "instrument + particle" relevant for the outcomes actually observed are identical when "a" is measured coincidentally with "b" and when "a" is measured with "c", despite the fact that the angle between "a" and "b" is different from the angle between "a" and "c".

It shouldn't be put that way. The "no conspiracy" assumption does not say that the state of the complete system is identical every time a is measured with b, etc. It says only that, on average, the statistical distribution of the different possible states (whatever the heck those might be) is the same, no matter which angles we measure along. That is, for the bajillion particle pairs that happened to get measured along a and b, the statistical distribution of states is about the same as for the bajillion particle pairs that happened to get measured along b and c, etc. That is, the source just makes particle pairs the same way each time (where "the same way" probably involves some randomness and hence a large set of possible states) regardless of which settings the polarizers will be in. Denying this requires a kind of "pre-established harmony" -- indeed, one might say "a conspiracy" -- between the random/hidden variables determining the settings, and those determining the particle states.

- You believe only conspiracy or non-locality can explain why all relevant properties of the complete system of "instrument + particle" for two separate runs, performed at different times, and filtered using coincidence circuitary governed by a different angular differences might be different, so long as they used the same macroscopic angle setting.

Subject to the clarifications above, that is basically correct. That is, after all, what the theorem shows: "no conspiracies" and "locality" jointly entail something that is found in the experiments to be false.

 

[ttn]

ttn, seriously I don't know how can you be so patient.

Thanks mattt, I appreciate that. I guess it was probably a rhetorical question, but I'll answer anyway for fun. Part of the answer is that this is the kind of thing one expects at a place like this, and it's kind of fun to engage with it every so often (but it does get old fast). A more serious part of the answer is that I feel about Bill more or less the way that most normal physicists no doubt feel about me. So I'm kind of "on the premise" of trying very hard to extend other people -- I mean, specifically, people who have a view that's unfamiliar to me and that sounds wrong to me and that I don't fully understand -- the same courtesy that I wish people would more often extend to me when I talk about Bohm's theory or other such things. Another part of the reason is that, both by profession and "demeanor", I'm a teacher. So I assume, sometimes for too long, that people are actually interested in understanding things better, that they will be open to good arguments if only they hear them put sufficiently clearly, etc. But, as you saw, I've basically given up with Bill. =)

So, is there anyone else here (apart from me) that actually has tried to check if the mathematical proof is correct or not?

I looked at it pretty carefully and I think it looks pretty convincing, too!

 

[billschnieder]

But then you won't agree either with other versions (weaker than this one) of Bell's Theorem.

The fact that the terms in the inequality do not correspond to the terms being measured in the experiment is a non-starter.

What I like of this mathematical theorem is that it is the strongest I have seen of this kind (Bell type theorem), the most general mathematical premises.

Then you will like Boole's proof even better. It is the most general of them all and it can never be violated unless there is a logical error. I encourage you to check out Itamar Pitowsky's exposition of it cited, or the original version.

Here is another one originally suggested by Sica (cited earlier in the thread http://dx.doi.org/10.1016/S0030-4018(99)00417-4):

Assume that we have three lists of numbers, each of length N, with each number restricted to values ±1.The lists are denoted a, b, and c and their respective members by ai, bi, and ci, i = 1...N.

It follows that
(1a) $a_ib_i - a_ic_i = a_i(b_i-c_i) = a_ib_i(1-b_ic_i)$

By summing this equation over the list, dividing by N and taking absolute values, noting that bi = 1/bi we get:(1b) $\left | \frac{\sum_{i=1}^{N} a_ib_i}{N} - \frac{\sum_{i=1}^{N} a_ic_i}{N}\right | \leq \frac{\sum_{i=1}^{N} \left | a_ib_i \right |\left | 1 - b_ic_i \right |}{N} = \frac{\sum_{i=1}^{N} (1 - b_ic_i)}{N}$

And finally:
(2) $\left | \frac{\sum_{i=1}^{N} a_ib_i}{N} - \frac{\sum_{i=1}^{N} a_ic_i}{N}\right | \leq 1 - \frac{\sum_{i=1}^{N} b_ic_i}{N}$

or

(3) | <ab> - <ac> | <= 1 - <bc>

Bells inequality from ONLY ONE assumption: That we have 3 lists of numbers with values ±1. This inequality can NEVER be violated by any 3 lists of numbers with values ±1. Starting with 4 lists, you get the CHSH.

Sica says:

It is perhaps startling to the reader to find that Bell's inequality has been obtained here with no mention of locality or nonlocality, properties of probability functions, factorization assumptions, etc. All these assumptions are peripheral to the central fact: identity (2) and inequality (3) follow from nothing but the arithmetic of ±1's and the assumption of limits.

He goes on to derive the CHSH inequality from similar assumptions.

And concludes:

The present paper has shown that the form of Bell's inequalities appropriate for comparison with experiments is an identity based on minimal assumptions. If these minimal assumptions are not met by the data, the conditions for validity of the identity will be violated, and the inequality may (or may not) be violated. This may happen if it is not noticed that the data for two correlation estimates uniquely determines the third in the three correlation case, and that data for three correlations determine the fourth in the four correlation case. That this has not been generally recognized may stem from the belief, based on early derivations, that Bell's inequality is a fact about statistics. But in fact, as has been shown above, it is a constraint of arithmetic, quite independently of statistics.

 

[billschnieder]

That is just out of the blue. Of course it's true that the angular difference between the two sides does affect the rate of coincidence detection. (Incidentally, this is *not* "Malus law". Malus' law is about the probability for light to pass through two successive polarizers with some relative angle between them.

It's not out of the blue. Rather it is out of the view that since the same angle value "a" was set during the a1,b1 run as during and a2,c2 run, a1 must be identical to a2. The view which believes that (a1|b1, ie outcome at angle "a" given that an outcome was measured at angle "b") = (a2|c2, outcome at angle "a" given that an outcome was measured at "c"). If you are now claiming that (a1|b1) ≠ (a2|c2) in Bell test experiments, then you are admitting that:
- the distribution of λ is not the same in each term.
- you have 6 unique terms not 3 as required by the inequality.

As concerns Malus Law.
(1)- Single stream of photons with 2 polarizers A & B in sequence. Probability of detection is the probability that the photon passed through B given that it also passed through A.

(2)- Two steams of correlated photon pairs with one polarizer each A & B, with coincidence circutary. Probability of detection for any photon, is the probability that it passed B given that it's counterpart passed A.

It is naive, given what we know classically about Malus Law and coincidence circuitary, to think that outcomes from freely setting the device to "a" will give you results that do not dependen on the "b" in Bell test experiments.

 

[rlduncan]

ttn,

billschnieder has provided three experiments relating to this thread for you to comment on.

1. Post # 102 - coin toss experiment
2. Post # 107 - Lyon, Paris, Lille study
3. Post # 125 – cyclic dependency

Your failure to make a comment is very telling. Why not start with the coin toss experiment and explain how it is possible this simple experiment can violate a Bell-type inequality? Notice the similarity to the EPR experiments. Am I to conclude that nature is nonlocal because the inequality was violated? If yes, then why do we need to use entangled photons?

 

[DrChinese]

Why not start with the coin toss experiment and explain how it is possible this simple experiment can violate a Bell-type inequality? Notice the similarity to the EPR experiments. Am I to conclude that nature is nonlocal because the inequality was violated? If yes, then why do we need to use entangled photons?

Although it has nothing to do with this thread, I will be glad to answer. Obviously, if there is a sufficient deviation from any fair sample, you can get even a classical analogy to give nonsensical results. When was the last time you saw 30 heads in a row? It is ridiculous to talk about "cyclic dependency" when it comes to Bell tests because they have been done with random choices of angle settings. Typical of billschnieder that he manages to get folks to bite on this obvious red herring. I especially love the part about it being "very telling". Do you really think science stands or falls on a comment in PF?

If you are so confident, take the DrChinese challenge! Give me a miniature sample of 30 with realistic results (3 angle settings, 0/120/240 degrees, plus or minus, labeled a/b/c). I will select 2 of the 3 settings for each trial of the 30 randomly. We'll see if you can get a sample with a match rate anywhere near 25%, the quantum prediction.

Good luck! You are going to need it!

a/b/c

1: ++-
2: -+-
3: +-+
...or whatever you want to make up.

By the way, this is basically the same test Richard Gill wrote about recently. But me being me, I choose to name it after me. LOL.

 

[harrylin]

I don't think any huge discussion is needed here, and this thread seems like a perfectly good place to have a short one, since after all your comments are about the scholarpedia article.

You suggest that our understanding/presentation of what constitutes "relativity" is superficial/thin.

Not exactly... I'll try to state it more precisely: my reading of parts of your writing that I can judge, gave me the impression that your writing is based on a rather superficial reading of a few books or articles. Sorry if that wasn't clear. However, happily your new reply changed my impression.

[..]
So, for purposes of communication, we tend to use the phrase "special relativity" to mean basically what most other people use that phrase to mean. But of course, in the discussion, we explicitly distinguish the "Einsteinian" and "Lorentzian" views, distinguish the idea of "relativity at the level of what can be observed" (which is compatible with both Einsteinian and Lorentzian approaches) and "fundamental relativity" (which the Lorentzian approach violates), etc. This is all more or less exactly following Bell, who for example notes repeatedly that Bohmian Mechanics (in so far as it requires a dynamically privileged reference frame, or some equivalent) fails to respect fundamental relativity, etc. It's true that in his "how to teach" article he described himself as teaching "special relativity" [..]

OK - but did you realize that such yielding to mislabeling results in contradictions with the existing literature? Not just with Bell's papers but also with textbooks and articles by Lorentz, Langevin and even some articles by Einstein. I hope that such things didn't occur with other definitions and labels concerning QM and EPR.

Basically the main point is just that it's incredibly easy to reconcile non-locality (which remember we know is there because of Bell's theorem and the experiments) with "lorentzian relativity" -- Bell always called this "the simplest solution", etc., and we agree. Indeed, since we all like Bohmian Mechanics, we are quite happy to agree! But reconciling quantum non-locality with *Einsteinian relativity* -- i.e., what most normal physicists think of as just plain "relativity" -- is much harder.

Einstein's metaphysical opinions flip-flopped so much that, depending on how you look at it, it's extremely easy or impossible.
It may be better to label the different models not with people's names but with the names of the models themselves. You could correct that little issue with a few minor changes, by simply removing some unnecessary statements and labels about relativity; an article on Bell's Theorem doesn't have use for them. Instead you can simply define your own labels when you introduce them, e.g. "fundamental relativity" as referring to the block universe interpretation of relativity.

It can in principle be done, sort of, probably. (See for example Tumulka's relativistic GRW model.) But it's very very difficult, and it's basically an open question whether non-locality can be reconciled with "fundamental relativity" in the context of a "fully serious" theory (e.g., something that makes all the predictions of ordinary QFT).

Do you disagree with any of this? Or do you merely prefer using the words "special relativity" in a less narrow way, like the way Bell evidently uses them in "how to teach"?

My answer is here above. Would you agree with using the label "quantum mechanics" in a narrow way, so that it refers to the Copenhagen interpretation? The objection is similar, and the solution is also similar. :tongue2:

 

[ttn]

OK - but did you realize that such yielding to mislabeling results in contradictions with the existing literature?

Well, contradictions (involving this sort of terminological issue, and much worse as well) are rampant in the literature already, so I don't think there's any set of terminology we could choose that would avoid all contradictions. We just tried to explain what we meant so it would be clear. You don't think it is clear? I find that slightly surprising, since what I wrote in the last post here (and which you evidently understood just fine and even seemingly agreed with for the most part) is just about the same as what we wrote in the article. So I'm really not sure what it was that gave you the original impression.

Not just with Bell's papers but also with textbooks and articles by Lorentz, Langevin and even some articles by Einstein. I hope that such things didn't occur with other definitions and labels concerning QM and EPR.

You mean, you hope there's nothing else in the physics part of the article that might be considered controversial or wrong by some people?? :rofl:

Einstein's metaphysical opinions flip-flopped so much that, depending on how you look at it, it's extremely easy or impossible.

Yes, I agree, it's hard to pin down "what Einstein thought" on this or other issues.

It may be better to label the different models not with people's names but with the names of the models themselves. You could correct that little issue with a few minor changes, by simply removing some unnecessary statements and labels about relativity; an article on Bell's Theorem doesn't have use for them. Instead you can simply define your own labels when you introduce them, e.g. "fundamental relativity" as referring to the block universe interpretation of relativity.

I don't see anything confusing/misleading about labeling the views with the names. I think an article on Bell's Theorem *does* need to go into this stuff. Bell's Theorem, properly understood, is a proof that nature is non-local, and basically the only reason anybody should care about that is because, for about 100 years, relativity has given us all a pretty strong reason to expect locality instead. So the question of how to reconcile non-locality with relativity (and whether it's even possible) is an obvious and important one. And here I think it's essential to get into the question of what "relativity" even means/says/requires, distinguish emergent/superficial/empirical relativity from "fundamental relativity", etc. So again I'm really just not sure what you're meaning to criticize.

My answer is here above. Would you agree with using the label "quantum mechanics" in a narrow way, so that it refers to the Copenhagen interpretation? The objection is similar, and the solution is also similar. :tongue2:

That's a good and fair question. I guess I think the two cases, (Copenhagen) QM and (Einsteinian) SR, are a little different. As I explained before, I think basically all physicists *actually believe* Einsteinian SR -- it's what they mean when they talk about "SR". And if you probe them by asking such things as whether they think maybe there is an "ether" that we just can't detect, they will answer unamibuously "no, SR doesn't just say we can't detect an ether, it says there isn't one!" And so on. That is, I think they really believe Einsteinian SR in a fully consistent way. On the other hand, although most physicists will claim to endorse Copenhagenish ideas, they don't really believe (or even really understand) what Copenhagen says -- it's just to them about one paragraph of vague words they read in a textbook 30 years ago in grad school, but never studied carefully or took too seriously. Instead, they were trained/dogmatized in the "shut up and calculate" attitude, with its hostility not just to alternatives to Copenhagen, but indeed to Copenhagen itself. And if you probe a normal physicist (don't quote that phrase out of context!) about foundations of QM issues, you find quickly that they don't have any particular view, but instead they have a contradictory hash of only-weakly-held slogans. For example, it is trivially easy to get a normal physicist to take whichever position you want on the question of whether the collapse of the wave function is a real physical process, or is instead merely an updating of our knowledge: just frame the question in the context of "hidden variables", or "non-locality", respectively.

For this reason, I think the only safe way to use the words "quantum mechanics" (with no explicitly qualifier) is to refer only to what's sometimes called "the quantum formalism", i.e., the mathematical algorithms for calculating things. That is, I think "QM" should really be used to refer to the shut-up-and-calculate (non-) interpretation, not Copenhagen. If you want to refer to Copenhagen, call it "Copenhagen QM".

So... that's why I think it's OK/proper to use "SR" to denote the *interpretation* of "the relativistic formalism" that physicists overwhelmingly and deeply endorse, while using "QM" to denote only the formalism itself devoid of any particular interpretation.

On the other hand, I doubt that this or any other choice of terminology causes any real problems of communication/clarity. So, although I'm certainly open to hearing what you found confusing/unclear in the article, I'm probably not interested in having a super long discussion about which terminology is best...

 

[ttn]

In response to rlduncan...

Three fair coins are tossed simultaneously by three individuals. For simplicity, let's them be a, b, and c and each coin is tossed eight times. It follows that the outcomes must obey the following inequality

nab(HH) + nbc(HH) ≥ nac(HH)

That's already not right. Bill gave an example of possible data, evidently to "prove" that the inequality has to be satisfied:

To see this, consider the following outcomes for the three coins
a=HTTTHTHH
b=TTHHTHHH,
c=HTHTTTHH,

2+3 ≥ 3 , the inequality is satisfied.

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".

However, if in an experiment you decide to perform three different runs of the experiment such that you obtain

a1=HTTHTHHH
b1=THHTTHTT,

b2=HTHHTHHT
c1=TTTTHHTH,

a2=THHTHTTH
c2=HHHTHTTT,

You now have 1+1 ≥ 3 which violates the inequality. Why is that? The reason is simply because the three terms in the inequality are not independent. They are calculated from only 3 lists of outcomes so that there is a cyclic dependency. However in the latter experiment, we have 6 distinct lists not reduceable to 3!

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.

 

[harrylin]

[..] Yes, I agree, it's hard to pin down "what Einstein thought" on this or other issues. [..] I don't see anything confusing/misleading about labeling the views with the names.

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 think an article on Bell's Theorem *does* need to go into this stuff. Bell's Theorem, properly understood, is a proof that nature is non-local, and basically the only reason anybody should care about that is because, for about 100 years, relativity has given us all a pretty strong reason to expect locality instead. So the question of how to reconcile non-locality with relativity (and whether it's even possible) is an obvious and important one. And here I think it's essential to get into the question of what "relativity" even means/says/requires, distinguish emergent/superficial/empirical relativity from "fundamental relativity", etc. So again I'm really just not sure what you're meaning to criticize.

If you read this part of your reply again and then compare it with my earlier suggestions, you will notice that I agree with it; my criticism is, again, that you evidently prefer to include remarks and labels that are controversial to say the least and for which there is absolutely no need. Why would you want to do that in an encyclopedia article?

That's a good and fair question. I guess I think the two cases, (Copenhagen) QM and (Einsteinian) SR, are a little different. As I explained before, I think basically all physicists *actually believe* Einsteinian SR -- it's what they mean when they talk about "SR".
And if you probe them by asking such things as whether they think maybe there is an "ether" that we just can't detect, they will answer unamibuously "no, SR doesn't just say we can't detect an ether, it says there isn't one!" And so on. That is, I think they really believe Einsteinian SR in a fully consistent way. [..] On the other hand, although most physicists will claim to endorse Copenhagenish ideas, they don't really believe (or even really understand) what Copenhagen says [..]

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 completely useless at best, even worse than "Copenhagen". Thus, again, and for a last time (I won't continue about this either): if you want to present a quality article, you scrap this kind of debatable things which you don't need at all, and simple say for example that with "fundamental relativity" the article refers to a block universe model. BTW, I agree with you about QM, that was to illustrate the issue.

 

[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?

:rofl:

 

[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?