Is Bell's Theorem a Valid Solution to the Locality Versus Nonlocality Issue?

[harrylin]

And just to make the EPR argument clear:

There is an element of reality IF I can predict Alice's result in advance. [..]

Just to be sure: does EPR according to Bell also assume that if I can not predict Alice's result in advance, there may still be an element of reality? I ask as that is rather common for modern local realist theories.

 

[DrChinese]

Such papers demonstrate that there is no scientific consensus. Instead this is, as physicsforums phrases it, "part of current professional mainstream scientific discussion". That it doesn't conform to your opinion is irrelevant for such a discussion (and nobody cares); only your scientific arguments are relevant (and highly appreciated!).

Thanks for the comment. I try to identify areas in which there are scientific consensus, so my personal opinion is usually not that important and I identify it where it is "deviant". But there is no more scientific disagreement over Bell than over evolution or the big bang. Articles by billschnieder notwithstanding. By the way, I maintain an entire list of local realists and their papers; so I can tell you it's not that large a group.

 

[Varon]

So do Aspect Experiment and the like prove that non-local influence with randomness encryption occurs in nature with properties there before measurement or does it prove Bohr original views that properties like position doesn't exist before measurements? Is it:

1. Non-local reality with randomness encryption, or
2. Realism rejected and there is nothing to be non-local about because properties don't exist prior to measurement so no non-local influence at all for non-existent properties.

Which one is the mainstream view??

 

[DrChinese]

Just to be sure: does EPR according to Bell also assume that if I can not predict Alice's result in advance, there may still be an element of reality? I ask as that is rather common for modern local realist theories.

No element of reality if the observable cannot be predicted with certainty, according to EPR.

But be careful here, there is a mistake that trips up people: the realist says the elements exist simultaneously and do not need to be measured to exist. This is tacitly assumed in EPR because they didn't think it was necessary to spell that out. The reader is to deduce this. That would be the a, b and c I talk about.

 

[harrylin]

Thanks for the comment. I try to identify areas in which there are scientific consensus, so my personal opinion is usually not that important and I identify it where it is "deviant". But there is no more scientific disagreement over Bell than over evolution or the big bang. Articles by billschnieder notwithstanding. By the way, I maintain an entire list of local realists and their papers; so I can tell you it's not that large a group.

I have the impression that that group is expanding. Also BTW, the interesting discussions here about QM motivated me to join physicsforums.

 

[harrylin]

No element of reality if the observable cannot be predicted with certainty, according to EPR.

According to EPR or according to Bell's version of EPR? For a precise discussion that may be relevant... would you (or someone else) have a citation by any chance?

But be careful here, there is a mistake that trips up people: the realist says the elements exist simultaneously and do not need to be measured to exist. This is tacitly assumed in EPR because they didn't think it was necessary to spell that out. The reader is to deduce this. That would be the a, b and c I talk about.

OK, thanks for the precision.

 

[harrylin]

[..]
Which one is the mainstream view??

For perhaps the most recent poll (and the only one that I know of), see:
https://www.physicsforums.com/showthread.php?t=489958&highlight=poll

According to that (certainly imperfect*) poll there are only many minority views; the "Copenhagen Interpretation" has the most adherents here in physicsforums (currently 21/93=23%).

*Depending on how the poll is formulated other results are possible. From the discussion it appeared that "the" Copenhagen interpretation may need to be split up in two; moreover, realist interpretations have been split in several groups.

Cheers,
Harald

 

[JesseM]

No. If you reject counterfactual definiteness (CFD), then there are no problematic correlations. You need three binary strings in order to have a problem.

Not true, even if the particles don't have predetermined results for all three settings, there is still the fact that they must have predetermined identical results for setting A in those specific cases where the experimenters are both going to measure A in the future, and likewise for B and C. If you reject the idea that they have predetermined results for all three settings on every trial, then you get the conclusion that if you could know their hidden variables and see which (if any) settings they have predetermined results for, you could also know in advance that 1 year later the experiments might both choose that setting, but that they won't both choose whatever setting the variables don't give predetermined results for.

 

[JesseM]

Yes I disagree, as stated in earlier post. Bell's theorem like any theorem can never be violated under the conditions of the theorem. It only takes one counter example to disprove a theorem.

But your counter example must actually match the conditions of the theorem! You can't give a counter example where Alice and Bob are not guaranteed to get the same outcome if they make the same measurement, for example, as your second example involving a1 and a2 seems to do (see below).

Also note that Bell's theorem is a statistical theorem, so random violations are actually quite possible, the idea is just that in the limit as the number of trials goes to infinity the probability of the inequality being violated approaches zero, a counterexample would have to provide some sort of rule for generating outcomes (in a local realist way) where you can reliably get violations even as the number of trials becomes large.

If any of the sample statistics violate the theorem then the theorem is disproved or the conditions of the theorem have not been adhered to. I am suggesting the latter is true. In my original post I stated that his theorem is a mathematical truth, a tautology meaning it is always true.

If you think that's the case then you don't understand it very well, Bell is not simply making the claim that for a set of objects which each either have or don't have properties A,B,C, we must have Number(A, not B) + Number(B, not C) ≥ Number(A, not C). That would indeed be a mathematical tautology, but it is not Bell's theorem. Bell's theorem deals with probabilities of measurement outcomes, not simply objective (but unknowable) truths about the unmeasured hidden variables associated with all particles. Bell's theorem would be more like a derivation of this inequality:

P(measured that particle 1 had A, particle 2 did not have B given that we measured particle 1 for A, and particle 2 for B)
+
P(measured that particle 1 had B, particle 2 did not have C given that we measured particle 1 for B, and particle 2 for C)
≥
P(measured that particle 1 had A, particle 2 did not have C given that we measured particle 1 for A, and particle 2 for C)

This one is obviously not a tautology, you need a number of additional conditions to derive it. And of course we don't measure "probabilities" directly, we only measure fractions of trials where some event occurred, so what Bell's theorem is telling us is that in a situation that matches his conditions, the probability approaches zero that we would get a violation of this inequality:

(Number of trials where particle #1 was measured for property A and it did have A, and particle #2 was measured for property B and it did not have B)
+
(Number of trials where particle #1 was measured for property B and it did have B, and particle #2 was measured for property C and it did not have C)
≥
(Number of trials where particle #1 was measured for property A and it did have A, and particle #2 was measured for property C and it did not have C)

You can of course have violations of this in a small number of measurements, but if the setup of the experiment matches Bell's conditions and the underlying laws of nature are local realist and respect the no-conspiracy condition, then according to Bell's theorem the probability this will be violated approaches zero as the number of trials approaches infinity.

Again this is Bell's inequality and you are not addressing my point. If a1≠a2 or b1≠b2 or c1≠c2 then a violation will occur.

I don't understand what a1 and a2 are supposed to represent! In your example where a,b,c represented the result recorded for one of three coins on a glass table (with Bob always recording the opposite of what he sees from under the table), on any trial where Alice and Bob both chose to look at the same coin (say "a"), they're both guaranteed to get the same result on that trial, no? Give me a concrete example (like the coin/glass table one) where it's possible that a1≠a2, but I can see clearly what "a1" and "a2" represent, and I can also see that there are a series of trials and on each trial, if Alice and Bob both make the same measurement they are guaranteed to get the same result. If your model doesn't fulfill these conditions, it has no relevance to Bell's theorem, which is specifically about a scenario where this is the case!

Each trial must be indexed

What does "indexed" mean? Each time the two experimenters make observations, they already know what trial number that observation belongs with--there can be no possibility of retroactively changing the numbers assigned to each observation. After all, Bell's theorem is supposed with pairs of entangled particles, we have to make sure that each of Alice's measurement of one member of a pair is assigned the same number as Bob's measurement of the other member of that same pair, not a member of a different pair.

and the sequences checked to see if a1=a2, etc.

Alice and Bob cannot check this, they can only measure a single property on each trial. Yes or no, are you claiming it is possible to have a probability of violating this inequality that doesn't approach zero as the number of trials goes to infinity, and where the measurements actually fit the experimental conditions Bell was describing? (which would include the fact that Alice and Bob pick in a random or pseudorandom manner what property to measure on each trial, the fact that Alice's cannot causally influence either Bob's choice or the properties associated with the particle/sequence Bob is measuring and vice versa, and the fact that they always get the same answer on any trial where they both pick the same property to measure)

(Number of trials where object #1 was measured for property A and it did have A, and object #2 was measured for property B and it did not have B)
+
(Number of trials where object #1 was measured for property B and it did have B, and object #2 was measured for property C and it did not have C)
≥
(Number of trials where object #1 was measured for property A and it did have A, and object #2 was measured for property C and it did not have C)

Here the "objects" can be anything you like--particles, triplets of coins as viewed from above or underneath under a glass table, game show contestants being asked one of three questions in separate rooms, whatever. If you think this inequality can be reliably violated (i.e. the probability of violation doesn't approach zero even in the limit as the number of trials goes to infinity) in a situation that matches the experimental preconditions, then please give me a situation that clearly respects all those conditions, not just a vague list of symbols with no clear meaning or connection to Bell's experimental preconditions.

 

[DrChinese]

I have the impression that that group is expanding. Also BTW, the interesting discussions here about QM motivated me to join physicsforums.

Happy to see you interested here.

I would say that the scientific LR group is very small. It is so small, I can't really say if it is growing much. As I have said many times, this group is not influential and not really accepted within the community, and for good reason. In fact, some mainstream physics publications have a policy to reject anti-Bell papers out of hand. They do the same thing with papers on perpetual motion machines.

 

[DrChinese]

According to EPR or according to Bell's version of EPR? For a precise discussion that may be relevant... would you (or someone else) have a citation by any chance?

Per EPR (1935), the following is sufficient:

"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity."

 

[jtbell]

1. Non-local reality with randomness encryption,

What is "randomness encryption?" You've used this phrase in at least two threads now, the first time I've ever seen it. A Google search turns up mostly pages related to cryptography. The only physics-related hits I found on the first few pages of search results were your posts.

 

[rlduncan]

If you think that's the case then you don't understand it very well...

Not the case, however, by your own admission you apparently don't understand the OP or Post #27 which addresses the EPRB connection both which are self explanatory.

Here the "objects" can be anything you like--particles, triplets of coins as viewed from above or underneath under a glass table, game show contestants being asked one of three questions in separate rooms, whatever. If you think this inequality can be reliably violated (i.e. the probability of violation doesn't approach zero even in the limit as the number of trials goes to infinity) in a situation that matches the experimental preconditions, then please give me a situation that clearly respects all those conditions, not just a vague list of symbols with no clear meaning or connection to Bell's experimental preconditions.

Sorry, (considering all the posts in this thread) the above paragraph is not worth responding to. It is clear to me you don't understand my concerns about the applicability of Bell's theorem to the EPRB experiments and the conclusions drawn.

 

[DrChinese]

Let me restate my concern: If the polarizer angle is set to ab and a string of photons are measured, then a sequence of spin detections result for a1. Now change the polarizer to orientation c and measure the angle ac, experimentally this is a different run and presumably a different string of photons is being measured resulting in a2, that is, a different sequence. If a1≠a2, then a violation of Bell’s theorem can occur. As demonstrated in Example 2.

Please clarify your position. Are you saying that a1=a2 and no violation can occur (for this cause), or a1≠a2 and is irrelevant to the conditions of Bell’s theorem.

Thanks in advance.

You have the requirements backwards. The realist says that a, b and c exist simultaneously. If so, what are their values? Per your example 1, any time you "fill in" the unmeasured (counterfactual) values, you get results that do not match experiment.

In your parlance, if a1≠a2 then you are saying that there is communication between Alice and Bob and locality is not respected. You may not realize you are saying this, but you are. Clearly, if I change a1 based on the value of bc (or whatever pair I am actually measuring), the result is no longer local realistic.

 

[JesseM]

Not the case

If you think Bell's theorem is just a simple mathematical tautology, then it is the case that you don't understand it.

however, by your own admission you apparently don't understand the OP or Post #27 which addresses the EPRB connection both which are self explanatory.

No, post #27 does not address how it can be that Alice and Bob have a choice of which three to measure on each trial, which is required for your example to have an "EPRB connection". In post #27 you say:

Coin tossing also compares to the ERPB experiment. Imagine a glass top where Alice’s views from the top and Bob from the bottom. When viewing the same coin they always get opposite results. Now flip coins ab to generate a sequence of flips. Repeat a second time using coins bc and record the sequence. Finally do the same for ac, where the first coin is viewed by Alice and the second coin by Bob.

This would imply that on the first "sequence of flips" where you only flipped coins ab, Alice and Bob were restricted to looking at only a or b but were forbidden from picking c. Likewise on the second sequence they were forbidden from picking a, and on the third sequence they were fobidden from picking b. This is a flagrant violation of the experimental conditions assumed by Bell, where you have a sequence of trials and on each trial the experimenters can choose between any of the measurement settings.

And of course, you also said in post #27 that "Bell's theorem pertains to any two-valued variables." This is a grossly ignorant statement, Bell's theorem only applies to scenarios that meet the experimental conditions he stated, if you violate these conditions (for example by telling the experimenters in advance that they are only allowed to pick two of the three available measurement settings, and calibrating the properties of the entities being measured based on this foreknowledge of which two settings they will be using) then it is trivial to violate the Bell inequalities. If you think you are a great genius who has slain the mighty Bell-dragon because you've found a way to violate the inequality in a setup which does not match the experimental conditions assumed by Bell, then you really are acting like a complete crackpot. If on the other hand you would prefer to avoid looking like an ignoramus, you need to discuss an example that actually matches these basic conditions assumed by Bell:

1. A series of trials, on each trial Alice and Bob are choosing in a random (or pseudorandom) manner one of the three possible binary properties to measure (for example, both might be standing near a set of three coins A,B,C and can choose anyone to record whether it's heads or tails)
2. Alice's choice of which property to measure cannot causally influence Bob's choice or the properties of what he is measuring, and vice versa
3. On each trial both of them record a single definite outcome to their measurement (like Bob measuring B and recording "heads", Alice measuring C and recording "tails")
3. On any trial where they both choose the same property to measure, they always get identical results

 

[rlduncan]

You have the requirements backwards. The realist says that a, b and c exist simultaneously. If so, what are their values? Per your example 1, any time you "fill in" the unmeasured (counterfactual) values, you get results that do not match experiment.

In your parlance, if a1≠a2 then you are saying that there is communication between Alice and Bob and locality is not respected. You may not realize you are saying this, but you are. Clearly, if I change a1 based on the value of bc (or whatever pair I am actually measuring), the result is no longer local realistic.

There is not any communication between Alice and Bob in the Example 2 activity in OP. Alice randomly generates her own coin selections and measured outcomes without the knowledge of Bob’s coin selections or outcomes. Your suggestion that there is communication comes from not actually performing the activity as described in my posts.

Flip the three coins on the glass table. These are your three values that you request. Let Alice randomly choose a coin and record the coin selection (a,b,c) and the outcome (H,T) while viewing from the top from a defense satellite. Now let Bob randomly choose a coin while viewing from the bottom of the table and again record the coin selection and outcome for Bob. This is trial #1. No communication! Now repeat the trials 50 or more times. Decide on which Bell inequality you would like to test, I will suggest a different one from the OP.

Bell’s Theorem, nab(HT) + nbc(HT) ≥ nac(HT)

Now tabulate the nab(HT), that is, Alice picked coin “a” and got a H, Bob picked coin “b” and got a T. Do the same for nbc(HT) and nac(HT). These will inevitable result in a violation of the theorem. The reason (IMO) is because of picking only two coins at a time. In addition, the data will show that the “a” sequence in ab is not the same as the “a” sequence in ac, same for “b” and “c”. However, in Example 1 of the OP where the a,b, and c sequences remain the same a violation never occurs no matter the sequence length. Explain this?

Note to JesseM: When Alice and Bob choose the same coin 100% of the time they are opposites. The data will verify this, no? Also the data includes all possible outcomes, such as: ba(HH), ca(TH), etc. They are not necessary in analyzing the above Bell’s theorem but they were definitely recorded. Example 2 of the OP only listed the necessary information in testing Bell’s theorem: nab(HH) + nbc(HH) ≥ nac(HH)

This alternate analysis is given to determine a possible cause for the violation of Bell’s theorem when applied to EPR experiments. Bell framed his analysis using probability theory. Please don’t confuse the two. Bill Schnieder can give a better account of a logical error(s) in Bell’s probability theory (if they exist). Based the literature this has not been an easy task. Thus the reason for my post. This is a valid alternative. There is nothing in the OP suggesting that probability theory is needed to demonstrate Bell’s inequality, this was intentional.

 

[rlduncan]

If you think Bell's theorem is just a simple mathematical tautology, then it is the case that you don't understand it.

No, post #27 does not address how it can be that Alice and Bob have a choice of which three to measure on each trial, which is required for your example to have an "EPRB connection". In post #27 you say:

This would imply that on the first "sequence of flips" where you only flipped coins ab, Alice and Bob were restricted to looking at only a or b but were forbidden from picking c. Likewise on the second sequence they were forbidden from picking a, and on the third sequence they were fobidden from picking b. This is a flagrant violation of the experimental conditions assumed by Bell, where you have a sequence of trials and on each trial the experimenters can choose between any of the measurement settings.

And of course, you also said in post #27 that "Bell's theorem pertains to any two-valued variables." This is a grossly ignorant statement, Bell's theorem only applies to scenarios that meet the experimental conditions he stated, if you violate these conditions (for example by telling the experimenters in advance that they are only allowed to pick two of the three available measurement settings, and calibrating the properties of the entities being measured based on this foreknowledge of which two settings they will be using) then it is trivial to violate the Bell inequalities. If you think you are a great genius who has slain the mighty Bell-dragon because you've found a way to violate the inequality in a setup which does not match the experimental conditions assumed by Bell, then you really are acting like a complete crackpot. If on the other hand you would prefer to avoid looking like an ignoramus, you need to discuss an example that actually matches these basic conditions assumed by Bell:

1. A series of trials, on each trial Alice and Bob are choosing in a random (or pseudorandom) manner one of the three possible binary properties to measure (for example, both might be standing near a set of three coins A,B,C and can choose anyone to record whether it's heads or tails)
2. Alice's choice of which property to measure cannot causally influence Bob's choice or the properties of what he is measuring, and vice versa
3. On each trial both of them record a single definite outcome to their measurement (like Bob measuring B and recording "heads", Alice measuring C and recording "tails")
3. On any trial where they both choose the same property to measure, they always get identical results

Please see Post #51

 

[JesseM]

Flip the three coins on the glass table. These are your three values that you request. Let Alice randomly choose a coin and record the coin selection (a,b,c) and the outcome (H,T) while viewing from the top from a defense satellite. Now let Bob randomly choose a coin while viewing from the bottom of the table and again record the coin selection and outcome for Bob. This is trial #1. No communication! Now repeat the trials 50 or more times.

Great, this actually does match the conditions Bell requires, unlike your post #27 where you suggested first only flipping ab a bunch of times and having Alice and Bob choose between those, then only flipping bc a bunch of times and having them choose between those, then only flipping ac a bunch of times and having them choose between those. If instead you flip all three coins a series of times, and each time Alice and Bob choose randomly which of a,b,c to record, then this example is a good fit for the conditions needed to derive Bell's inequality.

However, in these terms I still have no idea what you mean when you write a1≠a2. The only idea I could come up with was that a1 was supposed to be the value Alice recorded on a given trial when she picked coin a, and a2 was supposed to be the value Bob recorded on the same trial when he picked coin a (as always, assuming the value he records is the opposite of what he sees from under the table). But if that's the case then a1 should always equal a2 since they are both looking at the selfsame coin! If a1 and a2 are supposed to represent something different in terms of this example, maybe you could actually explain it when I ask you direct questions like this one from post #44 (which you ignored):

I don't understand what a1 and a2 are supposed to represent! In your example where a,b,c represented the result recorded for one of three coins on a glass table (with Bob always recording the opposite of what he sees from under the table), on any trial where Alice and Bob both chose to look at the same coin (say "a"), they're both guaranteed to get the same result on that trial, no?

Bell’s Theorem, nab(HT) + nbc(HT) ≥ nac(HT)

Now tabulate the nab(HT), that is, Alice picked coin “a” and got a H, Bob picked coin “b” and got a T. Do the same for nbc(HT) and nac(HT). These will inevitable result in a violation of the theorem.

Again, the theorem is statistical (from what I've seen, Bell always writes the inequalities he derives in terms of probabilities or expectation values, not mere numbers of trials), a short sequence can violate it but the probability of getting a violation approaches zero as the number of trials becomes large. This follows from the fact that the choice of which coins Alice and Bob record on each trial is random and should in the long term have no statistical correlation with what the three coins are on each trial. To see this, try writing the above as

P(a=H,b=T|measured ab) + P(b=H,c=T|measured bc) ≥ P(a=H,c=T|measured ac)

Assuming no correlation between the probability of picking a given pair like ab and the probability between a given sequence of three like P(a=H,b=H,c=T), then we should have:

P(a=H,b=T|measured ab) = P(a=H,b=T,c=H) + P(a=H,b=T,c=T)

and

P(b=H,c=T|measured bc) = P(a=H,b=H,c=T) + P(a=T,b=H,c=T)

and

P(a=H,c=T|measured ac) = P(a=H,b=H,c=T) + P(a=H,b=T,c=T)

Do you disagree? If so please tell me the first step above you disagree with. If you don't disagree with the above, you should agree that

P(a=H,b=T|measured ab) + P(b=H,c=T|measured bc) ≥ P(a=H,c=T|measured ac)

is equivalent to:

[P(a=H,b=T,c=H) + P(a=H,b=T,c=T)] + [P(a=H,b=H,c=T) + P(a=T,b=H,c=T)] ≥ [P(a=H,b=H,c=T) + P(a=H,b=T,c=T)]

And if you cancel out like terms from both sides, you're left with

P(a=H,b=T,c=H) + P(a=T,b=H,c=T) ≥ 0

Which is naturally going to be true, regardless of the specific values of those probabilities!

If the abstract proof doesn't convince you we could also demonstrate this empirically. Try writing down a reasonably large series of trials which give 3 results on each trial, like this:

1. a=H,b=T,c=H
2. a=T,b=H,c=T
3. a=T,b=T,c=H
4. a=H,b=H,c=T
...

and so on, for say 50 trials or something. Then for each trial, determine randomly which two will be measured using this random number generator with Min=1 and Max=6, using:

1=ab
2=ac
3=ba
4=bc
5=ca
6=cb

If you use this method to generate nab(HT), nbc(HT), nac(HT) for a reasonably large number of trials (again, let's say 50) I'd bet that you would not see a violation of nab(HT) + nbc(HT) ≥ nac(HT). And certainly the larger the number of trials, the lower the chance of a violation.

Note to JesseM: When Alice and Bob choose the same coin 100% of the time they are opposites. The data will verify this, no?

That's true if on a single trial you have only one possible value for a, one for b, and one for c. But again if that's the case then I don't understand what it could mean to write a1≠a2. What do a1 and a2 represent, in terms of this example?

Also the data includes all possible outcomes, such as: ba(HH), ca(TH), etc. They are not necessary in analyzing the above Bell’s theorem but they were definitely recorded. Example 2 of the OP only listed the necessary information in testing Bell’s theorem: nab(HH) + nbc(HH) ≥ nac(HH)

This alternate analysis is given to determine a possible cause for the violation of Bell’s theorem when applied to EPR experiments. Bell framed his analysis using probability theory. Please don’t confuse the two.

Your sentence structure is unclear, what are the "two" things you don't you want me to confuse? Bell's analysis and "EPR experiments"? Or the "alternate analysis" of "example 2 of the OP" (which once again I don't understand how to apply to the coin example, since I don't know what a1 and a2 represent) vs. the original analysis of example 1? Or some other pair?

 

[Rap]

Not true, even if the particles don't have predetermined results for all three settings, there is still the fact that they must have predetermined identical results for setting A in those specific cases where the experimenters are both going to measure A in the future, and likewise for B and C. If you reject the idea that they have predetermined results for all three settings on every trial, then you get the conclusion that if you could know their hidden variables and see which (if any) settings they have predetermined results for, you could also know in advance that 1 year later the experiments might both choose that setting, but that they won't both choose whatever setting the variables don't give predetermined results for.

I'm sorry, I don't understand exactly what you are saying. Please allow me to change notation. There are six strings to consider, Alice's A1, A2, and A3 corresponding to her orienting her detector at -45, 0, and 45 degrees, and Bob's B1, B2, and B3, where in case B1, his detector is aligned with Alice's when she measures A1, etc. Only two strings are actually measured: one "A" string and one "B" string. Could you rephrase what you said in terms of these six strings, it would really help me to understand what you are saying.

 

[rlduncan]

Great, this actually does match the conditions Bell requires, unlike your post #27 where you suggested first only flipping ab a bunch of times and having Alice and Bob choose between those, then only flipping bc a bunch of times and having them choose between those, then only flipping ac a bunch of times and having them choose between those. If instead you flip all three coins a series of times, and each time Alice and Bob choose randomly which of a,b,c to record, then this example is a good fit for the conditions needed to derive Bell's inequality.

Yes great and sorry for any confusion.

However, in these terms I still have no idea what you mean when you write a1≠a2. The only idea I could come up with was that a1 was supposed to be the value Alice recorded on a given trial when she picked coin a, and a2 was supposed to be the value Bob recorded on the same trial when he picked coin a (as always, assuming the value he records is the opposite of what he sees from under the table). But if that's the case then a1 should always equal a2 since they are both looking at the selfsame coin! If a1 and a2 are supposed to represent something different in terms of this example, maybe you could actually explain it when I ask you direct questions like this one from post #44 (which you ignored):

No you missed the meaning of a1 and a2. a1 is the sequence of values when Alice randomly chooses coin "a" and Bob randomly chooses coin "b". a2 is the sequence of values when Alice randomly chooses coin "a" and Bob randomly chooses coin "c". See Post #51.

Again, the theorem is statistical (from what I've seen, Bell always writes the inequalities he derives in terms of probabilities or expectation values, not mere numbers of trials), a short sequence can violate it but the probability of getting a violation approaches zero as the number of trials becomes large. This follows from the fact that the choice of which coins Alice and Bob record on each trial is random and should in the long term have no statistical correlation with what the three coins are on each trial. To see this, try writing the above as

P(a=H,b=T|measured ab) + P(b=H,c=T|measured bc) ≥ P(a=H,c=T|measured ac)

Assuming no correlation between the probability of picking a given pair like ab and the probability between a given sequence of three like P(a=H,b=H,c=T), then we should have:

P(a=H,b=T|measured ab) = P(a=H,b=T,c=H) + P(a=H,b=T,c=T)

and

P(b=H,c=T|measured bc) = P(a=H,b=H,c=T) + P(a=T,b=H,c=T)

and

P(a=H,c=T|measured ac) = P(a=H,b=H,c=T) + P(a=H,b=T,c=T)

Do you disagree? If so please tell me the first step above you disagree with. If you don't disagree with the above, you should agree that

P(a=H,b=T|measured ab) + P(b=H,c=T|measured bc) ≥ P(a=H,c=T|measured ac)

is equivalent to:

[P(a=H,b=T,c=H) + P(a=H,b=T,c=T)] + [P(a=H,b=H,c=T) + P(a=T,b=H,c=T)] ≥ [P(a=H,b=H,c=T) + P(a=H,b=T,c=T)]

And if you cancel out like terms from both sides, you're left with

P(a=H,b=T,c=H) + P(a=T,b=H,c=T) ≥ 0

Which is naturally going to be true, regardless of the specific values of those probabilities!

If the abstract proof doesn't convince you we could also demonstrate this empirically. Try writing down a reasonably large series of trials which give 3 results on each trial, like this:

1. a=H,b=T,c=H
2. a=T,b=H,c=T
3. a=T,b=T,c=H
4. a=H,b=H,c=T
...

and so on, for say 50 trials or something. Then for each trial, determine randomly which two will be measured using this random number generator with Min=1 and Max=6, using:

1=ab
2=ac
3=ba
4=bc
5=ca
6=cb

Probability theory is not needed in analyzing this sequence method and its application to Bell type inequalities.

If you use this method to generate nab(HT), nbc(HT), nac(HT) for a reasonably large number of trials (again, let's say 50) I'd bet that you would not see a violation of nab(HT) + nbc(HT) ≥ nac(HT). And certainly the larger the number of trials, the lower the chance of a violation.

Not true for reasons already stated.

That's true if on a single trial you have only one possible value for a, one for b, and one for c. But again if that's the case then I don't understand what it could mean to write a1≠a2. What do a1 and a2 represent, in terms of this example?

Answered above.

Your sentence structure is unclear, what are the "two" things you don't you want me to confuse? Bell's analysis and "EPR experiments"? Or the "alternate analysis" of "example 2 of the OP" (which once again I don't understand how to apply to the coin example, since I don't know what a1 and a2 represent) vs. the original analysis of example 1? Or some other pair?

Don't confuse my post using the sequence theory in framing the EPRB experiments and Bell's probability theory for they are two different approaches. Yes the nab(HT), nbc(HT), nac(HT) vaules can be converted to probabilities. However, the number of events (nab(HT), etc.) is simpler in explaining this sequence method. Many times you default to probabilities in your responses and I understand why for that's Bell. If you stay on my method in which probabilities are not need the discussion will improve significantly.

I hope I have adequately addressed your concerns and made my position clear.

 

[JesseM]

I'm sorry, I don't understand exactly what you are saying. Please allow me to change notation. There are six strings to consider, Alice's A1, A2, and A3 corresponding to her orienting her detector at -45, 0, and 45 degrees, and Bob's B1, B2, and B3, where in case B1, his detector is aligned with Alice's when she measures A1, etc. Only two strings are actually measured: one "A" string and one "B" string. Could you rephrase what you said in terms of these six strings, it would really help me to understand what you are saying.

The idea I was getting at was that on any trial where Alice picks A1 and Bob picks B1, the particles at some time prior to measurement must have had hidden (or hidden and observable) variables that predetermined their results for setting A1 and B1. So just knowing the hidden variables of the particle at that time, without knowing about other conditions in the rest of the past light cone of the measurement at the same time, would allow you to say with certainty "if the experimenters select settings A1 and B1 (which depends on a huge other set of factors in the past light cone that I don't know about), then I can predict in advance they will get the same result X". Knowing the variables associated with the particles alone might not be sufficient to determine what result they would give at other settings, but they should be enough to predetermine A1 and B1 on any trial where the experimenters actually pick A1 and B1.

Now, I suppose it's possible that the properties of the particles alone are not enough to determine with certainty what results they would give with setting A1 and B1, that you would have to know the full set of conditions throughout some cross section of the past light cone of each measurement (like region C in Bell's figure 6.4 here) in order to predict what the result would be. For example, we might suppose that the particle's response to encountering a detector is not just determined by properties it has carried with it from the time of emission to the time of measurement, but rather is influenced chaotically by almost everything in its past light cone, much like the "butterfly effect" in the weather which implies that the weather today depends sensitively on pretty much every microscopic event 1 week ago that lies in the past light cone of Earth today. But in this case it would seem even more astonishing and "conspiratorial" if, without fail, every time both experimenters chose the same setting (like A1 and B1) they always got identical results. That would be a bit like if on each successive day, experimenters on opposite sides of the Earth always selected one of three chaotic experiments to run--say the http://www.fas.harvard.edu/~scdiroff/lds/MathamaticalTopics/ChaoticPendulum/ChaoticPendulum.html, the chaotic dripping faucet, or a chaotic chemical reaction--and then the would observe the state after some time T, recording "+" if it was in one region of the phase space and "-" if in a different region. If on any trial where both experimenters selected the same experiment to run, they always were found to the same value for the +/-, wouldn't this also imply a very strange "conspiracy" between seemingly unrelated events?

 

[JesseM]

No you missed the meaning of a1 and a2. a1 is the sequence of values when Alice randomly chooses coin "a" and Bob randomly chooses coin "b". a2 is the sequence of values when Alice randomly chooses coin "a" and Bob randomly chooses coin "c". See Post #51.

Post 51 doesn't say anything about a1 and a2, but OK.

Probability theory is not needed in analyzing this sequence method and its application to Bell type inequalities.

"Bell type inequalities" seems overly vague, any of the specific inequalities that Bell derived and showed were incompatible with QM, or any inequality which physicists say is violated in QM, is always an inequality involving probabilities or expectation values. Do you disagree? If so please provide a counterexample, preferably from one of the papers of Bell or another prominent quantum physicist.

If you use this method to generate nab(HT), nbc(HT), nac(HT) for a reasonably large number of trials (again, let's say 50) I'd bet that you would not see a violation of nab(HT) + nbc(HT) ≥ nac(HT). And certainly the larger the number of trials, the lower the chance of a violation.

Not true for reasons already stated.

What "reasons already stated"? If you're going to avoid addressing my questions/statements directly because you claim you've addressed them, could you at least quote the specific previous comment of yours that you think is relevant to my question/statement?

Also, when you say "not true" do you just mean my statement isn't relevant to your argument because it talks about probabilities and you don't want to talk about that, or are you actually claiming that as a statement about probabilities, "certainly the larger the number of trials, the lower the chance of a violation" is incorrect? If you disagree with that, then to show why you're wrong I need to make arguments involving probability, obviously.

Also, if you actually think my statement about probabilities is "not true", why not try the experiment I suggested? You give me a list of 50 triplets of results for each trial, I'll use the random number generator to see what Alice and Bob measure on each trial, and then I'll add the numbers and see if nab(HT) + nbc(HT) ≥ nac(HT) is violated. We can even try this a bunch of times (perhaps using the same list of 50 trials and just randomly varying the choice of what measurements are made on each trial, if you don't want to generate a new list of 50 each time) and see how frequently it gets violated, my bet would be "hardly ever". If you would bet differently, this would be an easy way of demonstrating you are right and I am wrong.

Your sentence structure is unclear, what are the "two" things you don't you want me to confuse? Bell's analysis and "EPR experiments"? Or the "alternate analysis" of "example 2 of the OP" (which once again I don't understand how to apply to the coin example, since I don't know what a1 and a2 represent) vs. the original analysis of example 1? Or some other pair?

Don't confuse my post using the sequence theory in framing the EPRB experiments and Bell's probability theory for they are two different approaches. Yes the nab(HT), nbc(HT), nac(HT) vaules can be converted to probabilities. However, the number of events (nab(HT), etc.) is simpler in explaining this sequence method. Many times you default to probabilities in your responses and I understand why for that's Bell. If you stay on my method in which probabilities are not need the discussion will improve significantly.

But how is the "discussion" supposed to be relevant to showing an error in Bell's theorem, if Bell's theorem is understood by Bell and other physicists to be a statement about probabilities or expectation values, and not a statement which Bell or any other competent physicist thinks is guaranteed to hold even for a small number of trials? Or do you disagree that this is how it is understood?

 

[Rap]

The idea I was getting at was that on any trial where Alice picks A1 and Bob picks B1, the particles at some time prior to measurement must have had hidden (or hidden and observable) variables that predetermined their results for setting A1 and B1. So just knowing the hidden variables of the particle at that time, without knowing about other conditions in the rest of the past light cone of the measurement at the same time, would allow you to say with certainty "if the experimenters select settings A1 and B1 (which depends on a huge other set of factors in the past light cone that I don't know about), then I can predict in advance they will get the same result X". Knowing the variables associated with the particles alone might not be sufficient to determine what result they would give at other settings, but they should be enough to predetermine A1 and B1 on any trial where the experimenters actually pick A1 and B1.

But the hidden or observable variables cannot ever be known, because they must be measured to be known, and it is assumed that no such measurements are made. The only measurements made are one by Alice, one by Bob. If you cannot, in principle, know them, then they are not valid subjects of scientific inquiry.

 

[JesseM]

But the hidden or observable variables cannot ever be known, because they must be measured to be known, and it is assumed that no such measurements are made. The only measurements made are one by Alice, one by Bob. If you cannot, in principle, know them, then they are not valid subjects of scientific inquiry.

But by definition when we ask if local realism might be true, we are asking about models that include hidden parameters that (at least if QM is empirically correct) can never be measured. If you don't even want to imagine what the objective reality beyond what we can measure might be like (and what might be deducible by a hypothetical being who knew the values of some of these nonmeasurable quantities), I don't see how the question of local realism vs. not local realism can even be meaningful to you, unless you are expecting an experimental violation of QM.

 

[rlduncan]

Post 51 doesn't say anything about a1 and a2, but OK.

"Bell type inequalities" seems overly vague, any of the specific inequalities that Bell derived and showed were incompatible with QM, or any inequality which physicists say is violated in QM, is always an inequality involving probabilities or expectation values. Do you disagree? If so please provide a counterexample, preferably from one of the papers of Bell or another prominent quantum physicist.

Also, if you actually think my statement about probabilities is "not true", why not try the experiment I suggested? You give me a list of 50 triplets of results for each trial, I'll use the random number generator to see what Alice and Bob measure on each trial, and then I'll add the numbers and see if nab(HT) + nbc(HT) ≥ nac(HT) is violated. We can even try this a bunch of times (perhaps using the same list of 50 trials and just randomly varying the choice of what measurements are made on each trial, if you don't want to generate a new list of 50 each time) and see how frequently it gets violated, my bet would be "hardly ever". If you would bet differently, this would be an easy way of demonstrating you are right and I am wrong.But how is the "discussion" supposed to be relevant to showing an error in Bell's theorem, if Bell's theorem is understood by Bell and other physicists to be a statement about probabilities or expectation values, and not a statement which Bell or any other competent physicist thinks is guaranteed to hold even for a small number of trials? Or do you disagree that this is how it is understood?

Apparently you have not read any of the papers listed by Bill Schneider. These simulations have already been published and shown to violate Bell's inequalities. You simply refuse to acknowledge their relevance to EPRB experiments.

 

[Rap]

But by definition when we ask if local realism might be true, we are asking about models that include hidden parameters that (at least if QM is empirically correct) can never be measured. If you don't even want to imagine what the objective reality beyond what we can measure might be like (and what might be deducible by a hypothetical being who knew the values of some of these nonmeasurable quantities), I don't see how the question of local realism vs. not local realism can even be meaningful to you, unless you are expecting an experimental violation of QM.

But Bell's theorem states that if you accept counterfactual definiteness, then no hidden variable theory can reproduce the results of QM. I don't expect an experimental violation of QM and I expect that Bell's theorem is correct, so I think the issue is settled for the case in which CFD is accepted - i.e. there can be no local realism (i.e. there are superluminal effects). However, my point was that maybe the resolution to Bell's paradox is not that there are superluminal effects, but rather that CFD is invalid.

 

[JesseM]

Apparently you have not read any of the papers listed by Bill Schneider. These simulations have already been published and shown to violate Bell's inequalities. You simply refuse to acknowledge their relevance to EPRB experiments.

I don't "refuse to acknowledge" anything, but I'm not going to waste my time wading through a lot of papers, I already read one of the papers Bill Schnieder mentioned, "Possible Experience: From Boole to Bell" and found it to contain nothing that refuted Bell (see Bill Schnieder's post [post=2766980]here[/post] which quoted extensively from that paper, and my responses [post=2780659]here[/post] and [post=2781956]here[/post]), nor did it contain a "simulation". If one of those papers has a simulation that meets the conditions of a Bell experiment that I mentioned, and finds consistent violations of some inequality, can you tell me which one. Note that most papers giving computer simulations are not actually denying Bell's theorem but rather are trying to model theories which exploit experimental loopholes like the one listed here, see for example this discussion of a model by de Raedt that DrChinese wrote up. If you think there are papers that have given simulations that violate Bell inequalities even in simulated loophole-free experiments, I suspect you're either misunderstanding something or else the simulated test conditions don't actually match those assumed by Bell in deriving the same inequality, but again feel free to point me in the direction of a specific example.

In any case, are you going to avoid answering my question #1 about whether you disagree that the "Bell inequalities" that are believed by physicists to follow from local realism but to conflict with QM always involve probabilities or expectation values, and my question #2 about whether you disagree that in your model where Alice and Bob are choosing randomly from a set of three coins on each trial, the probability of a violation of nab(HT) + nbc(HT) ≥ nac(HT) gets increasingly tiny the more trials are performed?

 

[JesseM]

But Bell's theorem states that if you accept counterfactual definiteness, then no hidden variable theory can reproduce the results of QM. I don't expect an experimental violation of QM and I expect that Bell's theorem is correct, so I think the issue is settled for the case in which CFD is accepted - i.e. there can be no local realism (i.e. there are superluminal effects). However, my point was that maybe the resolution to Bell's paradox is not that there are superluminal effects, but rather that CFD is invalid.

But are you trying to use the hypothetical violation of CFD to save local realism? If so I think you need a model which postulate physical facts beyond those measurable in quantum theory, quantum theory itself does not clearly satisfy the criteria for a local realistic model (for example there is a single quantum state for an entangled 2-particle system where the particles may be measured very far apart, and a measurement at either location instantaneously changes the whole state according to the formalism).

 

[Rap]

But are you trying to use the hypothetical violation of CFD to save local realism? If so I think you need a model which postulate physical facts beyond those measurable in quantum theory, quantum theory itself does not clearly satisfy the criteria for a local realistic model (for example there is a single quantum state for an entangled 2-particle system where the particles may be measured very far apart, and a measurement at either location instantaneously changes the whole state according to the formalism).

I'm just trying to follow the consequences of rejecting CFD, and it does remove the problem of superluminal effects. Also, as in Copenhagen, I consider the wave function to be an encoding of measurement-produced knowledge rather than an objective entity, so that the collapse of the wave function is a collapse of our uncertainty, not of some objective field. Thus there are no superluminal effects when the whole state collapses.

 

[DrChinese]

There is not any communication between Alice and Bob in the Example 2 activity in OP. Alice randomly generates her own coin selections and measured outcomes without the knowledge of Bob’s coin selections or outcomes. Your suggestion that there is communication comes from not actually performing the activity as described in my posts.

Flip the three coins on the glass table. These are your three values that you request. Let Alice randomly choose a coin and record the coin selection (a,b,c) and the outcome (H,T) while viewing from the top from a defense satellite. Now let Bob randomly choose a coin while viewing from the bottom of the table and again record the coin selection and outcome for Bob. This is trial #1. No communication! Now repeat the trials 50 or more times. Decide on which Bell inequality you would like to test, I will suggest a different one from the OP.
...

Apparently, you want to be a realist without giving any meaning or definition to it. If you look at your example 1, which is classical, you get results which are experimentally refuted by a Bell test. If you relax the realism requirement to match your example 2, then you get results which match the predictions of QM. This is Bell at work.

P.S. I wouldn't reference billschnieder's comments if I were you, his name is mud to me.

In fact, he can't even spell his last name correctly.

 

[DrChinese]

I'm just trying to follow the consequences of rejecting CFD, and it does remove the problem of superluminal effects. Also, as in Copenhagen, I consider the wave function to be an encoding of measurement-produced knowledge rather than an objective entity, so that the collapse of the wave function is a collapse of our uncertainty, not of some objective field. Thus there are no superluminal effects when the whole state collapses.

If you reject CFD, then it is somewhat meaningless to declare yourself as occupying a position other than the standard one. And you are free to pick an interpretation.

 

[harrylin]

Per EPR (1935), the following is sufficient:

"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity."

Thanks! Apparently you (and Bell?) interpret "then" as "only then"... I'll look up the original to see if it was just formulated in an awkward way. If so, "EPR reality" is much more narrow than the common concept of "reality"!

 

[Rap]

If you reject CFD, then it is somewhat meaningless to declare yourself as occupying a position other than the standard one. And you are free to pick an interpretation.

Hmm - I don't understand - what is the "standard position"? And why am I free to pick an interpretation? I'm not saying you are wrong, I'm just trying to understand.

 

[DrChinese]

Thanks! Apparently you (and Bell?) interpret "then" as "only then"... I'll look up the original to see if it was just formulated in an awkward way. If so, "EPR reality" is much more narrow than the common concept of "reality"!

The originals:

http://www.drchinese.com/David/EPR_Bell_Aspect.htm

And yes, because it was so formulated, it has been well accepted as being fairly stringent. Which led to Bell being all the more respected.

 

[DrChinese]

Hmm - I don't understand - what is the "standard position"? And why am I free to pick an interpretation? I'm not saying you are wrong, I'm just trying to understand.

Most scientists do not accept that there is a value to unmeasured particle observables. They reject CFD. That is mainline QM. There are the various interpretations such as MWI, BM, Copenhagen, etc. which all make the same predictions.