50th anniversary of Bell's theorem

[atyy]

I would ask the same question as always: if there is an a, b and c in MWI, what values do they have?

Would I understand you correctly that for your definition of real, a,b and c don't appear in the same equation in MWI, so the Bell inequality cannot be applied, and hence the Bell inequality cannot be violated, hence MWI is not Bell nonlocal?

 

[DrChinese]

Would I understand you correctly that for your definition of real, a,b and c don't appear in the same equation in MWI, so the Bell inequality cannot be formed, and hence the Bell inequality cannot be violated, hence MWI is not Bell nonlocal?

I would say that, sure. In worlds in which no measurement is performed, there is no split to give the elements of reality a value. By my accounting, there must be a negative number of worlds with certain combinations of values. That is simply saying that a negative probability is as non-realistic as negative worlds. For example, when A=0, B=67.5 and C is 45 degrees, the likelihood of worlds with a=+ b=+ and c=- or a=- b=- and c=+ is -10%. Where are those worlds?

 

[Demystifier]

I would ask the same question as always: if there is an a, b and c in MWI, what values do they have?

Some of them may have no values at all, but that's not non-realism according to Bell. According to Bell, realism is not an assumption that all observables have values. It's an assumption that something has a value. That something Bell calls a beable.

In particular, in MWI there is no a, b, and c. There is only $\psi$, the wave function. So in MWI, the beable is $\psi$. So $\psi$ is real in MWI, but a, b, c are not. Since there is something real in MWI, proponents of MWI consider MWI realistic.

But you don't consider MWI realistic, because, for you, "realistic" means that a, b, and c must be real. Fine, but that's your definition of "real", not Bell's.

Nevertheless, the good thing is that for both definitions of reality (and with some reasonable additional tacit assumptions, which I can list if someone is interested) one can prove that such reality cannot be local.

 

[atyy]

I would say that, sure. In worlds in which no measurement is performed, there is no split to give the elements of reality a value. By my accounting, there must be a negative number of worlds with certain combinations of values. That is simply saying that a negative probability is as non-realistic as negative worlds. For example, when A=0, B=67.5 and C is 45 degrees, the likelihood of worlds with a=+ b=+ and c=- or a=- b=- and c=+ is -10%. Where are those worlds?

I'm don't understand MWI well enough to agree or disagree on this technical point, but it seems reasonable. Anyway, I think your conclusion is broadly in agreement with Demystifier's. If according to your definition, the Bell inequality doesn't apply and cannot be violated, then MWI is neither Bell nonlocal nor Bell local. I think this is why he said that MWI is Bell alocal.

I believe there is general agreement that nonrealism can prevent the Bell inequalities from applying, so locality can be saved in the sense that the there is no Bell proof of nonlocality. I think the controversy is whether there is a case where the Bell inequalities apply, and are violated, and one can still find a "Bell local" explanation.

 

[Demystifier]

I'm don't understand MWI well enough to agree or disagree on this technical point, but it seems reasonable. Anyway, I think your conclusion is broadly in agreement with Demystifier's. If according to your definition, the Bell inequality doesn't apply and cannot be violated, then MWI is neither Bell nonlocal nor Bell local. I think this is why he said that MWI is Bell alocal.

That's correct. DrChinese and I agree on locality issue in MWI. We disagree on the reality issue.

I believe there is general agreement that nonrealism can prevent the Bell inequalities from applying, so locality can be saved in the sense that the there is no Bell proof of nonlocality. I think the controversy is whether there is a case where the Bell inequalities apply, and are violated, and one can still find a "Bell local" explanation.

Any proof in physics or mathematics ever published contains not only a list of explicit assumptions, but also some implicit assumptions. The Bell proof is not an exception. Indeed, there are several "local realistic" interpretations of QM which violate some of the implicit assumptions in the Bell theorem, the assumptions which Bell didn't spelled out explicitly.

These implicit assumptions (violated by some interpretations) are a great source of confusion. Another source of confusion is the fact that Bell himself presented a few different versions of his proof by using somewhat different assumptions himself.

 

[bohm2]

As far as understand it, only Rovelli's relational interpretation can be considered both local and unreal. For instance have a look at the 2 categories under table of "comparison of interpretations". Only in that interpretation is locality maintained and the wave function is not real. Having said that, I'm not sure of some of the less popular interpretations like Relational Blockworld.

Interpretations of quantum mechanics
http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

 

[DrChinese]

These implicit assumptions (violated by some interpretations) are a great source of confusion. Another source of confusion is the fact that Bell himself presented a few different versions of his proof by using somewhat different assumptions himself.

Yes. To be fair, EPR made implicit assumptions too - and it is hard not to. Is the existence of a single world a tacit assumption?

And as to Bell: while I consider his follow on writings a source of much inspiration and knowledge, I don't consider them authoritative. His opinions changed over time, and it is not his opinion that made him famous. It was the 1964 paper. Although it was suitable for its audience then, it obviously raises a lot of questions today that are nowhere clearly answered. You have to piece a lot of stuff together.

 

[DrChinese]

As far as understand it, only Rovelli's relational interpretation can be considered both local and unreal.

According to EPR: non-realism and observer-dependent reality are the same thing (see the EPR quote I presented). So time symmetric and retrocausal interpretations, being observer dependent, are non-realistic.

 

[Demystifier]

Yes. To be fair, EPR made implicit assumptions too - and it is hard not to.

Not only hard, but impossible.

Is the existence of a single world a tacit assumption?

It certainly is.

And as to Bell: while I consider his follow on writings a source of much inspiration and knowledge, I don't consider them authoritative.

Fair enough.

His opinions changed over time, and it is not his opinion that made him famous. It was the 1964 paper.

I must admit, you are right about that.

Although it was suitable for its audience then, it obviously raises a lot of questions today that are nowhere clearly answered. You have to piece a lot of stuff together.

I tend to agree with that too.

 

[atyy]

According to EPR: non-realism and observer-dependent reality are the same thing (see the EPR quote I presented). So time symmetric and retrocausal interpretations, being observer dependent, are non-realistic.

Since reality is observer-dependent, could nonlocality also be observer-dependent? Would you accept Norsen's hypothesis in the form that for any (observer-dependent) assignment of reality in which according to that observer the Bell inequalities are violated at spacelike separation, that observer cannot assign any local deterministic explanation of his reality?

 

[Ilja]

Formula (15) is far too late. Everything what is used from realism and Einstein causality is already present in formula (2). What remains are elementary mathematical exercises. That all the values in different directions have to exist is not a consequence of some notion of realism used here, but a consequence of the EPR argument.

Such a reference to formula (15) with a "here realism is used" I would classify as a typical example of the misunderstanding which Maudlin has quoted from Bell's Bertlsman's socks : "It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred".

The formula (2) contains something nontrivial, worth to be named "realism", see my defintion in http://ilja-schmelzer.de/realism/definition.php where I also give a corresponding weaker notion of a statistical theory which restricts itself to give probability distributions for observables without caring about causal explanations.

 

[DrChinese]

Since reality is observer-dependent, could nonlocality also be observer-dependent? Would you accept Norsen's hypothesis in the form that for any (observer-dependent) assignment of reality in which according to that observer the Bell inequalities are violated at spacelike separation, that observer cannot assign any local deterministic explanation of his reality?

No, *I* wouldn't* agree with Norsen - because we are talking different "observer dependent" here. I am not talking about Alice and Bob seeing different things and that defining the observer dependence. The observer dependence that EPR defines takes into account Alice + Bob.

Sure, they are spacelike separated (usually). But the pair of them help to define reality by forming a measurement context along with the system being measured. The system itself is not spatially contained either - it's not like we have 2 independent objects, you have just one system until collapse occurs (whatever that is).

And of course I certainly agree that we could have a non-local and non-realistic situation. So I am agreeing with what you say: "could nonlocality also be observer-dependent". I personally think that Bohmian class interpretations are non-realistic, but I know most Bohmians don't agree. No one ever provides the answer to what a, b and c are at the same time. So without the answer to that, it is hard to say anything is realistic. Because even Bohmian interpretations - which successfully explain a Bell inequality violation - don't supply values for counterfactual questions. But this is just my opinion, I don't expect folks to agree with my assessment on this. :-)*Of course I agree that there is no local deterministic explanation of anyone's reality.

 

[DrChinese]

Formula (15) is far too late. Everything what is used from realism and Einstein causality is already present in formula (2). What remains are elementary mathematical exercises. That all the values in different directions have to exist is not a consequence of some notion of realism used here, but a consequence of the EPR argument.

Such a reference to formula (15) with a "here realism is used" I would classify as a typical example of the misunderstanding which Maudlin has quoted from Bell's Bertlsman's socks : "It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred".

The formula (2) contains something nontrivial, worth to be named "realism", see my defintion in http://ilja-schmelzer.de/realism/definition.php where I also give a corresponding weaker notion of a statistical theory which restricts itself to give probability distributions for observables without caring about causal explanations.

I can't agree, and as we have discussed above, Bell's later writing is not authoritative in this regard. Neither is Maudlin (sorry). Whether EPR "assumes" or "infers" something is a semantic issue, I mean really? I say that the EPR argument strongly "implies" that there must be hidden elements of reality (hidden variables) and therefore there is form of determinism, or at least a more complete specification than QM provides. I say that EPR assumes locality too because they specify that there is no way to disturb the separated part of the system.

Regardless, you simply can't get (15) from (2) - the separability condition - UNLESS you assume there are a, b and c simultaneously. If you could, you wouldn't need to insert unit vector c - which Quantum Mechanics does not provide for anywhere. In fact QM does not allow for a and b to be simultaneously real either. You can only predict commuting values from an entangled pair. Anything outside the scope of the HUP doesn't provably exist, and can therefore only be referenced in a single equation by assumption. So there is no simultaneous a, b and c - and there is no simultaneous a and b either (unless a=b or similar).

 

[Ilja]

I don't get your point. Of course EPR assumes locality. And the EPR criterion of reality. Only their combination gives values for a, b and c.

Bohmian mechanics is realistic, but not local. So, formula (2) does not hold in dBB theory, and we have to replace it by

$ P(a,b) = \int A(a,b,\lambda) B(a,b,\lambda) \rho(\lambda) d\lambda.$

And, of course, dBB theory predicts only what is required by realism. That means, it predicts the outcomes of experiments. Which depend on the whole configuration. If somebody names the particular experiment a "measurement", assuming that the result depends only on the state of one part of it, dBB theory is not obliged to follow.

So, there is this caricaturistic version of realism which presupposes that all results of spin measurements should have definite values. This is not used by Bell, and is not fulfilled by dBB theory.

What Bell uses is, the weaker form of realism, combined with Einstein causality, which allows to reduce the formula to

$ P(a,b) = \int A(a,\lambda) B(b,\lambda) \rho(\lambda) d\lambda.$

Then the EPR argument is used (formula 13). Without EPR there would be no way to continue.

This formula, of course, assumes that the corresponding functions $A(a,b,\lambda)$ exist as functions, thus, are defined for all $\lambda$ as well as all a and b.

 

[carllooper]

The following is unavoidably a massive generalisation:

The common definition of "realism" (to which Einstein might be said to subscribe) is one in which reality is understood as not necessarily directly observable, nor necessarily ever observable. Observables for their part (images/measurements) become a subset of such a reality, or an effect of such a reality. Reality is understood as that which would explain an image.

In relation to this definition, Bohr/Copenhagen is commonly called "non-realism".

But a less common definition of "realism" (and one with an equally respectable history) is one in which reality is understood as identical to an observation. Not just actual observations, but also that which is in principle observable. For example, although I am not presently observing what is in a box, I can take it as equally real that what is in the box is in principle an observation (or an observable), ie. if I open the box the resulting observation will correspond to that which was in principle observable before opening the box. An example would be a photograph sitting in a shoe box. The emphasis here being on what is visible, whether in principle, or in practice. A corollary of this is that the never-visible belongs to a category called: "non-real".

However these two definitions of realism are not the opposite of each other. One is not the "non" of the other. So although Bohr/Copenhagen is commonly called "non-realism", this should be understood as incorrect. It is not defined in terms of the first realism. It is a different concept.

But realism is also a term that is fought over. Concepts will compete for ownership of the term.Non-locality. Non-locality can be regarded as a fundamental property of the concept of space. To speak of a distance between A and B (where A does not equal B) means that A and B, although not the same, are related. The concept of space defines a relationship between A and B. There is not required communication between A and B for this relationship to be defined. It is a non-local relationship.

But if one limits the relationship between A and B, to communication between A and B, the concept of non-locality is being limited. One is replacing non-locality with a localist limitation on such. As if the fundamental non-locality in our conceptions of space should be limited in this way. In this sense, the concept of FTL communication can be understood as a localist version of non-locality, ie. not quite appreciating the general concept of non-locality.

Logic, a latecomer to mathematics, also defines non-local relationships. We can define two variables, by an XOR relationship between them without requiring communication between the variables in order to satisfy this relationship.

And these relationships are visible, in practice or in principle, so are compatible with the second realism.

C

 

[DrChinese]

1. Only their combination gives values for a, b and c.

2. And, of course, dBB theory predicts only what is required by realism. That means, it predicts the outcomes of experiments.

3. ...

This formula, of course, assumes that the corresponding functions $A(a,b,\lambda)$ exist as functions, thus, are defined for all $\lambda$ as well as all a and b.

1. There is NO connection between a, b and c as elements of reality, and locality. These are separate assumptions. Elements of reality are predictable with certainty, and it matters not for this definition whether locality is a constraint or is not.

2. You are confused. Realism is not only the result of experiments that can be performed. It INCLUDES counterfactual questions too.

3. As I said: you can't get a Bell inequality without a, b and c in one formula. You must ASSUME the existence of something which cannot be demonstrated by experiment: the simultaneous existence of a, b and c.

Please answer this question: does a single photon have simultaneous definite polarization values at 0, 120 and 240 degrees? (Probably an unfair question to ask a Bohmian though. :) )

 

[atyy]

*Of course I agree that there is no local deterministic explanation of anyone's reality.

I guess I don't understand where you and Norsen differ. I don't think Norsen is saying that reality is not required to derive and to test the Bell inequalities. I think he is saying that as long as one has enough reality to derive and test the Bell inequalities, their violation at spacelike separation rules out a local deterministic explanation of that reality.

 

[stevendaryl]

1. There is NO connection between a, b and c as elements of reality, and locality. These are separate assumptions. Elements of reality are predictable with certainty, and it matters not for this definition whether locality is a constraint or is not.

I don't know whether this is quibbling, or not, but it seemed to me that Einstein and his pals P and R were not saying that every element of reality was predictable with certainty. They were saying that IF something is predictable with certainty, then it must be an element of reality. It seems to me that there could be plenty of nonpredictable elements of reality.

 

[DrChinese]

I don't know whether this is quibbling, or not, but it seemed to me that Einstein and his pals P and R were not saying that every element of reality was predictable with certainty. They were saying that IF something is predictable with certainty, then it must be an element of reality. It seems to me that there could be plenty of nonpredictable elements of reality.

Sure, no requirement that all elements be predictable. If they are predictable, they are elements of reality.

But here's the rub: which ones are SIMULTANEOUSLY predictable? We know you can predict entangled photon spin at any angle. How many angles is that? Infinity? If it were 360 (chosen to have something to discuss) and you could predict any 1 of the 360 at a time: EPR would say that it is not reasonable to require all of them to be simultaneously predictable to consider them each to be real ("two or more"). That was their assertion as to why QM must be incomplete. QM says only 1 is real, that being the one you can actually predict. If you accept EPR's definition of realism (as Bell did since he used 3), then we are all good. If you accept the EPR realism definition itself (as reasonable) but reject the EPR realism assumption* because of Bell, then that is the mainstream as I see it. * Or the locality requirement.

 

[atyy]

Sure, no requirement that all elements be predictable. If they are predictable, they are elements of reality.

But here's the rub: which ones are SIMULTANEOUSLY predictable? We know you can predict entangled photon spin at any angle. How many angles is that? Infinity? If it were 360 (chosen to have something to discuss) and you could predict any 1 of the 360 at a time: EPR would say that it is not reasonable to require all of them to be simultaneously predictable to consider them each to be real ("two or more"). That was their assertion as to why QM must be incomplete. QM says only 1 is real, that being the one you can actually predict. If you accept EPR's definition of realism (as Bell did since he used 3), then we are all good. If you accept the EPR realism definition itself (as reasonable) but reject the EPR realism assumption* because of Bell, then that is the mainstream as I see it.* Or the locality requirement.

Is the disagreement between you and Norsen as follows?
1) Norsen: If we have enough reality to violate the Bell inequalities at spacelike separation, then that there is no local deterministic explanation of the result.
2) DrChinese: If we have enough reality to violate the Bell inequalities at spacelike separation, then that there is either no real local deterministic explanation of the result or there is a nonreal local deterministic explanation of the result.

 

[DrChinese]

Is the disagreement between you and Norsen as follows?
1) Norsen: If we have enough reality to violate the Bell inequalities at spacelike separation, then that there is no local deterministic explanation of the result.
2) DrChinese: If we have enough reality to violate the Bell inequalities at spacelike separation, then that there is either no real local deterministic explanation of the result or there is a nonreal local deterministic explanation of the result.

I'm not sure about the 2 above. The way I think of it: Norsen believes that violation of a Bell inequality must demonstrate non-locality. I say that it must demonstrate either non-locality, an observer-dependent reality (contextuality), or both. A lot of Bohmians like Norsen's program, I can see why. :-) He ever wrote a paper called "Against Realism" to drive it home.

Please keep in mind that I think that a single particle exhibits non-local attributes anyway. So I am not against non-locality per se. Bohmian mechanics may very well be right. I would call it quantum non-locality though, since you can distinguish that from signal locality (present in every interpretation).

On the other hand, I also believe a single particle cannot have simultaneous reality of non-commuting properties. I believe in contextuality, observer-dependent reality, non-realism or whatever you want to call it. I do not believe a single particle has more than 1 well-defined spin component at a time.

 

[stevendaryl]

Sure, no requirement that all elements be predictable. If they are predictable, they are elements of reality.

But here's the rub: which ones are SIMULTANEOUSLY predictable? We know you can predict entangled photon spin at any angle. How many angles is that? Infinity? If it were 360 (chosen to have something to discuss) and you could predict any 1 of the 360 at a time: EPR would say that it is not reasonable to require all of them to be simultaneously predictable to consider them each to be real ("two or more").

Okay. The way I see it is something like this: You might start off saying that only observations are real (sort of the Copenhagen view, maybe). So the reality is the unfolding history of observations. The "variables" are measurements, and their "values" are the measurement results. However, in certain circumstances, knowing about one observation tells you something about other observations, possibly not yet made. In such a case, you can think of the variable's value being already "set", even though the observation hasn't been made. So the "element of reality" is some fact about observations that exists prior to the actual observation. So that brings us to EPR-type correlations.

Suppose Alice and Bob both choose to measure spin (or polarization) in the same direction, \vec{A}. When Alice gets her result, she knows immediately what Bob's result will be. (For the moment, assume that Alice's measurement takes place slightly before Bob's, in Alice's frame). So by the perfect prediction criterion, there is an element of reality associated with Bob's result, some "variable" whose value implies "Bob will get such-and-such a result when he performs his measurement". So the question is: when did that "variable" get set?

If it happened when Alice got her measurement result, then it seems that something nonlocal is going on: how else could an event at Alice's detector change a "variable" that affects Bob's detector, far away? The only way it could have been local is if the variable was "set" in the common past of Alice's and Bob's measurements (the intersection of the two backwards light cones). But if the variable was set before Bob performed his experiment, then (unless there is superdeterminism or retro-causality of some sort), Bob might have changed his mind about which setting to use AFTER the variable was set.

So what that seems to be implying is that the "variable" that determines what Bob will get if he measures along axis \vec{A} must be set independently of whether Bob actually chooses that axis. So the conclusion that the results of all possible spin measurements must exist simultaneously seems to me to be an implication of locality (and lack of superdeterminism, and lack of retrocausality) and the quantum predictions.

 

[atyy]

As far as understand it, only Rovelli's relational interpretation can be considered both local and unreal. For instance have a look at the 2 categories under table of "comparison of interpretations". Only in that interpretation is locality maintained and the wave function is not real. Having said that, I'm not sure of some of the less popular interpretations like Relational Blockworld.

Interpretations of quantum mechanics
http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

I don't think the RQM approach contradicts Norsen's view.

In http://arxiv.org/abs/quant-ph/0604064, Smerlak and Rovelli say "Of course the price to pay for this solution of the puzzle is that the sequence of events as described by B is different from what it is as described by A. For B, there is a quantum event of β at time t′0 and there is no quantum event regarding α at time t′0." So there is no violation of the Bell inequalities at spacelike separation.

Smerlak and Rovelli also say "But Bell’s work showed that the simplest interpretation of EPR correlations as an indication that quantum mechanics is incomplete was not tenable: any hypothetical complete classical dynamics yielding the same correlations as quantum mechanics violates locality." While this is different language from Norsen's, I think it is also consistent with his view. If I understand Norsen correctly, a violation of Bell's inequality at spacelike separation rules out local determinism, which can also be called classical locality. Norsen does agree that local determinism involves an assumption of counterfactual definiteness, because it means one can write the result of a measurement of c, even though only a and b are measured. What he says is that this counterfactual definiteness is part of the definition of local determinism, so one cannot (by definition) save local determinism by rejecting counterfactual definiteness.

As far as I can tell, Norsen is correct for the usual derivation of the Bell inequality, which only addresses theories that can be generated by local determinism. I believe Norsen is open to other sorts of locality not being ruled out. In any case, RQM doesn't provide a counterexample, since the Bell inequalities are not violated at spacelike separation.

 

[DrChinese]

So what that seems to be implying is that the "variable" that determines what Bob will get if he measures along axis \vec{A} must be set independently of whether Bob actually chooses that axis. So the conclusion that the results of all possible spin measurements must exist simultaneously seems to me to be an implication of locality (and lack of superdeterminism, and lack of retrocausality) and the quantum predictions.

Please don't confuse my view's with Bell's or EPR's. I am not asserting realism at all. :-) When what happens is something I cannot explain.

EPR thought exactly as you say, that the implication was that elements of reality existed independently of the act of observation. This has nothing to do with locality, if you know something before it happens then presumably it is real. If I know that I will see + with certainty, then + must be real or be associated with something real. Who cares where it is at that point? In other words, forget the entangled side of things. Just ask: can I know attribute a of this particle? Yes. Can I know b? Yes. Can I know c? Yes. Can I know them all at the same time? No, QM does not support that. But EPR rejected that, and said: "Hey, if I can know each individually, they must each be simultaneously real!" I mean, that is only reasonable. But we know from Bell that approach(assumption) is wrong. Because when you model a, b and c they cannot be consistent at all times. But if you attempt to model only a and b, they CAN be consistent: it is just like Malus. But a, b and c don't relate that way.

So sure, you can say it seems like something non-local is occurring. It seems like when an observer decides what to measure, it causes a distant part of the system to change. But as you say, which causes which? And by the way, that has little to do with Bohmian mechanics even though there are non-local elements to it. In Bohmian Mechanics, presumably every particle position affects every other particle. That is a far cry from QM, in which there are some quantum non-local effects but otherwise everything occurs locally.

 

[atyy]

I'm not sure about the 2 above. The way I think of it: Norsen believes that violation of a Bell inequality must demonstrate non-locality. I say that it must demonstrate either non-locality, an observer-dependent reality (contextuality), or both. A lot of Bohmians like Norsen's program, I can see why. :) He ever wrote a paper called "Against Realism" to drive it home.

Please keep in mind that I think that a single particle exhibits non-local attributes anyway. So I am not against non-locality per se. Bohmian mechanics may very well be right. I would call it quantum non-locality though, since you can distinguish that from signal locality (present in every interpretation).

On the other hand, I also believe a single particle cannot have simultaneous reality of non-commuting properties. I believe in contextuality, observer-dependent reality, non-realism or whatever you want to call it. I do not believe a single particle has more than 1 well-defined spin component at a time.

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.

I think DrChinese and Demystifier are in agreement here, since DrChinese has defined nonrealism as contextuality. DrChinese thinks he is not in agreement with Norsen. Does Demystifier think Norsen is right? I think Norsen is saying if there is reality of spacetime, settings and measurement outcomes such that the Bell inequalities are violated at spacelike separation, then there is no local deterministic explanation, and removing counterfactual definiteness (which is a definition of realism that seems different from noncontextuality) cannot save local determinism, because counterfactual definiteness* is part of the definition of local determinism.

*Determinism means the outcome is determined once the state of the preparation and the measurement setting are known. This is counterfactual definite in the sense that the outcomes are known for all measurement settings regardless of which settings are chosen.

I suspect by these definitions Bohmian mechanics is real (deterministic) and nonlocal, and also nonreal (contextual)?

 

[Demystifier]

I say that it must demonstrate either non-locality, an observer-dependent reality (contextuality), or both.

I think the problem is in terminology and definitions, because many people do not consider
i) contextuality,
ii) observer-dependent reality, and
iii) non-reality
to be the same.

In fact, almost nobody (but you may be one of rare exceptions) considers i) and iii) to be the same.

 

[Demystifier]

I think DrChinese and Demystifier are in agreement here, since DrChinese has defined nonrealism as contextuality. DrChinese thinks he is not in agreement with Norsen. Does Demystifier think Norsen is right? I think Norsen is saying if there is reality of spacetime, settings and measurement outcomes such that the Bell inequalities are violated at spacelike separation, then there is no local deterministic explanation, and removing counterfactual definiteness (which is a definition of realism that seems different from noncontextuality) cannot save local determinism, because counterfactual definiteness* is part of the definition of local determinism.

*Determinism means the outcome is determined once the state of the preparation and the measurement setting are known. This is counterfactual definite in the sense that the outcomes are known for all measurement settings regardless of which settings are chosen.

I suspect by these definitions Bohmian mechanics is real (deterministic) and nonlocal, and also nonreal (contextual)?

Yes, I could agree with that, given the definitions you use.

 

[Demystifier]

Ah, now I think I understand the definitions used by DrChinese.

When he says "non-local", he means there is something which is non-local, whatever that is.

But when he says "real", he has more definite things in mind. The property of being real or non-real is only attributed to macroscopic things which, at least in some contexts, can be directly observed. In the context (experimental setup) in which it can be observed it is certainly "real", but in another context in which it cannot be observed, the reality of it is questioned. The Bell theorem then proves that, if there is nothing non-local involved, some of the questioned macroscopic things must actually be non-real. And if there is at least one macroscopic thing which is non-real in that sense, the theory (as a whole) is called non-real.

DrChinese, is the above a correct representation of your attitudes?
For if it is, then I have the following question for you:
Is there any viable interpretation of QM which, by being non-local, is also real (as a whole)?

 

[stevendaryl]

If I know that I will see + with certainty, then + must be real or be associated with something real. Who cares where it is at that point? In other words, forget the entangled side of things. Just ask: can I know attribute a of this particle? Yes. Can I know b? Yes. Can I know c? Yes. Can I know them all at the same time? No, QM does not support that. But EPR rejected that, and said: "Hey, if I can know each individually, they must each be simultaneously real!" I mean, that is only reasonable.

I don't agree with you that this notion of "elements of reality" is independent of considerations of locality and entanglement. You can imagine a probabilistic interpretation where outcomes of measurements are not determined ahead of time, but that the outcome is created by interaction between the particle and the measuring device. So the question: "What result would Bob get if he measured the spin/polarization along axis \vec{a}?" would simply have no answer unless Bob actually did measure the spin/polarization along that axis. In such a probabilistic model, I don't think you would associate an "element of reality" with each spin direction.

However, that's where entanglement comes in. The fact that Alice measuring the spin along axis \vec{a} implies what Bob would get, if he did measure the spin along axis \vec{a}, means (to EPR) that there is an element of reality associated with the counterfactual "What would Bob get if he measured along axis \vec{a}?", even when Bob doesn't choose to measure along that axis. That element of reality can't be created by Alice's choice of axis (because that choice was made far away). So the conclusion is that the element of reality exists whether or not Bob (or Alice) chooses to measure it. Since \vec{a} was arbitrary in this argument, it should be true for all possible axes.

So, to me, the question of "elements of reality" is not independent of locality and entanglement. Locality and entanglement is what implies that there should be an element of reality associated with spin measurements.

 

[DrChinese]

In http://arxiv.org/abs/quant-ph/0604064, Smerlak and Rovelli

Ah, now I think I understand the definitions used by DrChinese.

When he says "non-local", he means there is something which is non-local, whatever that is.

But when he says "real", he has more definite things in mind. The property of being real or non-real is only attributed to macroscopic things which, at least in some contexts, can be directly observed. In the context (experimental setup) in which it can be observed it is certainly "real", but in another context in which it cannot be observed, the reality of it is questioned. The Bell theorem then proves that, if there is nothing non-local involved, some of the questioned macroscopic things must actually be non-real. And if there is at least one macroscopic thing which is non-real in that sense, the theory (as a whole) is called non-real.

DrChinese, is the above a correct representation of your attitudes?
For if it is, then I have the following question for you:
Is there any viable interpretation of QM which, by being non-local, is also real (as a whole)?

Yes, that is basically perfect!

I mostly follow the line on categorizing the interpretations, because the essential elements of the interpretation is the mechanism it offers. So Bohmian is non-local realistic. It is observer dependent, so there is an example of where realism and observer-independence are different.

MWI is local. So it must be non-realistic. There is no a, b and c in MWI because every time you attempt to observer any of the 3, a new world is split off. So none of the 3 really have a definite value except at the time you measure and look at the result. You measure a, and see + or -. If you then measure b, a now has no specific value until you measure it again. There are no worlds in which all 3 have definite values at the same time.