50th anniversary of Bell's theorem

[bohm2]

A special issue on 50 years of Bell's theorem has been published in Journal of Physics with free access to all articles:


http://iopscience.iop.org/1751-8121/47/42

 

[jedishrfu]

Thanks for the reference. I'm sure others here will enjoy it.

 

[atyy]

Lots of good articles, I love Bertlmann's :)

 

[Demystifier]

I like the Maudlin's Reply to Comment.

 

[harrylin]

Cool :)
I bet this is going to generate new discussions. ;)

 

[bohm2]

I like the Maudlin's Reply to Comment.

R. Werner just wrote a follow-up piece to that paper by Maudlin:

What Maudlin replied to
http://arxiv.org/pdf/1411.2120.pdf

 

[harrylin]

R. Werner just wrote a follow-up piece to that paper by Maudlin:

What Maudlin replied to
http://arxiv.org/pdf/1411.2120.pdf

Interesting! Can someone guide me towards an elaboration of "algebraic quantum field theory provides an example of a theory with full relativistic signal locality and clear violations of Bell inequalities." ?

 

[bohm2]

Interesting! Can someone guide me towards an elaboration of "algebraic quantum field theory provides an example of a theory with full relativistic signal locality and clear violations of Bell inequalities." ?

Here is Stapp's paper on that idea:

Bell’s Theorem Without Hidden Variables
http://arxiv.org/pdf/quant-ph/0010047v2.pdf

I think the major controversial area still appears to be with respect to whether the Bell theorem includes 'realism' among its assumptions. Part of the difficulty may be due to delineating what one means by 'realism'.

 

[Demystifier]

Part of the difficulty may be due to delineating what one means by 'realism'.

A rather clear explanation of 'realism' is given in
http://lanl.arxiv.org/abs/1212.5214 [Am. J. Phys. 81, 854 (2013)]:
"Let us define “counterfactual-definite” [14, 15] a the-
ory whose experiments uncover properties that are pre-
existing. In other words, in a counterfactual-definite
theory it is meaningful to assign a property to a sys-
tem (e.g. the position of an electron) independently of
whether the measurement of such property is carried
out. [Sometime this counterfactual definiteness property
is also called “realism”, but it is best to avoid such philo-
sophically laden term to avoid misconceptions.]
Bell’s theorem can be phrased as “quantum mechanics
cannot be both local and counterfactual-definite”. A log-
ically equivalent way of stating it is “quantum mechanics
is either non-local or non counterfactual-definite” "

 

[harrylin]

Here is Stapp's paper on that idea:

Bell’s Theorem Without Hidden Variables
http://arxiv.org/pdf/quant-ph/0010047v2.pdf

I think the major controversial area still appears to be with respect to whether the Bell theorem includes 'realism' among its assumptions. Part of the difficulty may be due to delineating what one means by 'realism'.

Thanks a lot! - looking at the date I likely have seen this one before, but a quick look tells me that indeed it elaborates on Bell's so-called "reality" assumption (which he based on E-P-R's earlier arguments), and which subtly goes beyond the standard meaning of "reality". In earlier discussions on this forum we (or just me?) could not get a good grip on that issue. "Counterfactuals" and things like that. Maybe if I study this (again?) it will be possible to get a grip on this!

 

[Demystifier]

For a long time I was not able to understand how a physical theory can be non-counterfactual-definite (except by rejecting to talk about counterfactual definiteness), until I constructed my own model:
http://lanl.arxiv.org/abs/1112.2034 [Int. J. Quantum Inf. 10 (2012) 1241016]

 

[bohm2]

A rather clear explanation of 'realism' is given in http://lanl.arxiv.org/abs/1212.5214 [Am. J. Phys. 81, 854 (2013)]:"Let us define “counterfactual-definite” [14, 15] a theory whose experiments uncover properties that are pre-existing..

This is the part that is confusing me. Aren't such pre-existent properties (e.g. non-contextual) already ruled by Kochen-Specker theorem? This is what I take Laudisa to be arguing where he writes:

If REALISM _G&AL were an independent assumption of any hidden variable theory, Gleason-Bell-Kochen & Specker would have already proved their incompatibility with quantum mechanics needless of any locality requirement. But, as Bell showed, there is little significance in testing against quantum theory a theory (be it local or non-local) that is supposed to satisfy a condition that we already know quantum mechanics cannot possibly and reasonably satisfy.

Non-Local Realistic Theories and the Scope of the Bell Theorem
http://arxiv.org/ftp/arxiv/papers/0811/0811.2862.pdf

 

[atyy]

One of the things I misunderstood about Bell's theorem is that I thought it rules out hidden variables which are relativistically covariant. Maudlin discusses that this is not ruled out by Bell's theorem in the first of his articles in this collection. The first time I came across this possibility was in Demystifier's work, which I originally thought contradicted Bell. I haven't studied the work well enough to understand if it is correct, but I think I now understand Bell's theorem well enough to know that the possibility is not ruled out. The other case that Maudlin cites is the relativistic spontaneous collapse theory which violates a Bell inequality.

 

[Demystifier]

This is the part that is confusing me. Aren't such pre-existent properties (e.g. non-contextual) already ruled by Kochen-Specker theorem?

No. Kochen-Specker excludes properties which are both
1) pre-existent before the measurement, and
2) unchanged by the measurement.

Both KC and Bell agree that if 1) is satisfied then 2) is not. In other words, they both say that if properties exist before the measurement, then they must change by the measurement. But Bell goes a step further by proving that the required change must be non-local. That's why the Bell theorem is compatible with KC theorem, but also much stronger (and hence more important) than KC theorem.

 

[DrChinese]

A rather clear explanation of 'realism' is given in
http://lanl.arxiv.org/abs/1212.5214 [Am. J. Phys. 81, 854 (2013)]:
"Let us define “counterfactual-definite” [14, 15] a the-
ory whose experiments uncover properties that are pre-
existing. In other words, in a counterfactual-definite
theory it is meaningful to assign a property to a sys-
tem (e.g. the position of an electron) independently of
whether the measurement of such property is carried
out. [Sometime this counterfactual definiteness property
is also called “realism”, but it is best to avoid such philo-
sophically laden term to avoid misconceptions.]
Bell’s theorem can be phrased as “quantum mechanics
cannot be both local and counterfactual-definite”. A log-
ically equivalent way of stating it is “quantum mechanics
is either non-local or non counterfactual-definite” "

I agree: a very well worded description. In case anyone has a hard time finding where realism or counterfactual definiteness is explicitly assumed in Bell, look after his (14). He adds c as another unit vector and references it an equation in which a and b are also present. The assumption is that a, b and c all exist simultaneously.

 

[bohm2]

Kochen-Specker excludes properties which are both
1) pre-existent before the measurement, and
2) unchanged by the measurement.

Demystifier,
Do you think that Bell's theorem includes any "realism" among its assumptions? (And for "realism" you can substitute objectivity/classicality/counterfactual definiteness, etc.).

 

[morrobay]

I agree: a very well worded description. In case anyone has a hard time finding where realism or counterfactual definiteness is explicitly assumed in Bell, look after his (14). He adds c as another unit vector and references it an equation in which a and b are also present. The assumption is that a, b and c all exist simultaneously.

Can you post a link for (14) ? thanks

 

[bohm2]

Can you post a link for (14) ? thanks

I believe DrChinese is referring to equation 14 of Bell's famous 1964 paper. It is after equation 14 where Bell introduces unit vector c. DrChinese has argued that is where Bell brings in "realism". But this is far from being clear. See:

http://www.drchinese.com/David/Bell.pdf

 

[Demystifier]

Demystifier,
Do you think that Bell's theorem includes any "realism" among its assumptions? (And for "realism" you can substitute objectivity/classicality/counterfactual definiteness, etc.).

Yes I do. (In the paper in post #11 I substituted realism for non-solipsism and explained in detail how locality can be saved with a price of adopting solipsism.)

 

[DrChinese]

Can you post a link for (14) ? thanks

As bohm2 says, it is from the original paper. After a bit of manipulation, it becomes the more well known form presented as Bell's (15):

1 + P(b,c) >= | P(a,b) - P(a,c) |

There really is nothing to question about the realism assumption present here. There is a, b and c which must exist for this equation to make sense.

This is a direct representation of what EPR called the elements of reality, which they said did NOT need to be simultaneously predictable with certainty to be accepted as elements of reality (they said any other view was unreasonable). Bell is making this explicit by saying: they simultaneously exist even through they cannot be simultaneously observed.

 

[stevendaryl]

A rather clear explanation of 'realism' is given in
http://lanl.arxiv.org/abs/1212.5214 [Am. J. Phys. 81, 854 (2013)]:
"Let us define “counterfactual-definite” [14, 15] a the-
ory whose experiments uncover properties that are pre-
existing. In other words, in a counterfactual-definite
theory it is meaningful to assign a property to a sys-
tem (e.g. the position of an electron) independently of
whether the measurement of such property is carried
out. [Sometime this counterfactual definiteness property
is also called “realism”, but it is best to avoid such philo-
sophically laden term to avoid misconceptions.]
Bell’s theorem can be phrased as “quantum mechanics
cannot be both local and counterfactual-definite”. A log-
ically equivalent way of stating it is “quantum mechanics
is either non-local or non counterfactual-definite” "

I don't like this definition. There is a connection between "realism" and "counterfactual-definite", but I don't think they mean the same thing. To me, the word "counterfactual-definite" should mean that counterfactual questions have definite answers. I assume that's where the phrase "counterfactual-definite" comes from. So even though Alice happened to measure spin along axis $\vec{a}$, we can ask the counter-factual question "What result would she have gotten if she measured it along axis $\vec{b}$ instead?" If such questions have answers, then your theory is counterfactually definite.

But a nondeterministic theory would not be counterfactually definite, although a nondeterministic theory can still be realistic.

 

[harrylin]

Here is Stapp's paper on that idea:

Bell’s Theorem Without Hidden Variables
http://arxiv.org/pdf/quant-ph/0010047v2.pdf

I think the major controversial area still appears to be with respect to whether the Bell theorem includes 'realism' among its assumptions. Part of the difficulty may be due to delineating what one means by 'realism'.

OK I've now looked a bit longer at that paper. Probably I once saw it, but never read it! However perhaps I still don't "get" it: I don't see how such statements as "some kind kind of faster-than-light influence" and "This result places a strong condition on theoretical models that reproduce the predictions of quantum theory. This condition is similar to the failure of locality associated with Bell’s theorem" can be compatible with Einstein's SR ("Einstein-local"). I'm afraid that he merely argues, like Tim Maudlin, that no unreasonable "back-in-time" influences are necessary for QM interpretations that only at face-value are compatible with SR (or, only compatible with a to QM adapted version of SR, as in Maudlin's book). If so, then Einstein as well as Lorentz would have disagreed with calling that idea "full relativistic".

 

[morrobay]

As bohm2 says, it is from the original paper. After a bit of manipulation, it becomes the more well known form presented as Bell's (15):

1 + P(b,c) >= | P(a,b) - P(a,c) |

There really is nothing to question about the realism assumption present here. There is a, b and c which must exist for this equation to make sense.

This is a direct representation of what EPR called the elements of reality, which they said did NOT need to be simultaneously predictable with certainty to be accepted as elements of reality (they said any other view was unreasonable). Bell is making this explicit by saying: they simultaneously exist even through they cannot be simultaneously observed.

OK, and the elements of reality that are being counted in the above inequality are vector components of a,b,and c from Bell's (14) and (15)
Physical quantities like magnetic spin and polarization, both of which have different values that depend on theta at time of measurement.
So if P(b,c) , P(a.b) , P(a,c) are functions of theta then is there is a classical explanation whether inequality holds ?

 

[atyy]

As bohm2 says, it is from the original paper. After a bit of manipulation, it becomes the more well known form presented as Bell's (15):

1 + P(b,c) >= | P(a,b) - P(a,c) |

There really is nothing to question about the realism assumption present here. There is a, b and c which must exist for this equation to make sense.

This is a direct representation of what EPR called the elements of reality, which they said did NOT need to be simultaneously predictable with certainty to be accepted as elements of reality (they said any other view was unreasonable). Bell is making this explicit by saying: they simultaneously exist even through they cannot be simultaneously observed.

I think this shows why it is contested whether the realism assumption is present. If I use your definition that there is a meaningful equation in which a, b and c are present, then there is such an equation in quantum mechanics. One such example is Tsirelson's bound http://en.wikipedia.org/wiki/Tsirelson's_bound. So I think by this definition, quantum mechanics is a realistic theory, which would mean that quantum mechanics is nonlocal in the sense of Bell.

 

[Demystifier]

I think this shows why it is contested whether the realism assumption is present. If I use your definition that there is a meaningful equation in which a, b and c are present, then there is such an equation in quantum mechanics. One such example is Tsirelson's bound http://en.wikipedia.org/wiki/Tsirelson's_bound. So I think by this definition, quantum mechanics is a realistic theory, which would mean that quantum mechanics is nonlocal in the sense of Bell.

First let me note that the Tsirelson's bound is an upper bound on quantum non-locality, so it cannot be used as a proof of non-locality even when some reality assumptions are taken for granted. If it tells something about locality or non-locality at all, it only tells that non-locality, if there is any, cannot be arbitrarily large.

But the note above is actually red herring, because the crucial question here is whether Tsirelson's bound assumes reality, by the definition used by DrChinese. Is there an important difference between your example and DrChinese's example? Your example talks about quantities such as <AB>, which are average values. DrChinese's example talks about quantities such as p(A,B), which are probabilities. So the question reduces to the following one: Can we say that probabilities are somehow more "real" than average values? We could say so if we could argue that average value is only a property of a statistical ensemble, while probability is a property of a single member of an ensemble. But can we find a convincing argument for such a claim? I am not sure that we can.

So I kind of agree with you that DrChinese's argument is not totally convincing. The question of reality assumption in the Bell theorem is more subtle than he explained.

 

[Demystifier]

This is a direct representation of what EPR called the elements of reality, which they said did NOT need to be simultaneously predictable with certainty to be accepted as elements of reality (they said any other view was unreasonable).

EPR said there must be something predictable with certainty to have an element of reality associated with it. But in your case I don't see what exactly that "something" would be.

 

[DrChinese]

EPR said there must be something predictable with certainty to have an element of reality associated with it. But in your case I don't see what exactly that "something" would be.

a is an element of reality and is predictable with certainty. b is an element of reality and is predictable with certainty. And c (a unit vector) is an element of reality and is predictable with certainty. These are not simultaneously predictable, of course, and EPR acknowledges this.

 

[atyy]

First let me note that the Tsirelson's bound is an upper bound on quantum non-locality, so it cannot be used as a proof of non-locality even when some reality assumptions are taken for granted. If it tells something about locality or non-locality at all, it only tells that non-locality, if there is any, cannot be arbitrarily large.

But the note above is actually red herring, because the crucial question here is whether Tsirelson's bound assumes reality, by the definition used by DrChinese. Is there an important difference between your example and DrChinese's example? Your example talks about quantities such as <AB>, which are average values. DrChinese's example talks about quantities such as p(A,B), which are probabilities. So the question reduces to the following one: Can we say that probabilities are somehow more "real" than average values? We could say so if we could argue that average value is only a property of a statistical ensemble, while probability is a property of a single member of an ensemble. But can we find a convincing argument for such a claim? I am not sure that we can.

So I kind of agree with you that DrChinese's argument is not totally convincing. The question of reality assumption in the Bell theorem is more subtle than he explained.

Yes, I agree with your statement about Tsirelson's bound. About the quantities in Tsirelson being average values, while the quantities in DrChinese's example being probabilities, I think in Bell's notation (which DrChinese is using), P is an expectation value, so the Tsirelson example and DrChinese's example are on the same footing with respect to defining reality.

But anyway, I do agree with your larger point that even if such an equation were formulated using probabilities, it is not clear that probabilities are more real than expectation values. I'm too rusty on rigourous probability axioms, but I do know that one can formulate much (all?) of probability using expectation values.

(Bell's paper is on DrChinese's site, and bohm2 gave a link in post #18.)

 

[Demystifier]

I think in Bell's notation (which DrChinese is using), P is an expectation value

You are right, I overlooked it.

Which makes me even more confident that DrChinese's definition of reality is not appropriate.

So what is an appropriate meaning of reality in a claim that non-reality can save locality?

1) Non-realists claim that only observed phenomena are real. Fine, but observed by who? That's important because if we have two observers, each observing a different member of the EPR pair, then QM predicts a non-local correlation between these two realities perceived by two different observers. So realities perceived by two observers still contains too much reality to save locality.

2) So to save locality one possibility is to assert that, somehow, only one observer counts as real. But that's hard solipsism, which, nevertheless, adherents of non-reality usually do not accept.

3) The only remaining possibility I see is to accept a softer version of solipsism, in which all observers are real, but internal observations of one observer are not correlated with internal observations of another observer. (That may be relevant to the philosophy of mind because it may explain why one can never experience the qualia of other people, and consequently why qualia is such an illusive entity from the scientific point of view.)

4) In any case, I don't see how can anybody simultaneously believe that
i) local non-reality is the correct interpretation of QM, and
ii) observers play no fundamental role in QM.

 

[Demystifier]

a is an element of reality and is predictable with certainty. b is an element of reality and is predictable with certainty. And c (a unit vector) is an element of reality and is predictable with certainty. These are not simultaneously predictable, of course, and EPR acknowledges this.

But if they are not simultaneously predictable, does it (according to EPR) also mean that they are not simultaneous elements of reality?

 

[DrChinese]

But if they are not simultaneously predictable, does it (according to EPR) also mean that they are not simultaneous elements of reality?

According to EPR, yes. BUT... that is by ASSUMPTION. And therein is the assumption of reality: ie individual elements of reality a, b and c (which exist when observed individually and no one fundamentally denies) are also simultaneous members of the greater reality that is that quantum object. From EPR:

"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but no both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depends upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this".

Which is essentially what you ask in your post #29, 4 ii. I say observers play a fundamental role, in EPR parlance: "the reality of P and Q depends upon the process of measurement ". So reality is limited to the context of relevant observers and what can be predicted in an experiment ONLY (i.e. I take the more restrictive view, which should be labeled as "non-realistic"). Even if that is unreasonable to EPR.

So I obviously disagree with your assessment my assessment (LOL) of what realism means. My definition of reality is simply a) that of EPR (as can be read above); and b) that of Bell writing about EPR. Bell merely takes it a step further: whereas EPR talks of 2 physical quantities P and Q (which would be a and b to Bell), Bell goes to 3: a, b and c.

 

[atyy]

Which makes me even more confident that DrChinese's definition of reality is not appropriate.

So what is an appropriate meaning of reality in a claim that non-reality can save locality?

Maybe DrChinese doesn't intend for his definition to save locality? Maybe he would agree that quantum mechanics itself is realistic (according to his definition) and nonlocal in the sense of Bell?

 

[stevendaryl]

My definition of reality is simply a) that of EPR (as can be read above); and b) that of Bell writing about EPR. Bell merely takes it a step further: whereas EPR talks of 2 physical quantities P and Q (which would be a and b to Bell), Bell goes to 3: a, b and c.

I may have lost the critical context about the significance of the a, b, c, but I think you're talking about there being elements of reality associated with measurements that could have been done, but were not. Alice chooses to measure spin along axis a, so there is a corresponding "element of reality" associated with measurements along axis a (because Bob is guaranteed to get the opposite value if he measures spin along that axis, in the spin-1/2 case). Bob chooses to measure spin along axis b (and so there's an element of reality to that spin measurement). But neither measures along axis c, so there's no reason to associate an element of reality to this measurement that wasn't performed. It's hard to know whether Einstein would have agreed with this way out, or not. I doubt it, but I don't know.

The problem, which of course you already know, is that if we disallow faster-than-light propagation of effects, then it seems that the "element of reality" associated with Alice's spin result along axis a must actually exist before the particle reaches Alice. And if Alice is free to make up her mind at the last minute what axis to choose to perform her measurement, then it seems that there must be a corresponding element of reality for every possible axis Alice could choose. That leads to Bell's hidden variables. So the violation of Bell's inequality seems to me to mean one of the following:

• Einstein (and P and R) were wrong--definite predictions don't correspond to elements of reality.
• Einstein was wrong in a different way, and there are faster-than-light influences.
• Alice and Bob aren't really free to choose any old axis--the axis is already fixed long before the measurement is made.

I'm not sure how retrocausal interpretations would fit in.

 

[atyy]

I'm not sure how retrocausal interpretations would fit in.

I think it's widely agreed that no retrocausation is an assumption in Bell, so Bell doesn't exclude that retrocausal explanations can be "local deterministic". It doesn't mean that such an explanation exists, but a violation of the Bell inequalities doesn't rule it out, and I think the Transactional Interpretation tries to use this (I don't know it well enough to know if it fully reproduces quantum mechanics).

 

[DrChinese]

I may have lost the critical context about the significance of the a, b, c, but I think you're talking about there being elements of reality associated with measurements that could have been done, but were not. Alice chooses to measure spin along axis a, so there is a corresponding "element of reality" associated with measurements along axis a (because Bob is guaranteed to get the opposite value if he measures spin along that axis, in the spin-1/2 case). Bob chooses to measure spin along axis b (and so there's an element of reality to that spin measurement). But neither measures along axis c, so there's no reason to associate an element of reality to this measurement that wasn't performed. It's hard to know whether Einstein would have agreed with this way out, or not. I doubt it, but I don't know.

Bell assumes there is a c, and that's what you believe if you think there is realism. He can't use all 3 of a, b and c in a single equation if they do not all exist simultaneously.

I already quoted EPR's view verbatim, which was that a, b and c exist simultaneously if they exist separately (and other view is not reasonable, as an assumption we are supposed to accept - which Bell tried).

Keep in mind I am not saying that the quantum world is actually realistic. I don't think it is. EPR made an unwarranted but reasonable assumption that P and Q are simultaneous elements of reality. Bell used that assumption and extended it to spin components a, b and c. He then used it in an equation which leads to an inequality contradicted by QM in some cases. You can't get that inequality EXCEPT by assuming a, b and c are simultaneous elements of reality. There should be NO confusion between the 3 elements of reality a, b and c and the fact that entangled pairs are measured by 2 observers. The 2 observers look at P(a, b) or whatever pair of a, b or c, but that's it. If you could create an inequality with 4 simultaneous elements of reality, that would work too.