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

[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.

 

[harrylin]

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"!

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken:

"We shall be satisfied with the following criterion [..] far from exhausting all possible ways of recognizing a physical reality [...]." and "Regarded not as a necessary, but merely a sufficient condition of reality, this criterion [...]". -EPR1935.

Thus their predictibility criterion was for them (of course!) not a necessary condition of reality. If Bell's theorem would be based on the assumption that it is a necessary condition for EPR, then his theorem would be wrong. However, I'm not aware that such is the case.

Regards,
Harald

 

[JesseM]

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken

It depends if by "no element of reality" you just mean "we are not justified in concluding there is an element of reality in that case, though there could be" or "there is definitely no element of reality in that case". I think EPR (and DrChinese, and Bell) would say the first, but not the second.

 

[harrylin]

It depends if by "no element of reality" you just mean "we are not justified in concluding there is an element of reality in that case, though there could be" or "there is definitely no element of reality in that case". I think EPR (and DrChinese, and Bell) would say the first, but not the second.

This is about what EPR meant (and with less importance what DrChinese meant); and I think that everyone meant what they wrote:

"not as a necessary, but merely a sufficient condition of reality". -EPR

Which is exactly how I understood it in post #36. Then I asked:

" 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."

To which DrChinese answered:

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

Harald

 

[JesseM]

This is about what EPR meant (and with less importance what DrChinese meant); and I think that everyone meant what they wrote:

"not as a necessary, but merely a sufficient condition of reality". -EPR

Which is exactly how I understood it in post #36. Then I asked:

" 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."

To which DrChinese answered:

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

Hmm, I suspect there was some miscommunication there and DrChinese thought you were just asking if according to EPR's argument we are justified in inferring an element of reality in that case. But perhaps DrChinese can comment...

 

[DrChinese]

I now checked it (I downloaded it from the source but thanks for making it accessible for everyone!). It looks clear to me that your interpretation, "No element of reality if the observable cannot be predicted with certainty, according to EPR" is mistaken:

"We shall be satisfied with the following criterion [..] far from exhausting all possible ways of recognizing a physical reality [...]." and "Regarded not as a necessary, but merely a sufficient condition of reality, this criterion [...]". -EPR1935.

Thus their predictibility criterion was for them (of course!) not a necessary condition of reality. If Bell's theorem would be based on the assumption that it is a necessary condition for EPR, then his theorem would be wrong. However, I'm not aware that such is the case.

Regards,
Harald

I said it was sufficient as a definition when I quoted it. I also said that there is no element of reality without that. I meant that per the definition in use. Perhaps you have a better definition.

Strictly speaking, it is certainly possible there is an element of reality WITHOUT us being able to predict it in advance. For example, I had to pay when my son wrecked the car even though I could not predict the amount in advance with certainty. And believe me, that was very real to my pocketbook.

So if you take the contranegative (also being true), you get: IF you cannot predict in advance with certainty, THEN there is no element of reality. But what can you do with this statement? I don't think too much, because you cannot prove the antecedent.

So my point is: Bell used the well accepted EPR definition. That definition is one which is easy to follow, and because it is sufficient it is enough for our examples. I.e. for entangled pairs. The only issue to Bell would be if you could prove convince folks that this was not a sufficient condition. That would be a tough hurdle. Keep in mind that was a cornerstone of EPR.

 

[DrChinese]

Hmm, I suspect there was some miscommunication there and DrChinese thought you were just asking if according to EPR's argument we are justified in inferring an element of reality in that case. But perhaps DrChinese can comment...

Yes, I think a slight miscommunication. Per EPR's definition, they would not have ascribed an element of reality without meeting this requirement. Not that they themselves believed as such. They simply used it for convenience. I think it was a brilliant touch, personally.

That was why I mentioned it as a sufficient condition. There could exist a less restrictive definition, I just cannot imagine such which is also useful.

 

[DrChinese]

I ask as that is rather common for modern local realist theories."

To which DrChinese answered:

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

Harald

The local realist wants a MORE restrictive definition of reality, not less. That way Bell wouldn't apply. So the way you are headed (i.e. towards a lesser definition) doesn't do too much.

 

[JesseM]

So if you take the contranegative (also being true), you get: IF you cannot predict in advance with certainty, THEN there is no element of reality.

Why would that statement be true though? Let A=you can predict in advance with certainty, and B=there is an element of reality. A -> B is not logically equivalent to ~A -> ~B, so just because you believe the first there is no justification for believing the second.

 

[JesseM]

Yes, I think a slight miscommunication. Per EPR's definition, they would not have ascribed an element of reality without meeting this requirement. Not that they themselves believed as such. They simply used it for convenience. I think it was a brilliant touch, personally.

Right, if the requirement wasn't met then they wouldn't say there was any justification for believing there must be an element of reality (whereas if the requirement was met they would), but that doesn't mean they would definitely conclude there wasn't an element of reality either, they just wouldn't claim to know one way or another, and thus this scenario (where you can't predict with certainty) isn't useful to their argument. harrylin was interpreting you to mean they would say if you couldn't predict with certainty, then there is definitely no hidden element of reality that predetermines the measurement outcome, but that wouldn't be EPR's claim or Bell's.

 

[DrChinese]

Why would that statement be true though? Let A=you can predict in advance with certainty, and B=there is an element of reality. A -> B is not logically equivalent to ~A -> ~B, so just because you believe the first there is no justification for believing the second.

A-> B

implies

~B -> ~A

Too bad I reversed it.

 

[DrChinese]

Right, if the requirement wasn't met then they wouldn't say there was any justification for believing there must be an element of reality (whereas if the requirement was met they would), but that doesn't mean they would definitely conclude there wasn't an element of reality either, they just wouldn't claim to know one way or another, and thus this scenario (where you can't predict with certainty) isn't useful to their argument. harrylin was interpreting you to mean they would say if you couldn't predict with certainty, then there is definitely no hidden element of reality that predetermines the measurement outcome, but that wouldn't be EPR's claim or Bell's.

Yup. Somehow or another, he probably wants to draw some parallel to Bell tests where the angle settings lead to a fraction rather than certainty. But of course there is no connection there.

 

[JesseM]

A-> B

implies

~B -> ~A

Too bad I reversed it.

It's easy to get tripped up by these logic rules I can never keep them straight so I always have to think about examples, like A="an integer is prime and larger than 2", and B="the integer is odd"

 

[Rap]

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.

This is not my understanding of CFD. CFD means that, looking forward, if I can predict with 100% accuracy the outcome of a particular measurement, then I am justified in assuming, looking backward, that, not having made such a measurement, but if I had made such a measurement, it would have given the predicted results. Classically, this is so trivially true as to be not worth mentioning, but in QM, where one measurement may preclude another (e.g. measuring momentum precludes measuring position simultaneously), it needs to be examined.

In the case of Bell, you can illustrate the paradox with just one pair of measurements along with the statement "Although Alice and Bob did not align their detectors, had they aligned their detectors, they would have measured equal and opposite spins." This is an acceptance of CFD and produces the paradox. Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

 

[JesseM]

Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

But "superluminal effects" are only needed in a realistic model whose basic elements are localized "beables" (see Bell's paper The Theory of Local Beables), and predictions about experimental results are derived from the behavior of these beables. What Bell proves is that if you have such a model, there's no way to have it also be true that these local beables are only causally influenced by events in their past light cone. If you look at the definition of local realism I gave in [post=3231977]this post[/post], then the idea is that if you accept part 1) of my definition there, according to QM part 2) can't also be correct. But if you don't accept 1) in the first place, as your preference for pure QM with no hidden variables would suggest, then you're free to adopt some totally different definition of "locality" like one that just says that it's impossible to use measurements to transmit messages faster-than-light. The issue of QM being incompatible with locality only comes up when you use a definition of "locality" based on the realistic assumption that there must be a model that breaks up the state of a region at any given time into a collection of localized facts, as outlined in part 1) of my definition, and then says that causal influences between these localized facts shouldn't move faster than light.

 

[DrChinese]

This is not my understanding of CFD. CFD means that, looking forward, if I can predict with 100% accuracy the outcome of a particular measurement, then I am justified in assuming, looking backward, that, not having made such a measurement, but if I had made such a measurement, it would have given the predicted results. Classically, this is so trivially true as to be not worth mentioning, but in QM, where one measurement may preclude another (e.g. measuring momentum precludes measuring position simultaneously), it needs to be examined.

In the case of Bell, you can illustrate the paradox with just one pair of measurements along with the statement "Although Alice and Bob did not align their detectors, had they aligned their detectors, they would have measured equal and opposite spins." This is an acceptance of CFD and produces the paradox. Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

Counterfactual definteness does not require you be able to predict something in advance. That is more related to the EPR definition of elements of reality. They are related. This is certainly a classical concept regardless of where you draw the line.

The issue with Bell is quite different per your second paragraph. You don't really need the requirement that the spins be opposite. More that they have a value.

 

[yoda jedi]

Rejecting CFD removes the paradox, and the need for superluminal effects to resolve the paradox.

not necessarily, just postulating nonseparability is enough.


.

 

[yoda jedi]

"EPR reality" is much more narrow than the common concept of "reality"!

of course you are Right.
Reality is what exist, the state of things as they actually exist. "No Strings Attached".

with CFD or without CFD.


.

 

[billschnieder]

The issue with Bell is quite different per your second paragraph. You don't really need the requirement that the spins be opposite. More that they have a value.

Hidden in the highlighted phrase is a modal fallacy. A prediction MUST always be conditioned on the assumptions, ie it can not be true apart from its conditioning assumptions. For example "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s" These two statements can both be true at the same time because they both contain their conditioning statements built in. However, this does not mean "x, y, r, and s" must simultaneously exist. Which ones exist, will depend on which of the conditioning statements were actually realized based on which experiment has already been performed. Say Alice and Bob have measure the two photons at angles a and b. At that instance, "x and y" have independent truth values because it is a fact that Alice and Bob have measured at b and a. However, the other statement now becomes a counterfactual statement. "Had Bob and Alice measured the two photons at angles c and d, they would have obtained r, and s". This statement is still true, but "r and s" do not have independent truth values from the conditioning statements. In fact they can never have, because the two photons have already been measured and destroyed in the process.

Bell and his proponents insist that realism must mean "x, y, r and s" all have simultaneous reality independent of any conditioning statements. This is an unreasonable expectation and points to a naive understanding of simple modal logic. You can have a local realistic theory with hidden variables governing photons and still be limited by the fact that Bob and Alice can not repeat their measurement on the same two photons already measured and destroyed. You can even have non-locality with spooky action at a distance and still "x, y, r and s" will not have simultaneous reality for the same simple logical reasons.

Insisting that such a straw-man is the meaning of "realism", effectively renders impossible any experiment that could ever test it, no experimenter can ever recover their photons, restore them to their pristine condition and re-measure them.

 

[billschnieder]

The following highlights the modal error mentioned in my previous post. If you can see the error in the following argument, you will immediately see the logical error being made by Bell proponents:

A photon A is heading toward Alice's detector on a distant galaxy. They will interact tomorrow to produce an outcome of +1 or -1. But the 'laws' of the excluded middle (no third truth-value) and of noncontradiction (not both truth-values), mandate that one of the propositions "Alice's will get +1", "Alice's will get -1", is true (always has been and ever will be) and the other is false (always has been and ever will be). Suppose 'Alice's will get +1' is true today. Then whatever Alice does (or fails to do) before the photon hist her detector will make no difference: the outcome is already settled. Similarly if 'Alice's will get +1' is false today, no matter what Alice does (or fails to do), it will make no difference: the outcome is already settled. Thus, if propositions bear their truth-values timelessly (or unchangingly and eternally), then planning, or as Aristotle put it 'taking care', is illusory in its efficacy. The future will be what it will be, irrespective of our planning, intentions, etc. Free-will is an illusion."

Hint: admit the validity of CFD

 

[JesseM]

Bell and his proponents insist that realism must mean "x, y, r and s" all have simultaneous reality independent of any conditioning statements.

No, they don't. The notion of predetermined values prior to measurements is a deduction that physicists make in scenarios where both experimenters are guaranteed to get identical (or opposite) results whenever they measure the same property, and the deduction also depends on some other assumptions like the assumption of local realism, the no-conspiracy condition, and assumptions about the experimental setup like that the measurements are made at a spacelike separation. But as I pointed out to you in an [post=3275052]earlier post[/post], there are some inequalities like the CHSH inequality that don't depend on the condition that the experimenters always get identical results when they perform the same measurement. I haven't looked at the derivation of the CHSH inequality in a while but I'm fairly certain that here there is no assumption that the measurement results were predetermined prior to measurement, you're free to assume a local realist theory that contains a genuine random element, so that the outcome of any measurement could not have been predicted even with complete knowledge of all hidden and observable variables at some time just prior to measurement.

 

[SpectraCat]

Hidden in the highlighted phrase is a modal fallacy. A prediction MUST always be conditioned on the assumptions, ie it can not be true apart from its conditioning assumptions. For example "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s" These two statements can both be true at the same time because they both contain their conditioning statements built in. However, this does not mean "x, y, r, and s" must simultaneously exist. Which ones exist, will depend on which of the conditioning statements were actually realized based on which experiment has already been performed. Say Alice and Bob have measure the two photons at angles a and b. At that instance, "x and y" have independent truth values because it is a fact that Alice and Bob have measured at b and a. However, the other statement now becomes a counterfactual statement. "Had Bob and Alice measured the two photons at angles c and d, they would have obtained r, and s". This statement is still true, but "r and s" do not have independent truth values from the conditioning statements. In fact they can never have, because the two photons have already been measured and destroyed in the process.

Bell and his proponents insist that realism must mean "x, y, r and s" all have simultaneous reality independent of any conditioning statements. This is an unreasonable expectation and points to a naive understanding of simple modal logic. You can have a local realistic theory with hidden variables governing photons and still be limited by the fact that Bob and Alice can not repeat their measurement on the same two photons already measured and destroyed. You can even have non-locality with spooky action at a distance and still "x, y, r and s" will not have simultaneous reality for the same simple logical reasons.

Insisting that such a straw-man is the meaning of "realism", effectively renders impossible any experiment that could ever test it, no experimenter can ever recover their photons, restore them to their pristine condition and re-measure them.

That all seems like interpretation to me ... what experimental evidence can you offer that the world actually behaves the way you claim? The experimental evidence shows that coincident measurement statistics for entangled photons violate Bell inequalities (or CHSH inequalities, which I believe are even weaker than Bell inequalities in terms of the assumptions upon which they are based). The experiments do not assume anything a priori about which values will be measured ... can you explain the results in a local realistic fashion?

 

[Rap]

That all seems like interpretation to me ... what experimental evidence can you offer that the world actually behaves the way you claim? The experimental evidence shows that coincident measurement statistics for entangled photons violate Bell inequalities (or CHSH inequalities, which I believe are even weaker than Bell inequalities in terms of the assumptions upon which they are based). The experiments do not assume anything a priori about which values will be measured ... can you explain the results in a local realistic fashion?

If I may answer for billschnieder - The first paragraph is not a description of how the world behaves, it is pure logic, noting that CFD is an additional assumption needed to yield the paradox. The only part where he describes how the world works is to note that it impossible to test for the given description of reality. So, it seems to me, you are asking for experimental evidence that there can be no experimental evidence for the given description of reality.

 

[Rap]

Hidden in the highlighted phrase is a modal fallacy. A prediction MUST always be conditioned on the assumptions, ie it can not be true apart from its conditioning assumptions. For example "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s" These two statements can both be true at the same time because they both contain their conditioning statements built in. However, this does not mean "x, y, r, and s" must simultaneously exist. Which ones exist, will depend on which of the conditioning statements were actually realized based on which experiment has already been performed. Say Alice and Bob have measure the two photons at angles a and b. At that instance, "x and y" have independent truth values because it is a fact that Alice and Bob have measured at b and a. However, the other statement now becomes a counterfactual statement. "Had Bob and Alice measured the two photons at angles c and d, they would have obtained r, and s". This statement is still true, but "r and s" do not have independent truth values from the conditioning statements. In fact they can never have, because the two photons have already been measured and destroyed in the process.

I agree

 

[JesseM]

If I may answer for billschnieder - The first paragraph is not a description of how the world behaves, it is pure logic, noting that CFD is an additional assumption needed to yield the paradox.

But it's not an assumption, it's derived from the basic assumption of a local realist model, along with the no-conspiracy condition.

 

[Rap]

The following highlights the modal error mentioned in my previous post. If you can see the error in the following argument, you will immediately see the logical error being made by Bell proponents:

A photon A is heading toward Alice's detector on a distant galaxy. They will interact tomorrow to produce an outcome of +1 or -1. But the 'laws' of the excluded middle (no third truth-value) and of noncontradiction (not both truth-values), mandate that one of the propositions "Alice's will get +1", "Alice's will get -1", is true (always has been and ever will be) and the other is false (always has been and ever will be). Suppose 'Alice's will get +1' is true today. Then whatever Alice does (or fails to do) before the photon hist her detector will make no difference: the outcome is already settled. Similarly if 'Alice's will get +1' is false today, no matter what Alice does (or fails to do), it will make no difference: the outcome is already settled. Thus, if propositions bear their truth-values timelessly (or unchangingly and eternally), then planning, or as Aristotle put it 'taking care', is illusory in its efficacy. The future will be what it will be, irrespective of our planning, intentions, etc. Free-will is an illusion."

Hint: admit the validity of CFD

I object to the language - "Then whatever Alice does (or fails to do)" implies she has a choice, while the idea that CFD denies free will contradicts this.

I think "free will" may be a classical concept, with more and more limited applicability as you go to the quantum realm. I say "may be" because I cannot prove it. Thus, I think accepting CFD may be a classical prejudice. When you say "Hint: admit the validity of CFD"... why?

 

[Rap]

But it's not an assumption, it's derived from the basic assumption of a local realist model, along with the no-conspiracy condition.

I think you might be right. I had blinders on, when billschnieder said "If Bob and Alice measure the two photons at angles b and a, they will obtain x, and y" and "If Bob and Alice measure the two photons at angles c and d, they will obtain r, and s". I took that to mean the particular case where a=b and they will obtain x and y=!x (equal and opposite spins), and c=d and they will obtain r and s=!r. This is the only case that is experimentally true, and then the statement is just logic and the acceptance of an experimental truth. His conclusion is still valid, I think.

 

[harrylin]

I said it was sufficient as a definition when I quoted it. I also said that there is no element of reality without that. I meant that per the definition in use. Perhaps you have a better definition.

Strictly speaking, it is certainly possible there is an element of reality WITHOUT us being able to predict it in advance. For example, I had to pay when my son wrecked the car even though I could not predict the amount in advance with certainty. And believe me, that was very real to my pocketbook.

So if you take the contranegative (also being true), you get: IF you cannot predict in advance with certainty, THEN there is no element of reality. But what can you do with this statement? I don't think too much, because you cannot prove the antecedent.

So my point is: Bell used the well accepted EPR definition. That definition is one which is easy to follow, and because it is sufficient it is enough for our examples. I.e. for entangled pairs. The only issue to Bell would be if you could prove convince folks that this was not a sufficient condition. That would be a tough hurdle. Keep in mind that was a cornerstone of EPR.

The issue here is that roughly speaking, Bell tried to prove the inverse of what EPR tried to prove, and that EPR stressed that the inverse of their condition is not true - if I state that an apple is a fruit (so that always apple=>fruit), it does not imply that a fruit is necessarily an apple (NOT fruit=>apple).

However, so far I have not found out if it matters for Bell's Theorem that EPR's condition of predictability is not a necessary condition for reality. I'm just aware that any subtle difference of interpretation about this topic can have great consequences.

I'll be grateful if someone can clarify this to me.

 

[harrylin]

of course you are Right.
Reality is what exist, the state of things as they actually exist. "No Strings Attached".

with CFD or without CFD.

.

You misquoted me: I said if EPR's view was correctly interpreted. However, it appears that they meant with "reality" quite the same as you and me.

 

[harrylin]

A-> B

implies

~B -> ~A

Too bad I reversed it.

OK [edit: I first misread] - using my earlier illustration:

<Apple> => <Fruit> is true;

and

<NOT Fruit> => <NOT Apple> is also true. So we agree now

Harald

 

[JesseM]

The issue here is that roughly speaking, Bell tried to prove the inverse of what EPR tried to prove, and that EPR stressed that the inverse of their condition is not true - if I state that an apple is a fruit (so that always apple=>fruit), it does not imply that a fruit is necessarily an apple (NOT fruit=>apple).

No, Bell did not try to prove the inverse, i.e. he never tried to prove that NOT (values predictable in advance)=>NOT (predetermined values prior to measurement)