I Does realism imply locality or vice versa?

[Sunny Singh]

Through Bell's inequality, we can see that any hidden variable theory of QM will have to satisfy the inequality, but as it doesn't, wave function must be the whole story and so we have to do away with realism. So when a measurement is done on one detector in the EPR experiment, the wave function collapses for both the observers simultaneously and so locality must also be violated. So in this sense, by violation of realism, locality is also violated as a consequence. So i was wondering if they imply each other or i am misunderstanding something here since i have read in some books that they do not necessarily imply each other.

 

[Demystifier]

Through Bell's inequality, we can see that any hidden variable theory of QM will have to satisfy the inequality

Not any hidden variables, just local ones. Non-local hidden variables can violate the inequality and be compatible with QM.

 

[Sunny Singh]

So if locality is violated, it does not necessarily mean that realism is out as there can be non local hidden variable theories but what if we find out that there are no hidden variables (local or non-local), that realism doesn't exist. Then according to my above logic does it necessarily implies that locality is also violated?
I'm sorry if i am missing some key points as i am very new to Bell's inequality and the concept of hidden variables.

 

[m k]

An italian team did an entanglement test thru optical wire and got a result.

Means that eighter wire is there or don't.

 

[atyy]

There are at least two types of locality.

(1) Local realism. Local realism assumes realism. Thus if realism does not hold, then local realism also does not hold.

(2) Signal locality. Signal locality does not assume realism. Thus if realism does not hold, signal locality can still hold.

 

[Demystifier]

So if locality is violated, it does not necessarily mean that realism is out as there can be non local hidden variable theories but what if we find out that there are no hidden variables (local or non-local), that realism doesn't exist. Then according to my above logic does it necessarily implies that locality is also violated?
I'm sorry if i am missing some key points as i am very new to Bell's inequality and the concept of hidden variables.

If realism is missing, then locality can be saved.

 

[ueit]

If realism is missing, then locality can be saved.

Can you provide an example of a local, non-realist theory that can explain the observed correlation?

 

[Demystifier]

Can you provide an example of a local, non-realist theory that can explain the observed correlation?

Yes, I made such an example by myself:
https://arxiv.org/abs/1112.2034
It is non-realistic in the sense that observed objects are not real, even though the observations are real.

 

[Sunny Singh]

If realism is missing, then locality can be saved.

But sir, in case of the EPR experiment, if realism is missing, how can locality be saved since that would collapse the wave function for both observers and information has to travel instantaneously. Can you please explain this point of yours a bit further?

 

[Demystifier]

But sir, in case of the EPR experiment, if realism is missing, how can locality be saved since that would collapse the wave function for both observers and information has to travel instantaneously. Can you please explain this point of yours a bit further?

If realism is missing, then wave function is not real. If so, then collapse is also not real, so non-locality is also not real.

 

[Nugatory]

Mentor's note: A side discussion based on superdeterministic ideas has been moved to another thread, because it is not especially responsive to the original question.

 

[DrChinese]

But sir, in case of the EPR experiment, if realism is missing, how can locality be saved since that would collapse the wave function for both observers and information has to travel instantaneously. Can you please explain this point of yours a bit further?

Realism is missing when there are no predetermined outcomes of measurements. Keep in mind that EPR's "perfect correlations" imply predetermination, but Bell implies the opposite.

If the outcomes are NOT predetermined, there are several other possibilities: a) the outcomes are determined at time of measurement, which implies non-local (instantaneous) interactions of some kind; or b) the future affects the past. Please note that for b) you can preserve locality (there would need to be some form of time symmetry). This is done by having the observers become part of the context of the measurement process. There still is no instantaneous effect, although it might look otherwise superficially.

Although this may seem crazy at first: all entangled systems do trace out locally if you allow backward-in-time connections. This is especially notable when you attempt to create a spacetime diagram of entanglement swapping. +/- c is a limiting factor for these setups, and direct FTL action (between Alice and Bob) does not *appear* to describe anything on these.

Of course, whenever you talk about dropping realism vs. dropping locality, you are wading into the interpretations of QM. And there is no experimental evidence to select one of those over another at this time.

 

[Xu Shuang]

Local realism is not simply a combination of locality and realism, realism alone dictates $(a,b)=f(\hat a , \hat b,{\cal R})$ , in which $\cal R$ denotes "the reality" of the system in question, $(a,b)$ are two measurement results, and $\hat a$ and $\hat b$ denotes how the measurements are carried out for two particles. In comparison, local realism dictates $a=f(\hat a , {\cal R})$ and $b=f(\hat b, {\cal R})$, if the two measurement events are space-like connected. The two equations defines local realism gives Bell inequality, while the equation that defines realism doesn't, hence when Bell inequality is violated, it violates local realism, but not realism alone. Alternatively, if realism is not right to begin with, then local realism cannot be defined, while locality alone can be intact in its phenomenological definition, as in information cannot travel faster than light.

 

[RUTA]

Here is an article you might find helpful https://arxiv.org/ftp/arxiv/papers/1408/1408.1826.pdf

 

[stevendaryl]

Realism is missing when there are no predetermined outcomes of measurements. Keep in mind that EPR's "perfect correlations" imply predetermination, but Bell implies the opposite.

If the outcomes are NOT predetermined, there are several other possibilities: a) the outcomes are determined at time of measurement, which implies non-local (instantaneous) interactions of some kind; or b) the future affects the past. Please note that for b) you can preserve locality (there would need to be some form of time symmetry). This is done by having the observers become part of the context of the measurement process. There still is no instantaneous effect, although it might look otherwise superficially.

Although this may seem crazy at first: all entangled systems do trace out locally if you allow backward-in-time connections. This is especially notable when you attempt to create a spacetime diagram of entanglement swapping. +/- c is a limiting factor for these setups, and direct FTL action (between Alice and Bob) does not *appear* to describe anything on these.

Of course, whenever you talk about dropping realism vs. dropping locality, you are wading into the interpretations of QM. And there is no experimental evidence to select one of those over another at this time.

Do you have a url to an essay talking about entanglement swapping from the point of view of time symmetry?

 

[DrChinese]

Do you have a url to an essay talking about entanglement swapping from the point of view of time symmetry?

Good one, let me see what I have.

 

[Denis]

Alternatively, if realism is not right to begin with, then local realism cannot be defined, while locality alone can be intact in its phenomenological definition, as in information cannot travel faster than light.

The funny thing is that "locality" in this sense - no observable/usable information transfer - remains untouched even if we do not reject realism.

So, we can have realism, together with weak locality. Or simply the same weak locality alone. Or, in other words, we can throw away realism gaining nothing.

 

[Simon Phoenix]

So i was wondering if they imply each other . . .

The short answer to your question is, no, they do not imply each other. The words 'realism' and 'locality' can be confusing and the discussions can get a bit technical with other terms like 'counterfactual definiteness' bandied about. All that is fine, and it's important to be as precise as possible, but I sometimes feel that the jargon obfuscates what is in essence a very simple question: can the world be described by a 'common sense' model?

Of course the devil in the detail here is what is meant by the term 'common sense'. In essence we might describe the world of classical physics pre-QM and pre- special relativity as 'common sense'. In this world an object in motion, such as golf ball, could be (approximately) modeled as a point particle for which we could assign a position and a momentum at some instant in time. We construct the equations of motion that show us how the position and momentum evolve in time and we learn how to do this in high school. The model, of course, is not the physical system itself, but until QM came along nobody had any real problem with thinking of the position and momentum for something like a golf ball as being anything other than a faithful representation of reality - the golf ball really was somewhere and it really was traveling with some specified velocity at some given instant in time.

OK maybe 'nobody' here is too strong - but I think someone who felt that things like position and momentum weren't 'real' things would probably have had a hard time defending their position pre-QM.

So there's this notion that's kind of implicit in classical physics that we can describe things using a set of variables that have some meaning out there in the real world. Special relativity didn't really change this but added an extra feature that one event can only be the cause of another event if there was enough time for a light signal to be transmitted between the events. In other words, if two remote objects interacted with one another that interaction could not occur faster than some minimum time interval, and certainly not instantaneously; so no instantaneous action-at-a-distance.

So the two notions 'realism' and 'locality' are really quite distinct, but both eminently reasonable from the perspective of classical physics. Realism says that things really do have some properties and it doesn't matter whether we measure them or not, those properties exist. Locality says that if one object interacts with another then there's a speed limit imposed on how fast that interaction can get from place to place.

So in a nutshell, can we construct a model of the world from things (properties) which are realistic and local? What Bell showed was that there were certain kinds of experiments we could do and, if we assumed the results could be modeled by some theory that had these 'common sense' properties of realism and locality, then those results had to be constrained to lie within a certain range of values. The amazing thing is that the QM predictions for these experiments can lie outside this range. Bell's inequality is actually nothing at all to do with QM - it is a constraint that classical-like theories which have these 'common sense' properties must satisfy.

Bell's own masterful exposition of all this is still, for me, the best : https://cds.cern.ch/record/142461/files/198009299.pdf

Now of course everything I've written above needs quite a bit of technical 'pinning down' - the intuition needs precise codification and translation into maths, but in essence the underlying problem is simple and ultimately very, very profound. Can we build a kind of clockwork classical model of the world? The answer to that is remarkable; yes we can, but if we want our model to consist of things which have some real objective existence (like position or momentum for example) then the only way to do it is to have these 'realistic' elements connected in some way that violates the bounds of special relativity.

The only successful model I'm aware of that has this property of realism, but is non-local, is the Bohmian version of QM. It still looks nothing at all like traditional classical physics - and I think it's nuts (subjective, non-scientific opinion) but it is at least one counter-example to the supposition that realism and locality imply one another.

Actually in my opinion the issue of 'non-locality' is almost a red herring. It's important to be able to exclude certain kinds of theories as contenders for 'explanations' of QM, but for me the real issue is that even if we admit non-local interactions (instantaneous action at a distance, for example) then the physics we need to explain stuff is still going to look very, very different to traditional classical physics.

 

[Denis]

I sometimes feel that the jargon obfuscates what is in essence a very simple question: can the world be described by a 'common sense' model?
...
In other words, if two remote objects interacted with one another that interaction could not occur faster than some minimum time interval, and certainly not instantaneously; so no instantaneous action-at-a-distance.
...
The answer to that is remarkable; yes we can, but if we want our model to consist of things which have some real objective existence (like position or momentum for example) then the only way to do it is to have these 'realistic' elements connected in some way that violates the bounds of special relativity.
...
Actually in my opinion the issue of 'non-locality' is almost a red herring. It's important to be able to exclude certain kinds of theories as contenders for 'explanations' of QM, but for me the real issue is that even if we admit non-local interactions (instantaneous action at a distance, for example) then the physics we need to explain stuff is still going to look very, very different to traditional classical physics.

The basic question is indeed a very interesting one, not only for scientists, but also for the general public. It would be important to discuss the possibility of interpretations of modern physics as close to "common sense" as possible. Unfortunately, this is almost forbidden to discuss here.

In general, I do not think that a "common sense interpretation" of modern physics would be so very different from traditional classical physics. dBB is the most famous realistic QT interpretation, but not the closest one to common sense, where my favorite is Caticha's entropic dynamics (even if it has a problem with the Wallstrom objection). And interpretations of the Einstein equations of GR much closer to classical "common sense" are also not a big problem.

The use of "locality" is very misleading, because the common sense meaning of this word is very different from the actual use in Bell discussions. The accurate name would be Einstein causality, of Einstein locality. Which connects it to the very special theory it belongs too. A theory which would have a maximum speed of information transfer of 10000000 c would be nonetheless local in the common sense meaning, and not at all excluded by actual observations, and even if our best existing theories are really non-local, like dBB theory, they all may be limits of local theories.

 

[facenian]

..., wave function must be the whole story and so we have to do away with realism...

That's not the correct way to see at Bell's inequalities. The violation of Bell' s inequalities(VBI) does not mean that the wave function is the whole story it only means both assumptions, realism and locality can not hold simultineously. Bell stated a theorem that like any other theorem has an hypothesis and a Tesis
H) realism and locality(both valid at the same time)
T) there is an inequality that must be satisfied by any local realistic hidden variable theory
Then he proves VBI by QM so the hypotheis is false which means there are three posibilities
1_ realism is true and locality is violated
2_ realism is false and locality holds
3_ both realism and locality are false

To add to the existing confusion I must say that there are more than one version of Bell's theorem that he himself generalize throuhg out the years. Here we are dealing with his first version published in 1964

... So when a measurement is done on one detector in the EPR experiment, the wave function collapses for both the observers simultaneously and so locality must also be violated...

This is only true if we accept the Copenhagen interpretation and this we must not do when trying to interpret Bell' theorem

 

[Zafa Pi]

Not any hidden variables, just local ones. Non-local hidden variables can violate the inequality and be compatible with QM.

Would Bohmian mechanics provide an example of non-local hidden variables? If not what would would?

 

[Demystifier]

Would Bohmian mechanics provide an example of non-local hidden variables?

Yes. Indeed, this is the best known example of non-local hidden variables.

 

[Zafa Pi]

If realism is missing, then locality can be saved.

Please note that for b) you can preserve locality

Here is an article you might find helpful https://arxiv.org/ftp/arxiv/papers/1408/1408.1826.pdf

So @Demystifier and@DrChinese say locality can be preserved and like the article recommended by @RUTA which says Bell showed nonlocality.
Perhaps one of Demystifier or DrChinese or John Bell could help me out here.

 

[Demystifier]

So @Demystifier and@DrChinese say locality can be preserved and like the article recommended by @RUTA which says Bell showed nonlocality.
Perhaps one of Demystifier or DrChinese or John Bell could help me out here.

Bell proof is a mathematical theorem which, like any other mathematical theorem, rests on certain unproved assumptions. It is always legitimate to question the unproved assumptions, even if the assumptions seem very reasonable. For various ways to save locality by rejecting certain reasonable but unproved assumptions see
https://arxiv.org/abs/1703.08341 Sec. 5.3.

 

[Simon Phoenix]

Perhaps one of Demystifier or DrChinese or John Bell could help me out here.

I'm just going to re-iterate what Demystifier has said here.

Mathematical theorems are usually of the form of an IF . . .THEN statement. So IF we have $A$ and $B$, THEN $x$ follows.

In the context of Bell's work we have something like (and crudely),

IF (realism, locality) THEN (correlation functions bounded by inequality)

where I'm just focusing on these two properties and excluding things like superdeterminism.

QM predicts correlation functions that don't have to be bounded by this inequality, therefore QM cannot be equivalent to a theory constructed from quantities which have the properties 'realism' AND 'locality'.

It is therefore possible (in principle) to find a theory for which the correlations are not bounded by the inequality by :
(i) dispensing with 'realism' but keeping 'locality'
(ii) dispensing with 'locality' but keeping 'realism'
(iii) dispensing with both 'locality' and 'realism'

It is NOT possible, in principle, to find a theory that agrees with the QM predictions for the correlation functions constructed from variables/quantities which possesses BOTH of the properties 'realism' and 'locality'.

Note that we're only talking about the violation of the bound on the correlation functions here - just because we construct some theory (eg by dispensing with 'locality') that has a violation for a particular experiment (eg the singlet state of QM) does not imply that it will also agree with other predictions of QM, or even the predictions of QM for other entangled systems (eg the GHZ state)

 

[Denis]

With preserving locality there is a subtle point.

There is a weak notion of Einstein locality, which is simply that no signals can be send FTL. This weak notion is not even questioned.

There is the stronger notion of Einstein locality, which is that there can be no causal influence, not even a hidden one, FTL. This is all what is endangered by Bell's theorem.

But if one rejects realism, there is no difference between the two. Once there is no reality anyway, it makes no sense to tell us that there are also no real causal influences FTL. So, Einstein locality in this case is, anyway, reduced to weak Einstein locality. So, by throwing away realism, you gain essentially nothing.

 

[Zafa Pi]

I apologize for not making myself clear in post #23. I agree with @Demystifier, @DrChinese, and @Simon Phoenix that locality can be preserved, and for the reasons you provided.

What puzzled me was that @Demystifier, and @DrChinese gave likes to:

Here is an article you might find helpful https://arxiv.org/ftp/arxiv/papers/1408/1408.1826.pdf

And in the linked article Tim Maudlin contends from Bell that: "actual physics is non-local", which contradicts what you guys have shown.
So what I am asking is, why didn't you take issue with the article rather than merely liking it?

 

[Zafa Pi]

So, by throwing away realism, you gain essentially nothing.

You "gain" the inability to prove Bell's inequality, for what that's worth.

 

[Denis]

You "gain" the inability to prove Bell's inequality, for what that's worth.

This inability you "gain" also with realism and weak (signal) Einstein locality.

 

[Simon Phoenix]

And in the linked article Tim Maudlin contends from Bell that: "actual physics is non-local",

I can't agree with Maudlin's conclusion at all here. I didn't properly read the article (it is a bit long and wordy) but Maudlin does seem to take pains to stress that 'local' here means what Bell took it to mean in his original paper. So in Bell's own words :

"It is the requirement of locality, or more precisely, that the result of an experiment on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty."​

Yet in these terms QM is a fully local theory - results of experiments 'here' are not affected by anything that is done 'there'. That's easy enough to demonstrate by considering how the reduced density matrix 'here' is affected by operations (including measurements) done 'there' - and it is not affected.

So Maudlin, it would seem, has arrived at an untenable position. He claims "actual" physics is non-local, and yet in the very definition of the term he stresses in his article, QM is manifestly local.

Now, if we look at unmeasureable things, like the wavefunction for example, and we think of this as having some 'real' character (in some ill-defined sense) then we are indeed led to the conclusion that QM is non-local since measurements 'here' can indeed force a change of state 'there' - but that depends on us adopting this interpretation, and it also is with reference to something we can't actually measure.

 

[zonde]

Yet in these terms QM is a fully local theory - results of experiments 'here' are not affected by anything that is done 'there'. That's easy enough to demonstrate by considering how the reduced density matrix 'here' is affected by operations (including measurements) done 'there' - and it is not affected.

Only statistical properties of experimental results 'here' are not affected by anything that is done 'there'. But to get coincidence frequencies you need more than just statistical properties of experimental results 'here' and statistical properties of experimental results 'there'.

 

[Demystifier]

I apologize for not making myself clear in post #23. I agree with @Demystifier, @DrChinese, and @Simon Phoenix that locality can be preserved, and for the reasons you provided.

What puzzled me was that @Demystifier, and @DrChinese gave likes to:

And in the linked article Tim Maudlin contends from Bell that: "actual physics is non-local", which contradicts what you guys have shown.
So what I am asking is, why didn't you take issue with the article rather than merely liking it?

Maybe I was not sufficiently clear. I think that actual physics is most likely non-local. There is a possibility that it is local if some reasonable assumptions are not true, but I think that it is not very likely that those reasonable assumptions are not true.

 

[Simon Phoenix]

Only statistical properties of experimental results 'here' are not affected by anything that is done 'there'.

But you think individual results are so affected? Please clarify.

you need more than just statistical properties of experimental results 'here' and statistical properties of experimental results 'there'.

You need more than these if you want to examine correlation sure. So what? That's not really the issue here - the issue is whether there is a measureable change 'here' caused by something that is done remotely, i.e. 'there'. The definition of 'locality' adopted by Bell in his original paper is based on this. In these terms QM is a fully-local theory. If you don't think so - then please find me an example in QM where the result of a measurement 'here' is different dependent on whether or not something is done 'there' (and then construct the FTL signalling scheme from it )

If you want to use an alternative definition of 'locality', then sure it might be that QM is non-local according to that definition.

 

[stevendaryl]

Now, if we look at unmeasureable things, like the wavefunction for example, and we think of this as having some 'real' character (in some ill-defined sense) then we are indeed led to the conclusion that QM is non-local since measurements 'here' can indeed force a change of state 'there' - but that depends on us adopting this interpretation, and it also is with reference to something we can't actually measure.

This sort of reminds me of the situation in classical field theory. In Maxwell's equations, the scalar potential in the Coulomb gauge changes instantaneously in response to changes in distant charge distributions. It doesn't imply FTL effects, however, because potentials in Maxwell's equations are not considered physical, only the electric and magnetic fields are, and they do not change instantaneously.

I feel that there is a difference with the quantum case, though. In electromagnetism, there is a clearer criterion for what is physical and what is not. Physical quantities are gauge-invariant. Quantum mechanics, in contrast seems positivistic---what's physical is just what we observe.

 

[zonde]

But you think individual results are so affected? Please clarify.

Yes, I think so based on Bell inequality violations.

That's not really the issue here - the issue is whether there is a measureable change 'here' caused by something that is done remotely, i.e. 'there'. The definition of 'locality' adopted by Bell in his original paper is based on this.

Here is Bell's definition of locality in his original paper: "result of measurement on one system be unaffected by operations on a distant system with which it has interacted in the past".
I do not see how you arrived at your conclusion unless you take "measurable" as synonym for "affected".

 

[Simon Phoenix]

Here is Bell's definition of locality in his original paper: "result of measurement on one system be unaffected by operations on a distant system with which it has interacted in the past".
I do not see how you arrived at your conclusion unless you take "measurable" as synonym for "affected".

Erm, let's see: "result of measurement on one system be unaffected by operations on a distant system"

Which says that the results of measurement are unaffected - which means that there are no measureable consequences, doesn't it?

Yes, I think so based on Bell inequality violations.

Then I'm afraid you think wrong

 

[RUTA]

Here is Maudlin's argument as it pertains to the EPR claim.

If I disagree with EPR’s conclusion, i.e., that QM is incomplete, I have only two ways to deny its validity. One, claim that QM formalism is wrong (in its prediction about the S2 outcome given the S1 outcome). Two, claim there is a FTL influence on S2 given the outcome S1. The option of rejecting “realism” is not on the table. Here is why.

He’s looking at this in time-evolved fashion. After S1, we know S2 before the measurement is made (assuming same measurement on both). Realism in this case is simply to believe that claim (as he argues in his article). Since that claim comes from QM, if you believe the QM formalism is correct, you cannot reject that claim (of realism).

Now to finish the argument that the EPR claim implies reality is nonlocal, we simply accept that the QM formalism is correct and complete. That comes from the fact that we didn’t know S2 before making measurement S1. So, if there is a fact of the matter for S2 before S1, then QM is incomplete because it says we don’t know S2. If not, reality is nonlocal (in SR sense) because S1 is spacelike related to S2 and must be responsible for S2 becoming definite. You can see that “realism” just isn’t an issue in this view.

Here Maudlin is using the term “nonlocal” to mean spacelike separated, causally related events. Price would argue that the SR nonlocality can be avoided by making timelike connections and allowing causes to propagate backwards in time. I argue that Price’s retrocausality does not avoid the PROBLEM of spacelike causal relationships in the least, which is that effects will precede causes in some frames of reference if the events are spacelike separated. The complaint about that is precisely what retrocausality posits, i.e., information comes from the future to inform the present. So, Maudlin is correct.

Maudlin's argument tacitly assumes there really are two independent systems as evidenced by the spatial separation of the measurements S1 and S2. That means S1 must somehow be communicated to S2. But this is where you may disagree, S1 and S2 are just two parts of a single "entity." Thus, there is no causal relationship needed between S1 and S2, so no FTL nonlocality, and QM formalism is correct and complete. It comes down to his tacit dynamical view which, in leading him to reject realism (per his dynamical interpretation thereof), doesn’t even permit consideration of independence.

 

[zonde]

Erm, let's see: "result of measurement on one system be unaffected by operations on a distant system"

Which says that the results of measurement are unaffected - which means that there are no measureable consequences, doesn't it?

Yes. But your claim was sort of the other way around: as there are no measurable consequences 'here' of operations done 'there' it means that the results of measurement 'here' are unaffected by operations done 'there'.

 

[fanieh]

Realism is missing when there are no predetermined outcomes of measurements. Keep in mind that EPR's "perfect correlations" imply predetermination, but Bell implies the opposite.

If the outcomes are NOT predetermined, there are several other possibilities: a) the outcomes are determined at time of measurement, which implies non-local (instantaneous) interactions of some kind; or b) the future affects the past. Please note that for b) you can preserve locality (there would need to be some form of time symmetry). This is done by having the observers become part of the context of the measurement process. There still is no instantaneous effect, although it might look otherwise superficially.

Is there no standard usage of the word "Non-locality"? Demystifier just commented that "If realism is missing, then wave function is not real. If so, then collapse is also not real, so non-locality is also not real." So if outcomes are NOT predetermined, realism is missing, so non-locality is also not real.. but why did you use the word "non-local" in your paragraph above?

Should we follow the convention of DrChinese or Demystifier.. and which general physicists follow?

Although this may seem crazy at first: all entangled systems do trace out locally if you allow backward-in-time connections. This is especially notable when you attempt to create a spacetime diagram of entanglement swapping. +/- c is a limiting factor for these setups, and direct FTL action (between Alice and Bob) does not *appear* to describe anything on these.

Of course, whenever you talk about dropping realism vs. dropping locality, you are wading into the interpretations of QM. And there is no experimental evidence to select one of those over another at this time.

 

[Denis]

Realism is missing when there are no predetermined outcomes of measurements. Keep in mind that EPR's "perfect correlations" imply predetermination, but Bell implies the opposite.

No. EPR does not imply predetermination without strong Einstein causality (Einstein locality not only for signals, but also for hidden but real causal influences). This is the "without in any way disturbing" part of the EPR criterion.

Of course, whenever you talk about dropping realism vs. dropping locality, you are wading into the interpretations of QM. And there is no experimental evidence to select one of those over another at this time.

No. All this can be discussed without even mentioning QT at all. We have the experimental facts - BI are violated for space-like separated measurements - and the theorems which allow to derive the BI.

It is important to discuss the various definitions of realism and causality which would allow to derive the BI, and those which are insufficient. But above notions are important from the start, they are important already for classical mechanics, even to reject astrology, given that the decisive argument against astrology is not that the observed correlations are weak (at least the readers of astrological predictions think otherwise), but that it refuses to give any realistic and causal explanations for the hypothetical influences.

QT increases the probability that the BI are indeed violated, because it predicts a violation itself. And the only point where QT interpretation becomes relevant is the point that there exists at least one real and causal interpretation of it - which is relevant only as a rejection of the argument that QT somehow shows that realism or have to be given up anyway.

Is there no standard usage of the word "Non-locality"?

What is standard is to distinguish a weak notion of Einstein locality, which is only about the impossibility to send FTL signals, and the strong notion of Einstein locality, which forbids even hidden causal influences FTL.

What is also unfortunate standard is the "simplification" of naming "Einstein locality" simply "locality", which forces us to name completely local theories, which simply have higher limits for the speed of information transfer, "non-local" because they violate Einstein locality.

So, it would be meaningful to distinguish at least three notions: weak (signal) Einstein locality, strong (realistic) Einstein locality, and simply locality.

 

[Zafa Pi]

Maybe I was not sufficiently clear. I think that actual physics is most likely non-local. There is a possibility that it is local if some reasonable assumptions are not true, but I think that it is not very likely that those reasonable assumptions are not true.

Bell proof is a mathematical theorem which, like any other mathematical theorem, rests on certain unproved assumptions. It is always legitimate to question the unproved assumptions, even if the assumptions seem very reasonable. For various ways to save locality by rejecting certain reasonable but unproved assumptions see
https://arxiv.org/abs/1703.08341 Sec. 5.3.

Maudlin was quite definite, physics and the world are non-local.
You, however, seem a little wishy washy, "likely non-local"?? The odds are two to one the world is non-local?? I don't think your avatar would approve.
I wonder if Maudlin was being sentimental?

 

[Simon Phoenix]

Is there no standard usage of the word "Non-locality"?

It's probably a good idea to see where the various concepts get inserted into the actual derivation - it's much clearer. I love words and have a regrettable tendency to overuse them, but they can lead one astray

So imagine the set up where we have Alice, Bob and some source as follows

Alice <---------- source -----------> Bob

Alice and Bob each have a measurement device to measure properties of whatever it is the source produces. The outcomes are just 0 and 1 (or yes/no, or +/-, whichever convention you prefer) - it's just a binary outcome. If we let $A$ stand for the results of Alice and $B$ stand for the results of Bob we have that $A \in \left\{ 0,1 \right\}$ and $B \in \left\{ 0,1 \right\}$

Now Alice and Bob also have dial by which they can adjust the setting on their respective measurement devices. We'll suppose each of them have only 2 settings so that Alice can pick $a$ or $a'$ and Bob can pick $b$ or $b'$

So we could do experiments and collect enough data to construct a joint probability distribution $P(A,B)$. But that's not really getting what we want - we have to remember that we have different settings and so what we're really interested in are the distributions for different settings - hence we're really interested in the conditional distributions $P(A,B|a,b)$, $P(A,B|a',b)$, $P(A,B|a,b')$, and $P(A,B|a',b')$. These are all measureable quantities - there's no 'magic' here, we're just recording device settings and seeing whether our measuring machine goes 'ping' or 'pong'.

Analysing the results we see that there is some correlation and so we'd like to construct some kind of model. A correlation cries out for explanation - so we assume there are some extra variables that explain the correlation - these are the so-called 'hidden' variables (which is a bit of an unfortunate nomenclature, but it's the one that's stuck). These are given the symbol $\lambda$ and this single symbol is a shorthand for what could be a set of variables which might be discrete continuous, or functions, or even wavefunctions, it really doesn't matter in the slightest - they're just the things that explain why the results are correlated.

So if there are some variables we've not accounted for so far, we'd best put them in our model and write $P(A,B | a,b,\lambda)$ so our measured distribution is going to depend on the experimental settings and these extra variables. All is sweet smelling in the state of Denmark at the moment.

We then make the critical observation that if our variables $\lambda$ account for all of the correlations then any residual fluctuation in our results must be statistically independent so that : $$P(A,B | a,b,\lambda) = P(A | a,b,\lambda)P(B | a,b,\lambda)$$All very reasonable so far. Now we make the assumption of locality in the following sense. We assume the distribution of the results $A$ is not conditioned upon the settings at Bob, and vice versa, so that we can now write $$P(A,B | a,b,\lambda) = P(A | a,\lambda)P(B | b,\lambda)$$It's this step where the 'locality' assumption gets inserted and we can see it's quite specific.

I often make the mistake of saying 'non-local hidden variables' - and I've done so in this thread, but as Bell points out the hidden variables can be 'non-local' - which all gets very confusing. What has to remain local though is the effect of switching device settings - the hidden variables cannot be such that information about device settings is transferred from place to place in a non-local (FTL) fashion. Loosely then, there can be no mechanism by which the system (device plus measured thingy) at Alice 'knows' about the setting of Bob, and vice versa.

It's very important to note that no assumptions have been made about the nature of the source or what it produces - it's just some unspecified thing that produces some hoojamaflips which might be fields or particles, or something else - and, critically, no quantum mechanics at all has intruded here. We just have some source event that leads to measuring devices going 'ping' or 'pong'.

Where does the notion of 'realism' come in then? Well that's a bit more subtle. Essentially in the derivation it is tacitly assumed that different measurement settings can be meaningfully included in the same expression so that something like $P(A | a,\lambda)$ and $P(A | a',\lambda)$ can be meaningfully manipulated in the same expression. This is fine and valid provided we assume counterfactual definiteness (that is, 'realism'). This is tantamount to the assertion that things have objective properties independent of measurement - essentially a cornerstone of classical physics.

Everything is now set up and it's just straightforward (but ingenious) manipulations of probability distributions to arrive at the celebrated inequality. The assumptions are clear (although as Dr Chinese has beautifully pointed out above there are actually a couple of other implicit assumptions that I've not mentioned in the above - like the 'no-conspiracy' assumption, for example).

I don't know whether this clarifies things, or just muddies things even more - I've taken most of it from Bell's masterful exposition in his Bertlmann's socks paper - and if the above is unclear I urge you to read that - it really is the best explanation I've ever seen. I can't hope to match Bell's clarity and insight but I hope that I've been clear enough to show where the notions of 'locality' and 'realism' actually impact the analysis.

 

[fanieh]

I'm just going to re-iterate what Demystifier has said here.

Mathematical theorems are usually of the form of an IF . . .THEN statement. So IF we have $A$ and $B$, THEN $x$ follows.

In the context of Bell's work we have something like (and crudely),

IF (realism, locality) THEN (correlation functions bounded by inequality)

where I'm just focusing on these two properties and excluding things like superdeterminism.

QM predicts correlation functions that don't have to be bounded by this inequality, therefore QM cannot be equivalent to a theory constructed from quantities which have the properties 'realism' AND 'locality'.

It is therefore possible (in principle) to find a theory for which the correlations are not bounded by the inequality by :
(i) dispensing with 'realism' but keeping 'locality'
(ii) dispensing with 'locality' but keeping 'realism'
(iii) dispensing with both 'locality' and 'realism'

your (ii) is Bohmian Mechanics.. but what interpretations can describe (i) dispensing with 'realism' but keeping 'locality' and especially (iii) dispensing with both 'locality' and 'realism'?

It is NOT possible, in principle, to find a theory that agrees with the QM predictions for the correlation functions constructed from variables/quantities which possesses BOTH of the properties 'realism' and 'locality'.

Note that we're only talking about the violation of the bound on the correlation functions here - just because we construct some theory (eg by dispensing with 'locality') that has a violation for a particular experiment (eg the singlet state of QM) does not imply that it will also agree with other predictions of QM, or even the predictions of QM for other entangled systems (eg the GHZ state)

 

[Zafa Pi]

No. All this can be discussed without even mentioning QT at all. We have the experimental facts - BI are violated for space-like separated measurements - and the theorems which allow to derive the BI.

Right on! But I doubt @DrChinese would disagree.

QT increases the probability that the BI are indeed violated, because it predicts a violation itself.

Better would be QT predicts violation as well, and chuck the increased probability. But as you say it's not needed.

which is relevant only as a rejection of the argument that QT somehow shows that realism or have to be given up anyway.

?? Would you please clarify by correcting grammar.

What is standard is to distinguish a weak notion of Einstein locality, which is only about the impossibility to send FTL signals, and the strong notion of Einstein locality, which forbids even hidden causal influences FTL.

To me signals are information, and strong locality forbids such at FTL. Isn't what you want for weak locality is the inability to to make the entangled correlations from separated measurements? Is there a better word than signal? Spookiness, for example, is more in keeping with Einstein.

 

[Simon Phoenix]

your (ii) is Bohmian Mechanics.. but what interpretations can describe (i) dispensing with 'realism' but keeping 'locality' and especially (iii) dispensing with both 'locality' and 'realism'?

Well Bohmian mechanics is an example of a theory of the kind (ii) - not sure if there are any others. I also have no idea whether theories like (i) and (iii) have been constructed. Ultimately the message I take away from Bell's fabulous work is that 'classical' thinking isn't going to work - an idea already well-established before Bell, but Bell beautifully pinned it down and made it accessible to experimental proof. The gears and wheels and levers and fields of classical physics - all the notions of a 'clockwork' universe - these are simply not up to the job and Bell managed to tell us precisely why and described how to validate that experimentally - spectacular stuff

If we want to have a theory in which the quantities involved in that theory (like momentum, spin, etc) have some objective existence independent of measurement, then the only theory we have recourse to is one in which somehow the information about device settings gets transferred FTL from place to place (or appears to do so). That could be Bohmian mechanics, or some backward in time signals - or some cosmic conspiracy - but whatever it is we've already left Kansas a long time ago.

 

[fanieh]

Well Bohmian mechanics is an example of a theory of the kind (ii) - not sure if there are any others. I also have no idea whether theories like (i) and (iii) have been constructed. Ultimately the message I take away from Bell's fabulous work is that 'classical' thinking isn't going to work - an idea already well-established before Bell, but Bell beautifully pinned it down and made it accessible to experimental proof. The gears and wheels and levers and fields of classical physics - all the notions of a 'clockwork' universe - these are simply not up to the job and Bell managed to tell us precisely why and described how to validate that experimentally - spectacular stuff

If we want to have a theory in which the quantities involved in that theory (like momentum, spin, etc) have some objective existence independent of measurement, then the only theory we have recourse to is one in which somehow the information about device settings gets transferred FTL from place to place. That could be Bohmian mechanics, or some backward in time signals - or some cosmic conspiracy - but whatever it is we've already left Kansas a long time ago.

the (iii) or dispensing with both 'locality' and 'realism' is the better choice.. because it is opposite to Newton and more modern.. but I can't quite decide what convention of our two non-local masters, Demystier or DrChinese to follow.. in Demystifier context.. if you dispense with realism.. you already dispense locality.. so the phase "dispensing with both 'locality' and 'realism' is redundant.. "dispensing with realism" is enough. But for DrChinese, even if realism is dispense with, the words non-locality can still be used.. which of these do Sean Carrol, Weinberg or others follow? majority wins

 

[Demystifier]

I don't think your avatar would approve.

Why do you think so? I think he would, because he would not completely accept a proof based on a questionable assumption.

 

[Denis]

?? Would you please clarify by correcting grammar.

I'm not a native English speaker, but I will try to say it in other words.

The fact that there is a realistic causal interpretation of QM is relevant only because sometimes arguments against realism are proposed which rely on claimed properties of QM. For example, people who know only the Copenhagen interpretation may argue that quantum theory has already shown that classical realism has to be rejected.

To me signals are information, and strong locality forbids such at FTL. Isn't what you want for weak locality is the inability to to make the entangled correlations from separated measurements? Is there a better word than signal? Spookiness, for example, is more in keeping with Einstein.

"Signal locality" is an established phrase, and means the impossibility to send signals FTL. I think this is clear enough. It is clearly a weaker notion than the "Bell locality" used in the BI proof, so naming them "weak" vs. "strong" seems also unproblematic. All I want is to have clear notions, which do not cause confusion.

 

[RUTA]

A less technical description of locality and realism can be found in Mermin's work. I reproduced his argument concerning the Hardy experiment here https://www.physicsforums.com/insig...elayed-choice-no-counterfactual-definiteness/ . Just scroll down to the paragraph starting with "The Hardy experiment is shown and explained in Figure 2 (reference therein)." The entire explanation is only one paragraph long.

 

[DrChinese]

No. EPR does not imply predetermination without strong Einstein causality (Einstein locality not only for signals, but also for hidden but real causal influences). This is the "without in any way disturbing" part of the EPR criterion.

Of course EPR elements of reality imply predetermination. Of every possible outcome! But that makes the assumption there is no observer dependency. They thought any other view was unreasonable.