50th anniversary of Bell's theorem

[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.

 

[morrobay]

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).

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.

So in deriving the inequality, Bell is making the assumption of realism that is also the EPR view of realism. Now can there simultaneously be a model that agrees with QM predictions and inequality violation that is non realistic and saves locality ? Ie, what would the definition of non realism be in this case ?

 

[DrChinese]

So in deriving the inequality, Bell is making the assumption of realism that is also the EPR view of realism. Now can there simultaneously be a model that agrees with QM predictions and inequality violation that is non realistic and saves locality ? Ie, what would the definition of non realism be in this case ?

I can't say that this is the only way to look at things, but here is an answer:

EPR says: IF you follow the more restrictive definition of elements of reality (which is our "non-realistic" because there are only those elements which are simultaneously predictable with certainty), THEN the reality of Alice can be determined by the nature of an observation by Bob. That translates to an OBSERVER DEPENDENT viewpoint, which is fully consistent with everything we know anyway and is consistent with most interpretations in some form or fashion. The only point I add is: Bob does not determine the reality alone: it is always Alice and Bob together that determine context.

So next you asked: can locality be saved? I don't know the final answer on that, but... In every variation of an context: there is never an influence on the final context that cannot be accounted for by direct relationships that individually respect c. In other words: the relationship of Alice and Bob may easily be non-local, but that is not the direct relationship. Alice and the source particle A she observed are related by action that respects c, and so does Bob and his source particle B. Even in cases in which Alice's source A and Bob's source B are completely non-local at all times to each other (and there are such cases): there is still a connection between them (via other particles C and D) that IS local. So I would say that if that can be modeled by QM, the answer is YES - respect for c and locality is preserved in some fashion.

Look at it another way: the Bohmian program* asserts that there is NO per se impediment or limitation on non-local action. And yet there are absolutely no experiments ever proposed that show Alice doing something here that Bob can see non-locally there. There is always signal locality! You wouldn't really expect that, if you are honest about it. So you tell me whether non-realism (EPR's observer dependent reality) makes less sense than non-locality (EPR's "two systems no longer interact") as a base principle, when either way we see signal locality. *Please note that I am not trying to diss the Bohmian program in any way, as there is nothing wrong with it as far as anyone is aware. I only mention it to say that non-locality is not the only option "out" when we say that local realism is excluded. Locality and realism are both touched on in EPR (not using those words of course) but only locality is mentioned in Bell (because the realism assumption was simply slipped in without fanfare).

 

[bohm2]

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.)

That is an interesting suggestion but how is it that we can have enough agreement to do stuff like science? I think Norsen sees Rovelli's model in a somewhat similar fashion:

What’s “relational” in “relational QM” (RQM) is reality itself: there is no such thing as reality simpliciter ; there is only reality-for-X (where X is some physical system or conscious observer). Advocates of RQM thus use the word “reality” to mean what people normally mean by the word “belief”. That some fact is, say, “real-for-Alice” simply means (translating from RQM back to normal English) that Alice believes it. And, crucially, what is real-for-Alice need not be real-for-Bob: “different observers can give different accounts of the same sequence of events.”...

http://arxiv.org/pdf/quant-ph/0607057.pdf

 

[bohm2]

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 managed to locate Bell's "La nouvelle cuisine" on-line. With respect to c, Bell writes:

In region 3 let c stand for the values of any number of other variables describing the experimental set-up, as admitted by ordinary quantum mechanics.

La nouvelle cuisine
http://cqi.inf.usi.ch/qic/Bell1990.pdf

Anyway, this point was hi-lited previously by Maaneli:

And again, the variable c here is nothing but part of the specification of the experimental set-up (as allowed for by 'ordinary quantum mechanics'), just as are the polarizer settings a and b (in other words, a, b, and c are all local beables); and the introduction of c in the joint probability formula follows from the local causality condition, as part of the complete specification of causes of the events in regions 1 and 2. So, again, there is no notion of realism in c that is any different than in a and b and what already follows from Bell's application of his principle of local causality.

https://www.physicsforums.com/threads/understanding-bells-logic.409161/page-2#post-2758101

But I suppose if one can come up with a way to explain the perfect correlations locally and without "realism", then it seems like a moot point, I think.

 

[atyy]

La nouvelle cuisine
http://cqi.inf.usi.ch/qic/Bell1990.pdf

"When space-time itself is ‘quantized’, as is generally held to be necessary, the concept of locality becomes very obscure. And so it does also in presently fashionable ‘string theories’ of ‘everything’. So all our considerations are restricted to that level of approximation to serious theories in which space-time can be regarded as given, and localization becomes meaningful."

How interesting, now that we know how far that has come. Bell seems to always have been interested in gravity. In "Against 'measurement', he says something like wouldn't it be interesting if the measurement problem pointed to gravity? Of course, hidden variables was just his "hobby", and his real work was particle physics, he being one of the co-discoverers (with Jackiw, and Adler) of the chiral anomaly.

 

[DrChinese]

I managed to locate Bell's "La nouvelle cuisine" on-line. With respect to c, Bell writes:
...

Anyway, this point was hi-lited previously by Maaneli:
...

Bell is defining c in a different manner than in his paper, in which a, b and c are all equivalent.

Maaneli's point is made in reference to a discussion with me about the exact point being discussed here. You cannot start with Bell's locality/separability condition - Bell's (2) - and do anything with it as it sits. Unless, of course, you have a 3rd hidden variable (element of reality) c which exists simultaneously. The simultaneous requirement, as quoted from EPR above, being the added assumption which creates "realism".

To summarize: the EPR argument works fine for entangled particles IF you are asserting there are only 1 or 2 elements of reality. There is no contradiction with the predictions of QM in that case. But if you assume 3 elements of reality are simultaneously real (and of course any 2 can be measured independently without affecting the other), like Bell did, the EPR argument falls victim to contradictions with the predictions of QM.

If you have any question about the above, simply go as far as you can without c in an equation alongside a and b... and see how far you get! Keep in mind that Bell was simply expressing in accordance with this quote from EPR: "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." Bell said: OK, I will assume EPR is correct and assume that a, b and c are simultaneous elements of reality - even though I can only measure 2 at a time.

 

[Demystifier]

That is an interesting suggestion but how is it that we can have enough agreement to do stuff like science?

In a solipsistic view of the world, there is no "we". There is "me", and there are my observations (of nature, of scientific journals, of texts at Physics Forums, of speeches produced by other scientists, etc). These observations by me more-or-less agree with my thoughts.

In a soft-solipsistic view of the world, there is also "you", with your observations which agree with your thoughts.

For more details see my paper.

And I am not saying that such a view is reasonable. I am saying that I do not see any other way to make local non-reality logically consistent.* So if you think it is still unreasonable I am fine with it, but then it is the starting assumption of local non-reality which is unreasonable. And if it is so unreasonable that one does not even need to assume that this is not the case, then Bell theorem does not need to assume reality, but is simply a proof of non-locality.

(*A belief or hypothesis may be unreasonable but logically consistent. For example, a belief in dragons or in creationism may be unreasonable, but is logically consistent. On the other hand, a belief that dragons are green and not green is not only unreasonable, but is much worse: logically inconsistent.)

 

[stevendaryl]

"When space-time itself is ‘quantized’, as is generally held to be necessary, the concept of locality becomes very obscure. And so it does also in presently fashionable ‘string theories’ of ‘everything’. So all our considerations are restricted to that level of approximation to serious theories in which space-time can be regarded as given, and localization becomes meaningful."

How interesting, now that we know how far that has come. Bell seems to always have been interested in gravity. In "Against 'measurement', he says something like wouldn't it be interesting if the measurement problem pointed to gravity? Of course, hidden variables was just his "hobby", and his real work was particle physics, he being one of the co-discoverers (with Jackiw, and Adler) of the chiral anomaly.

I think that quantum gravity (whether through string theory or other approaches) is expected to be nonlocal at the microscopic level, but the nonlocal effects are supposed to become unobservable at macroscopic distances. So the nonlocality of quantum gravity is not expected to have anything to directly do with the nonlocality of EPR type phenomena, which are completely unrestricted in range. Right?

 

[atyy]

I think that quantum gravity (whether through string theory or other approaches) is expected to be nonlocal at the microscopic level, but the nonlocal effects are supposed to become unobservable at macroscopic distances. So the nonlocality of quantum gravity is not expected to have anything to directly do with the nonlocality of EPR type phenomena, which are completely unrestricted in range. Right?

I don't know. Bell goes on to say that he is assuming the a classical spacetime and local quantum mechanical observables have already emerged. At that level of approximation, there is no nonlocal quantum gravity. But I don't understand the gauge/gravity duality well enough to know how spacetime and quantum mechanics emerge from the boundary, and there are all these speculative ideas like ER=EPR for black holes.

 

[DrChinese]

In a solipsistic view of the world, there is no "we". There is "me", and there are my observations (of nature, of scientific journals, of texts at Physics Forums, of speeches produced by other scientists, etc). These observations by me more-or-less agree with my thoughts.

In a soft-solipsistic view of the world, there is also "you", with your observations which agree with your thoughts.

EPR failed to explain a crucial point in their characterization of the Observer-Dependent option: it is not relative to a single observer, it is relative to ALL observers as a group. And again, almost by definition, those observers can easily be positioned so that they are "non-local" relative to each other. And yet they are in fact connected indirectly by individual world lines that respect c.

So I don't see any particular observer's viewpoint - in this context - as needing to have a special position. My view is no more preferred than yours.

 

[Demystifier]

So I don't see any particular observer's viewpoint - in this context - as needing to have a special position. My view is no more preferred than yours.

I agree. But my point is that my view should not be correlated with your view, if we want a logically consistent version of "local non-reality". This implies that my view may be different from your view. For example, a particle may have spin-up in my view and spin-down in your view.

 

[atyy]

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]

Would it be right to say that in your model there is no violation of the Bell inequalities by particle detections at spacelike separation, because the detectors are not real and thus not at spacelike separation? There is only the real apparent violation of Bell inequalities at spacelike separation? So there is no known counterexample to the hypothesis that given a violation of Bell inequalities at spacelike separation, there is no way to save locality by nonrealism?

 

[DrChinese]

...given a violation of Bell inequalities at spacelike separation, there is no way to save locality by nonrealism?

That view is usually advanced by Bohmians, such as Norsen. But of course there are a number of interpretations that do just that, so that hypothesis is not correct. Without debating these interpretations themselves: MWI, Time Symmetric/Retrocausal, Blockworld. All claim to be completely local.

 

[bohm2]

That view is usually advanced by Bohmians, such as Norsen. But of course there are a number of interpretations that do just that, so that hypothesis is not correct. Without debating these interpretations themselves: MWI, Time Symmetric/Retrocausal, Blockworld. All claim to be completely local.

Do you consider all those models non-real/epistemic?

 

[atyy]

That view is usually advanced by Bohmians, such as Norsen. But of course there are a number of interpretations that do just that, so that hypothesis is not correct. Without debating these interpretations themselves: MWI, Time Symmetric/Retrocausal, Blockworld. All claim to be completely local.

I don't know enough about Blockworld. Does Time-Symmetric really claim to be local - as far as I can tell it is just Copenhagen written in a very interesting way? Retrocausation is an accepted loophole to the Bell derivation, so the Bell inequalities don't rule out that retrocausation could provide a real and local deterministic explanation of quantum mechanics. MWI also uses an accepted loophole, which is the assumption of one measurement outcome, so the Bell inequalities also don't rule out MWI can be a real and local deterministic explanation of quantum mechanics. So unless retrocausation or having more than one measurement outcome is "unreal", those don't seem to be counterexamples. MWI is considered real by Norsen, and also by some proponents like Wallace.

Incidentally, I don't know if there is agreement that MWI is local, but I think it is agreed that the question of locality in MWI is not affected by the Bell inequalities.

 

[DrChinese]

Do you consider all those models non-real/epistemic?

They are non-realistic because EPR elements of reality are limited to those that can be predicted with certainty. That would be one of P or Q, one spin component, etc.

Note: There are MWIers that insist that MWI is both local and realistic. But that is not canonical to MWI, it is an added assumption. In MWI, the splits occur at observations and there are no splits when there is no observation. So saying there are universes in which a, b and c are all simulateously real is not accurate there either, Bell's Inequality would separate that out too if there were.

 

[atyy]

Hmmm, after reading Demystifier's solipsistic hidden variables, I think he would say MWI is unreal? Would it be right to say solipsistic hidden variables is MWI (taken as unreal), but then you only add "real" Bohmian trajectories so that Alice is real in one world and Bob is not real in her world, but in Bob's world he is real and Alice is unreal?

Does this mean that BM can prove the correctness of MWI? After all, there is the Deutsch argument that BM is MWI with one world picked out. If MWI is simply BM with all possible initial conditions being realized, then it seems BM might prove MWI to be right. In fact, since BM doesn't have canonical hidden variables, nor trajectories, it seems BM could prove MMMWI.

Edit: I see my first question is answered in the paper! "Finally note that our result that different observers may live in different branches of the wave function is very similar to the many-world interpretation [16, 17], briefly discussed in Sec. 2.2. Yet, there is one crucial difference. In the many-world interpretation, there is a copy of each observer in any of the branches. In our solipsistic interpretation, for each observer there is only one copy living in only one of the branches."

OK, Demystifier, I don't know if I agree that you have provided a "local deterministic" theory that shows how nonrealism can save nonlocality. But it is a very nice paper! :) Also, the paper does not answer my second question as to whether this shows that BM can prove MWI to be right. Now that we have in BM also the freedom to choose what is real, it seems BM can prove MMMMWI :p

 

[bohm2]

Hmmm, after reading Demystifier's solipsistic hidden variables, I think he would say MWI is unreal?

Wouldn't the wavefunction be considered ontic/real in MWI?

 

[Demystifier]

Would it be right to say that in your model there is no violation of the Bell inequalities by particle detections at spacelike separation, because the detectors are not real and thus not at spacelike separation? There is only the real apparent violation of Bell inequalities at spacelike separation? So there is no known counterexample to the hypothesis that given a violation of Bell inequalities at spacelike separation, there is no way to save locality by nonrealism?

I guess you could say that, but that's not how I would say it. I would rather rephrase the above as follows: Bell inequalities are violated, but not at space-like separation. The violation happens locally (at the position of the observer), while the observer only thinks that it happens at space-like separation because he thinks that the violation happened in space-like separated detectors before he observed it.

 

[Demystifier]

MWI, Time Symmetric/Retrocausal, Blockworld. All claim to be completely local.

But neither of them claims to be non-real.

 

[Demystifier]

They are non-realistic because EPR elements of reality are limited to those that can be predicted with certainty.

Perhaps they are EPR-nonreal, but they are Bell-real.

Note: There are MWIers that insist that MWI is both local and realistic. But that is not canonical to MWI, it is an added assumption.

I have never seen that a MWIer claims that MWI is not realistic. Can you cite an example?

In MWI, the splits occur at observations and there are no splits when there is no observation. So saying there are universes in which a, b and c are all simulateously real is not accurate there either, Bell's Inequality would separate that out too if there were.

I guess your problem is to understand how can MWI be both real and combatible with the Bell theorem? That's because MWI is not Bell-local. But it is also not Bell-non-local. So what is it? It is Bell-alocal. What is the difference between non-local and alocal? Non-local lives in the 3-space but has action at a distance. Alocal does not even live in the 3-space. Bell theorem tacitly assumes that physics (either local or non-local) happens in the 3-space, but MWI violates this asumption.

 

[Demystifier]

OK, Demystifier, I don't know if I agree that you have provided a "local deterministic" theory that shows how nonrealism can save nonlocality. But it is a very nice paper! :)

Thanks! :)

Also, the paper does not answer my second question as to whether this shows that BM can prove MWI to be right. Now that we have in BM also the freedom to choose what is real, it seems BM can prove MMMMWI :p

I don't think that this paper helps to understand MWI. In this paper we can choose which particles are real, but (in a sense similar to that in BM) wave function is not considered real. MWI insists that wave function is real and that there is nothing else which is real.

 

[stevendaryl]

I have never seen that a MWIer claims that MWI is not realistic.

We need a definition of "realistic" here. Is there one? What I think is important is understanding the relationship between observation and whatever it is that your theory considers to be real. With normal (pre-quantum) theories, it is assumed that observations give us information about the state of the universe. There is a sense in which, for MWI, observations don't tell us anything about the universe that we don't already know. If you measure the spin of an electron, you know ahead of time that there will be a world in which the outcome is "spin up" and there will be a world in which the outcome is "spin down". Some people would say that you learn something, in the sense that you learn which of those two worlds you are in. But the concept of "which world you are in" isn't part of MWI, is it?

 

[Demystifier]

But the concept of "which world you are in" isn't part of MWI, is it?

I think it is. But instead of explaining why, I will just use an analogy with biology of identical twins. So for that purpose, let us suppose that you have a genetically identical twin brother. Then what you said above would be analogous to saying that the concept of "which of the twins you are" isn't part of biology.

 

[DrChinese]

1. Perhaps they are EPR-nonreal, but they are Bell-real.

2. I have never seen that a MWIer claims that MWI is not realistic. Can you cite an example?

3. I guess your problem is to understand how can MWI be both real and combatible with the Bell theorem? That's because MWI is not Bell-local. But it is also not Bell-non-local. So what is it? It is Bell-alocal. What is the difference between non-local and alocal? Non-local lives in the 3-space but has action at a distance. Alocal does not even live in the 3-space. Bell theorem tacitly assumes that physics (either local or non-local) happens in the 3-space, but MWI violates this asumption.

1. I say Bell is using the same definition as EPR: simultaneous elements of reality.

2. I don't think MWI is realistic. And I don't see how anyone can say - with a straight face - that MWI IS realistic. If you want to call it an additional assumption of realism that there be one world, that would do it for me.

I would ask the same question as always: if there is an a, b and c in MWI, what values do they have? Because there are definitely outcomes in which some values have negative probabilities of occurring (as soon as you assert realism) if QM is accurate. I presume there is no such thing as a negative world, which is what you would need to make everything balance out.

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