A Realism from locality?

Demystifier

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Summary
Bell's theorem is often interpreted as a claim that either locality or realism is wrong. A recent theorem claims that realism is a consequence of the assumption of locality, so that locality must be wrong in any case.
Recently, Bricmont, Goldstein and Hemmick wrote two (quite similar) papers
1. http://de.arxiv.org/abs/1808.01648
2. http://de.arxiv.org/abs/1906.06687
in which they present a Bell-like theorem that involves only perfect correlations and does not involve any inequalities. They claim that this version proves nonlocality, i.e. that the theorem cannot be interpreted merely as a disproof of realism. (By realism one means what is often called "hidden variables" in the literature, which in the papers is mathematically precisely defined as non-contextual value-maps.) The following quotes from the papers illustrate their main points:

Paper 1, pages 21-22:
"The main point of our paper is to show that no choice between the rejection of “realism” or of locality has to be made, since the existence of a non-contextual value-map is a consequence of locality and the perfect correlations.
It is also true that such a non-contextual value-map cannot exist (section 4). But, since the perfect correlations are a well-established empirical fact, the only logical conclusion is that locality is false.
So, “realism” (in the sense of the existence of a non-contextual value-map) is not an assumption in our reasoning but is a consequence of the assumption of locality (and the perfect correlations)."


Paper 2, pages 30-31:
"Here and in [11] we give a simpler argument, but using the maximally entangled states introduced by Schrödinger: for those states, one can, for each observable associated to one system, construct another observable associated to the second system,
possibly far away from the first one, such that the results of the measurement of both observables are perfectly correlated. Then, assuming locality, those results must preexist their measurement. But assuming that, in general, observables have values before their measurement leads to a contradiction. Hence, the assumption of locality is false."


If they are right, then local interpretations of QM are necessarily wrong. Nevertheless, I suspect that those who are convinced that QM is a local theory are unlikely to change their mind by the arguments of those two papers. There are several attitudes that can make those people immune to this proof of nonlocality. Some of the popular attitudes of this kind are
a) Anti-philosophic attitude: The theorem involves a mathematical object called non-contextual value-map which, by itself, does not help to make measurable predictions. Hence the theorem is philosophic and irrelevant for science.
b) Operational attitude: QM is local in the operational sense and the proved nonlocality is irrelevant for physics because it cannot be used for practical instantaneous signaling.
c) Informational attitude: Interpretations such as QBism and relational interpretation would deny that perfect correlation and locality imply the existence of the value maps. First, they would argue that values are created by measurements or interactions between the subsystems, which excludes the existence of value maps. Second, they would argue that correlations do not exist until someone or something observes or detects the correlation, which is a local physical process. For instance, they would argue that it does not make sense to talk about correlations between Alice and Bob until, for instance, Alice sends a signal to Bob so that Bob can know that he is correlated with Alice.

How about you? Does the theorem convince you that one must conclude that QM is necessarily nonlocal? Or if it doesn't, which attitude do you use against that conclusion?
 

vanhees71

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I think relativistic microcausal QFT is both "local", i.e., interactions are local in the sense that there is no causal faster-than-light signal-propagation probable and "non-local" (I'd prefer Einstein's term "inseparable") in the sense of long-ranged correlations described by entangled states. I do not know, in which of your three "isms" this view fits. I guess in neither of them. The minimal interpretation is simply not interesting enough for people inclined to "philosophy" and other esoterics.

Of course, I've to read the two preprints before I can decide, what I think about them specifically. Both are unpublished...
 

atyy

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(By realism one means what is often called "hidden variables" in the literature, which in the papers is mathematically precisely defined as non-contextual value-maps.)
It is also true that such a non-contextual value-map cannot exist (section 4). [Quoting the authors]
So it is not a choice between locality and realism. According to the authors, there is neither locality nor realism.
 
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Demystifier

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So it is not a choice between locality and realism. According to the authors, there is neither locality nor realism.
More precisely, according to the authors there is neither locality nor non-contextual realism. The authors are in fact Bohmians, so they fully accept contextual realism.
 

Demystifier

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I think relativistic microcausal QFT is both "local", i.e., interactions are local in the sense that there is no causal faster-than-light signal-propagation probable and "non-local" (I'd prefer Einstein's term "inseparable") in the sense of long-ranged correlations described by entangled states. I do not know, in which of your three "isms" this view fits. I guess in neither of them. The minimal interpretation is simply not interesting enough for people inclined to "philosophy" and other esoterics.
Your view fits with a) Anti-philosophical attitude.

For the philosophically inclined, it's not that the minimal interpretation is not interesting enough, it's rather that it is not complete enough.
 

martinbn

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Is any of this new? I have the impression this all that have been said here at PF many times in very old threads!

Anyway if this prove non-locality, my question is how do you violate relativity even if it is just in principle? The usual answer that I have seen is "Well, by non-locality we don't mean that, we mean something else."

Which leads me to the following understanding of the logic of the proof. It goes like this:
1) locality implies realism
2) locality and realism are incompatible
Therefore
3) we have non-locality
And of course the unsaid but always present in the mind of the Bohmian
4) BM is non-local, therefore it is the true description of nature

To me it seems that the words change meaning from line to line (at least some nuances). Locality in 1) is not exactly the same as locality in 2), and neither is the opposite of non-locality in 3), which is different from the one in 4). Not to mention that realism in 1) and 2) may be different and may depend on who wrote 1), 2) and 3).
 

vanhees71

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Your view fits with a) Anti-philosophical attitude.

For the philosophically inclined, it's not that the minimal interpretation is not interesting enough, it's rather that it is not complete enough.
Ok, yes, but "complete" is anyway a weak argument. If physics teaches you one thing: Nothing is "complete". There are still open questions like the very big and challenging one about "quantum gravity", but there's nothing "incomplete" visible in discussing the hitherto done (and today doable?) experiments with entangled states, realized in various systems (photons, atoms, molecules, cold Bose and/or Fermi gases and what not). There QT in the minimal interpretation, including relativistic microcausal/local QFT, nothing is "incomplete" in the sense of that it fails to describe any known phenomenon, and it's precisely the right balance between locality of interactions and the possiblity for long-range correlations and inseparability described by entanglement of long-distant parts of a quantum system, which makes it consistent with both the causality structure of Minkowski spacetime and the observed violation of Bell's inequality which shows that local deterministic hidden-variable theories are ruled out. What can be "non-local" however in relativistic microcausal QFT are by construction the correlations described by entanglement of distant parts of a quantum system, but what's "local" are the interactions as implement by the microcausality condition.

What's called with the intellectually sounding word "contextuality" very often simply means the selection of a subensemble due to measurements on entangled parts of a system and then measuring corresponding observables on the other subsystem (which then may be entangled due to the "right" choice of the selective measurements). That's what we discuss in the other thread about "entanglement swaping".
 

atyy

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More precisely, according to the authors there is neither locality nor non-contextual realism. The authors are in fact Bohmians, so they fully accept contextual realism.
So if we take the quantum state to be real, then the quantum state would be a nonlocal, non-contextual hidden variable?
 
Hi,

Does “elements of reality” here mean: “if, without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity” ?

And locality is link to space-time In the spirit of : The "elements of reality" in question are attached to the region of space where the experiment takes place13, and they cannot vary suddenly under the influence of events taking place in a very distant region of space ? Which is different from the notion of separability even if these two notions are often (but not always) related.

I read that the basic belief of EPR is that regions of space can contain "elements of reality" attached to them (attaching distinct elements of reality to separate regions of space is sometimes called “separability”) and that they evolve locally. In the literature, for brevity this is often called “local realism”.

The difficulty is that the notion of the locality itself contains several different concepts; various authors sometimes use the word with different definitions.

/Patrick
 
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Anyway if this prove non-locality, my question is how do you violate relativity even if it is just in principle?
Maybe the answer is that the non-local behavior can not directly be observed , but can only be inferred through statistics and therefore is completely compatible with special relativity. This is certainly the case with entangled photons.
 

Demystifier

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So if we take the quantum state to be real, then the quantum state would be a nonlocal, non-contextual hidden variable?
No, it would be nonlocal and contextual.
 

vanhees71

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So if we take the quantum state to be real, then the quantum state would be a nonlocal, non-contextual hidden variable?
I've my problems with saying a "quantum state would be local or non-local". What should that mean. The more I look at our (and of course the quantum-information/quantum-optics communitys') debate about the foundations of QT, I think it's about the meaning of the quantum state in general and entanglement in particular. In connection with QFT there's a tension between causality and long-ranged correlations described by entanglement of far-distant parts of a quantum system.

Given the possibility of such long-ranged strong correlations described by entanglement, I'd not say that the quantum state is in general local. It depends on the preparation of the system, whether one describes a very localized situation or one which is "spread over a larger region". Take the momentum and polarization entangled photon pairs from parametric down conversion: After a long enough time, when the corresponding "wave packets" of the photons have evolved the two photons are still entangled, but the probability to detect them at some far-distant places, determined by the momenta of these photons, becomes large, and in this sense the state as such describes a pretty "non-local situation", where two "far distant" photons are momentum and polarization entangled (where "far distant" means that the places where the detectors are located are far away from each other). That's also what Einstein dubbed "inseparability", and this was his biggest quibble with QT.

On the other hand, the successful relativistic QTs are all relativistic QFTs constructed to describe local interactions, i.e., obeying the microcausality constraint. This makes the inseparability of parts of entangled systems consistent with the causality structure of Minkowski space. So what's for sure is that you have to avoid to take what's called "collapse of the state" as a physical process since this would imply an instaneous action at a distance, where due to entanglement you could causally manipulate a far distant part of the quantum system with a manipulation of the other part at your place. This contradicts the microcausality constraint built into relativistic QFT from scratch.

For me the only resolution is to accept the minimal interpretation, according to which the quantum states describe probabilities and nothing else, and thus entanglement describes correlations but not a causal connection of far-distant parts.

This brings us to the even more vague and difficult question of "contextuality" or "non-contextuality". I think within standard quantum theory there's contextuality. Take the example of entanglement swapping leading through (local!) manipulations of parts of a quantum system to the entanglement of other far-distant parts, which latter have never been in causal contact. This is no contradiction to the fundamental properties of relativistic QFT (local interactions with the possibility of far-distant correlations through quantum entanglement). It's just using the entanglement to select partial ensembles based on local measurements at a part of the system, and which properties the other parts of the subensemble have, i.e., whether they lead to entanglement or not or whether you observe "wave-like" or "particle/which-way-information like" properties depend on what you measure. The choice of the particular sub-ensemble (which can be made much later given an appropriate measurement protocol, i.e., long after the entire setup of the experiment is gone) depends on what's measured. In this sense there's contextuality, i.e., the preparation of a state (i.e., an ensemble of equaly prepared systems) depends on the choosen selection criterion and thus the setup of the measurement on parts of the entangled system in the context of entanglement swaping or quantum erasure.
 

Demystifier

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For me the only resolution is to accept the minimal interpretation, according to which the quantum states describe probabilities and nothing else, and thus entanglement describes correlations but not a causal connection of far-distant parts.
If quantum state describes only the probabilities of measurement outcomes, then what describes the rest? If your answer is - nothing, then you can avoid nonlocality. But it seems more natural to assume that something does describe the rest, even if we do not know what exactly this is. The Bell theorem says that this something, whatever it is, must be nonlocal. There is no tension with locality of QFT because if one assumes that there is something more that is not described by QFT, then it does not need to have the locality property inherent to QFT.
 

vanhees71

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The question rather is: "Which rest?" This is equivalent to the question whether QT is a complete description, which is debated from day 1 on. Heisenberg was fighting like crazy for QT being complete, which is understandable, but in fact it's an empty question given that physics is an empirical science. As far as we know QT is complete only in a limited validity realm, namely as long as quantum effects of the gravitational interaction can be neglected. Quantum particles in an "external gravitational field" seem to be well described (at least for weak fields like the gravitational field of the Earth, where it has been tested on neutrons). Who knows, which new theory may be necessary to fill this gap. Otherwise, there's no hint at incompleteness today, i.e., all tests of QT in its validity range prove it correct.

Then one must be very concise in the use of the word "non-local". What's "non-local" are the correlations between far-distant parts of an entangled system. What's "local" are the interactions in relativistic QFT, which is constructed to fulfill the microcausality constraint and thus the linked-cluster principle for the S matrix. So there are long-ranged correlations due to entanglement/inseparability but no "spooky actions at a distance", i.e., causal effects between space-like separated events.

The question, whether there is more that is not described by QFT is in some sense the same as the corresponding question for QT as a whole. Of course, all our "realistic" QFTs (i.e., the Standard Model) are mathematically not strictly defined and in some sense are thus more or less intrinsically incomplete. Of course, if you take renormalized perturbative QFTs (or also lattice QCD as another effective description of a QFT) as effective models there's nothing found that clearly contradicts the Standard Model and thus QFT in this restricted sense is not incomplete within this (restricted!) sense of validity.
 

martinbn

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@Demystifier What is the answer to my question? In the context of these papers and this thread, how is relativity violated?
 

Demystifier

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Heisenberg was fighting like crazy for QT being complete, which is understandable, but in fact it's an empty question given that physics is an empirical science.
There is no doubt that physics is empirical, but what physicists mutually disagree on is whether physics is only empirical? In other words, is physics only about the results of observations and nothing else? For instance, if physics is only about the results of observations, then what is the point of doing research in cosmology which is supposed to tell us something about how the world looked like before there were observations?

If, on the other hand, the purpose of physics is also to tell us something about what, as you once put it, happens "behind the curtain", then physics cannot be only empirical. It must also have some meta-empirical elements. It is in this meta-empirical sense that the minimal interpretation of QT is incomplete. It is this meta-empirical aspect of QT that most quantum interpretations are about.
 

Demystifier

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@Demystifier What is the answer to my question? In the context of these papers and this thread, how is relativity violated?
There is no unique answer to your question. One possibility that I advocate in the paper linked in my signature below is that relativity is only an emergent long-distance phenomenon.
 

vanhees71

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There is no doubt that physics is empirical, but what physicists mutually disagree on is whether physics is only empirical? In other words, is physics only about the results of observations and nothing else? For instance, if physics is only about the results of observations, then what is the point of doing research in cosmology which is supposed to tell us something about how the world looked like before there were observations?

If, on the other hand, the purpose of physics is also to tell us something about what, as you once put it, happens "behind the curtain", then physics cannot be only empirical. It must also have some meta-empirical elements. It is in this meta-empirical sense that the minimal interpretation of QT is incomplete. It is this meta-empirical aspect of QT that most quantum interpretations are about.
It's of course not only about results of observations. That'll be what Rutherford once called "stamp collecting". There's of course also theory, i.e., the (mathematical) description of general laws, from which the observations can be derived or in the most interesting cases predicted.

That said, however, I think the strength of the natural sciences is that these theories describe general laws deduced from empirical reproducible objective evidence and just describing what's observable with these general laws. It's a mutual process of deducing the laws from observations, describing these phenomena based on these laws and, from the point of view of aiming at the "progress of science" most importantly, predicting new phenomena and initiating ideas for new experiments connected with them. Last but not least it enables the construction of all kinds of technical equipment needed to perform these measurements. As I said, it's not a straightforward progress from experiment and observation to theory, but a complicated mutual process, including also a lot of intuition by both experimenters and theorists. In this sense there's some meta-empirical element in this process, but finally it's strictly about what's observable and how to understand observations from the underlying laws and maybe (amazingly rarely in fact) find some completely new fundamental laws from a discrepancy between observations and expectations from presently thought to be valis fundamental laws (on the big picture this happened three times in the history of physics: (1) Newton's finding of his 3-4 "postulates", making the millenium-old knowledge a la Aristoteles obsolete; (2) Einstein's discovery of the necessity of a different space-time description, starting from the inconsistency with the (empirically found!) Maxwell description of electromagnetism; (3) Heisenberg's et al discovery of quantum theory, based on the incompatibility of the classical mechanical and field-theoretical models with the observed atomistic structure of matter and radiation). This close connection between observations/experiments/measurements and mathematical modelling and theorizing is what distinguishes the natural science from both the structural sciences (mathematics/informatics) and the humanities, including philosophy.

In my opinion, what natural sciences don't do is to answer "what happens behind the curtain" and that's what makes them so successful. For the purpose of what the natural sciences are after, namely to find the fundamental objectively valid descriptive laws behind the objectively observable phenomena, there's nothing "behind the curtain" except maybe unobserved phenomena and the corresponding theories describing them. E.g., what's missing today are observed phenomena concerning a possible quantum description of gravity or the observation of possibly existing particles making up dark matter in the universe, which however still may be just necessary due to the necessity to refine the description of gravity already on the classical scale of GR. Nobody knows, and I don't believe that we'll ever be able to find the solution of these unknowns without clear empirical evidence pointing towards the right direction. The huge effort going into the development of string theories and related theories is an example: It may be pretty interesting math, but without any relation to clearly observable facts, it's not a physical theory.

Now to QT. It's precisely this what makes for me these discussions about interpretations more and more obscure and even obsolete. All there is for a physical theory is to know, how to make predictions (and postdictions of course too) concerning objectively observable phenomena, i.e., to give a clear empirical meaning to the formalism in terms of measurement readings in the lab. E.g., in QT the "spectrum of self-adjoint operators" give the possible values of observables. The very word "spectrum" is of course from physics. One of the great breakthroughs of (modern) QT was to give a generally valid scheme to understand the observed spectra of the light emitted from the different kinds of atoms (molecules etc.). It also turned out that it enables us to understand the formation of macroscopic matter and understand a great deal about its properties from the first principles of QT (solid state/condensed-matter physics). That makes it a pretty comprehensive theoretical framework to describe and understand a broad range phenomena from pretty few fundamental principles (mostly symmetry principles). To ask, "what's behind the curtain", is not a question to be answered by the natural sciences. It's simply not in the ballpark to be answered by its defining methodology, and that's why you find as many answers to these metaphysical questions as there are scientists willing to talk about it. It's rather in the realm of religious believes than in the realm to science. The answer of "what's behind the curtain" is thus a subjective personal one rather than even a problem of the natural sciences.
 

ftr

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There is no tension with locality of QFT
This so called "locality" of QFT is not clear. See for instance John Baez " Therefore, the interaction can happen no matter how far the interacting particles are from each other. "
http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html
also our pf friend meopemuk post
 

Demystifier

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It's of course not only about results of observations. That'll be what Rutherford once called "stamp collecting". There's of course also theory, i.e., the (mathematical) description of general laws, from which the observations can be derived or in the most interesting cases predicted.

All there is for a physical theory is to know, how to make predictions (and postdictions of course too) concerning objectively observable phenomena, i.e., to give a clear empirical meaning to the formalism in terms of measurement readings in the lab.
What is still not clear to me is there any other purpose of general laws except of making predictions (and postdictions)?

Or let me present this question in an extreme form. Imagine that you have a black box machine that answers any empirical question you ask, with a perfect precision. What will be the cross section if I collide this and that particle? If you put this question in, you get the right number out. Will there be rain in Frankfurt 7 days from now? If you pose that question, you get the right answer. Such a (hypothetic) machine is empirically perfectly complete. But suppose that you don't know any theory about how this machine works. Wouldn't you be curious to know how does the machine work? Wouldn't you be interested to see a consistent theory that offers a possible explanation?
 
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martinbn

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There is no unique answer to your question. One possibility that I advocate in the paper linked in my signature below is that relativity is only an emergent long-distance phenomenon.
I understand that, but in these papers it is claim to be proven. So, I was hoping for something more specific.
 

ftr

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Wouldn't you be interested to see a consistent theory that offers a possible explanation?
Of course the squeaky machine of vanhees71 cannot predict the most important parameters (20 or so of them), the most important job of the machine.
 

vanhees71

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What is still not clear to me is there any other purpose of general laws except of making predictions (and postdictions)?

Or let me present this question in an extreme form. Imagine that you have a black box machine that answers any empirical question you ask, with a perfect precision. What will be the cross section if I collide this and that particle? If you put this question in, you get the right number out. Will there be rain in Frankfurt 7 days from now? If you pose that question, you get the right answer. Such a (hypothetic) machine is empirically perfectly complete. But suppose that you don't know any theory about how this machine works. Wouldn't you be curious to know how does the machine work? Wouldn't you be interested to see a consistent theory that offers a possible explanation?
Well, that's of course not what we'd consider science. Then I can as well just stick to the observations themselves. A black box providing answers is not what we aim at in science. We want to reduce it to some (as few as possible) fundamental laws, which then however are indeed a "black box".

In QT one example of fundamental postulates is the Born rule (in its most general form with statistical operators), which cannot be deduced from other postulates, and this seems to be the most debated postulate of all since it introduces an "irreducible probabilistic element" to the laws of nature, i.e., a probability that is not due to incomplete knowledge of us but is inherent in the laws of nature themselves. I think this is still an element which many people cannot easily accept. For me it's one of the most profound discoveries of the 20th century, and I think there's no way to accept it, if you don't want to ignore objective facts about how nature behaves.
 

vanhees71

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This so called "locality" of QFT is not clear. See for instance John Baez " Therefore, the interaction can happen no matter how far the interacting particles are from each other. "
http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html
also our pf friend meopemuk post
Well, you should also read the rest of this Sect. 4 in Baez's FAQ :-).
 

Demystifier

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I understand that, but in these papers it is claim to be proven. So, I was hoping for something more specific.
What is claimed to be proven? The papers claim that nonlocality is proven, but they don't claim that violation of relativity is proven.
 

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