Assumptions of the Bell theorem

[vanhees71]

Is QFT a statistical interpretation?

As any QT also QFT is a probabilistic description of Nature.

 

[vanhees71]

If one forgets all philosophical quibbles, the idea behind hidden variables is - nothing. Without philosophy, there is no idea at all behind hidden variables. Since you are good in math and natural sciences, you would like if everything that matters could be formulated in terms of math and natural sciences. But unfortunately, many things cannot be formulated so. Since you don't like this fact of life, you try to convince yourself that those things are irrelevant. But they are not. Even you care about some of those things, despite the fact that you would prefer if you didn't care and/or try to convince yourself that you don't care.

But Bell indeed DID finally formulate the philosophical quibbles in a clear mathematical way (as described in less than half a page in Weinberg's textbook). That's the great merit of his work: To make sense of some philosophical vaguely formulated quibbles by EPR (the vagueness mostly due to P, as Einstein lamented) such that it could be subject to clear quantitative observational tests.

 

[Demystifier]

But Bell indeed DID finally formulate the philosophical quibbles in a clear mathematical way

No, Bell formulated a part of his philosophical quibbles in a clear mathematical way. But the fact that we still argue about what his proof actually proves (for you it's absence of determinism, for me and Bell and Ballentine it's absence of locality, for some it's absence of observer-independent reality, or absence of statistical independence of apparatus settings, or ...) clearly demonstrates that an important part of his philosophical quibbles is not formulated in a clear mathematical way.

 

[vanhees71]

Well yes. The problem is that the disagreement is about philosophy and not about physics. The indication for that is that obviously we still have not a clear agreement on the meaning of the words, particularly locality. For me locality is simply microcausality. For you obviously it has a different meaning. The same holds for "reality", which is even harder to define. For me reality is objective, reproducible observability, i.e., what can be tested by experiments.

 

[Demystifier]

The problem is that the disagreement is about philosophy and not about physics.

Do you know why philosophy never makes progress? Because when it does, it's no longer called philosophy.

Philosophers deal with vague questions not because they are not capable of dealing with clear questions, but because the vague questions are a challenge. The challenge is to translate a vague question into a less vague one. But it's often very hard to make such a translation. It's hard to be a good philosopher, possibly even harder than to be a good scientist.

 

[Lynch101]

Well yes. The problem is that the disagreement is about philosophy and not about physics. The indication for that is that obviously we still have not a clear agreement on the meaning of the words, particularly locality. For me locality is simply microcausality. For you obviously it has a different meaning. The same holds for "reality", which is even harder to define. For me reality is objective, reproducible observability, i.e., what can be tested by experiments.

A word that seems to cause less consternation is the word 'universe' or 'nature'. We can define it as 'that which physics seeks to probe', 'that which physics seeks to describe', 'the subject of investigation of physics', or something along those lines. Even if we strictly define 'physics' as 'reproducible observability' it might be the case that there are limits to how far we can probe nature.

The universe itself is not, or at least does not appear to be, reproducible. To what extent the entirety of the universe is observable is a matter of debate.

 

[gentzen]

we still have not a clear agreement on the meaning of the words, particularly locality. For me locality is simply microcausality. For you obviously it has a different meaning.

Did it ever occur to you that locality might be a normal word present in nearly all human languages, and that this is an indication that its meaning is actually pretty clear? And that microcausality might simply one way in which a theory can be local?

I guess microcausality actually implies that there is no faster than light signaling, but the absence of faster than light signaling all by itself is also a way in which a theory can be local. And since more people are able to grasp that meaning, it might even be used more often than microcausality.

And to go further, there appears to be randomness in Bell type experiments, and that randomness seems to include correlations between spatially separated events. And this is one way in which the predictions of quantum mechanics (that have been confirmed in many experiments) seem to not be local. And therefore many people say that quantum mechanics is nonlocal. Can you accept that this meaning does not contradict microcausality, and that therefore both you are right when you point out that quantum theory satisfies locality, but the many other people who say that quantum mechanics is nonlocal are not wrong either?

But more importantly, did it ever occur to you that this is not the fault of philosophy? Philosophy did not invent the concept of locality, because locality is simply an intuivite concept that has been present in human thinking all along. And it is a totally unproblematic concept, if you ask me!

 

[Lynch101]

the many other people who say that quantum mechanics is nonlocal are not wrong either?

I think there is an important distinction to be made here. From my reading of discussions on here and elsewhere, it seems that those you refer to are not necessarily saying that QM is nonlocal rather that nature is nonlocal (or has some form of nonlocal mechanism).

Again, it seems to be bound up in the issue of 'completeness', since the contention - to my mind - appears to be that statistical interpretations are incomplete descriptions of the system and a more complete description would require either:
- nonlocal causal influence
- superdeterminsm
- anti-realism (in the sense of the system not existing until it is measured)
- [possibly others?]

 

[Lord Jestocost]

And therefore many people say that quantum mechanics is nonlocal.

It's clearly an error in thinking. Murray Gell-Mann puts it in “The Quark and the Jaguar” in the following way:

“The label ‘nonlocal’ applied by some physicists to quantum-mechanical phenomena like the EPRB effect is thus an abuse of language. What they mean is that if interpreted classically in terms of hidden variables, the result would indicate nonlocality, but of course such a classical interpretation is wrong.” [bold by LJ]

One should thus avoid the term “quantum non-locality”. “Quantum non-separability” is the correct term in this context. Quantum non-separabilty is indeed rooted in the way the quantum formalism represents systems and sub-systems. Franck Laloë in “Do We Really Understand Quantum Mechanics?”:

“The idea is that different quantum systems, when they have interacted in the past, no longer have in general their own physical properties; they are both part of a larger system, which is the only one possessing physical properties. One should then not try to separate (conceptually) the whole system into two smaller physical systems and attribute them properties; the whole system is non-separable.”

 

[vanhees71]

Did it ever occur to you that locality might be a normal word present in nearly all human languages, and that this is an indication that its meaning is actually pretty clear? And that microcausality might simply one way in which a theory can be local?

In science we cannot use everyday language but we have to clearly define what we mean. Microcausality for sure is a meaning of locality nobody has in mind when using the word in everyday language.

I guess microcausality actually implies that there is no faster than light signaling, but the absence of faster than light signaling all by itself is also a way in which a theory can be local. And since more people are able to grasp that meaning, it might even be used more often than microcausality.

As I said, you have to define what's meant by locality, because it has not a well-defined meaning. Microcausality is a clear property of relativistic QFTs and thus has a well-defined meaning, and it seems to me the meaning most physicists and textbook writers interpret the meaning in Bell's HV model, though one cannot always be sure, because all too often the meaning is not explicitly defined by the authors.

And to go further, there appears to be randomness in Bell type experiments, and that randomness seems to include correlations between spatially separated events. And this is one way in which the predictions of quantum mechanics (that have been confirmed in many experiments) seem to not be local. And therefore many people say that quantum mechanics is nonlocal. Can you accept that this meaning does not contradict microcausality, and that therefore both you are right when you point out that quantum theory satisfies locality, but the many other people who say that quantum mechanics is nonlocal are not wrong either?

That's cause of a lot of confusion (not only in quantum theory). A statistical correlation does not necessarily imply a causal connection, and that is the case for the correlations of observables on far-distant parts of an entangled quantum system. Einstein introduced the much more precise word "inseparability" for this. Of course, this does not locality (in the sense of microcausality), because it's consistently described by local relativistic QFT. That's why I reserve the word "locality" to mean microcausality and talk about "long-ranged correlations" or "inseparability" rather than (non)locality. Definitions are made to make language as simple and concise as possible and thus one should use different words for different things.

But more importantly, did it ever occur to you that this is not the fault of philosophy? Philosophy did not invent the concept of locality, because locality is simply an intuivite concept that has been present in human thinking all along. And it is a totally unproblematic concept, if you ask me!

Obviously it's totally problematic, because I have to repeatedly make clear what I understand using this word as well as you have to make clear what you understand. It would be better not to use the word anymore within physics, but this is of course impossible, because it's all too well established in the literature, including it's fuzzy meaning.

Again, as particularly quantum theory has taught us, intuitive concepts in human thinking is not a sufficient way to talk about the natural sciences.

 

[gentzen]

That's why I reserve the word "locality" to mean microcausality and talk about "long-ranged correlations" or "inseparability" rather than (non)locality.

If you have to tell me personally that you redefined "locality" to mean "microcausality", then this does not seem to be helpful from my perspective. If most introductory textbooks on quantum mechanics would make such a redefinition for some words with good reason, then maybe it could be helpful.

But I have not yet seen any introductory textbook on quantum mechanics that even defined microcausality. Some do talk about absence of faster than light signaling, and I do find it helpful when they explain to me that this is one sense in which QM can be made to respect special relativity and locality.

Fine with me if you want to use the word "inseparability". But please do take care to still explain the importance of absence of faster than light signaling. This an important concept, and no redefinition of the word locality or nonlocality or use of a different word will substitute a proper explanation of that concept. And an advanced technical concept like microcausality is no proper substitute either.

Obviously it's totally problematic, because I have to repeatedly make clear what I understand using this word as well as you have to make clear what you understand.

The negation of the word locality might be problematic, because the negation of a positive property can depend on the context. But trying to forbid the use of a perfectly clear and understandable word is unreasonable, if the only reason for that move is that its negation started to get used in somewhat confusing ways.

 

[vanhees71]

Introductory QM books are about non-relativistic QT, and thus of course you don't find microcausality discussed in them. Within non-relativsitic QT there's of course also no problem with nonlocality to begin with. Of course non-relativistic QT has a much more limited realm of validity than relativistic QFT.

Microcausality is at the heart of the conception of local relativistic QFT and thus contained in any introductory or advanced textbook about it, though not always with the careful emphasis this important concept deserves. It's most clearly described in Weinberg, The Quantum Theory of Fields vol. 1.

 

[Lynch101]

One should thus avoid the term “quantum non-locality”. “Quantum non-separability” is the correct term in this context. Quantum non-separabilty is indeed rooted in the way the quantum formalism represents systems and sub-systems. Franck Laloë in “Do We Really Understand Quantum Mechanics?”

When talking about “Quantum non-separability” is there the implication that the system is spatially extended?

 

[Lord Jestocost]

When talking about “Quantum non-separability” is there the implication that the system is spatially extended?

Franck Laloë in “Do We Really Understand Quantum Mechanics?”:

“In general, separability is a notion that is conceptually distinct from locality. It is not necessarily related to space: two physical systems could occupy the same region of space and remain distinct with their own physical properties (separable is not the same thing as separate).
...
Quantum non-separability is rooted in the way the quantum formalism describes systems and sub-systems, and clearly related to the notion of entanglement (§6.1): a perfect description of the whole does not contain a perfect description of the parts. We mentioned earlier that Schrödinger considered entanglement as one of the most fundamental properties of quantum mechanics. Entanglement drastically restricts the number of physical properties that can be attributed to the sub-systems; this number may even vanish in some cases. In other words, the ‘best possible description’ (with a state vector) is not available to the sub-systems; they have an additional level of indeterminacy, which never occurs in classical mechanics.” [bold and bold/red by LJ]

 

[Lynch101]

Franck Laloë in “Do We Really Understand Quantum Mechanics?”:

“In general, separability is a notion that is conceptually distinct from locality. It is not necessarily related to space: two physical systems could occupy the same region of space and remain distinct with their own physical properties (separable is not the same thing as separate).

Thanks LJ.

The emboldened part seems to be a different scenario to where we have the single [entangled] system measured in spatially separated locations. Can we infer, from the spatially separated detection events, that the quantum system is also spatially extended? Or do such concepts not apply to the quantum system?

I'm asking because it would seem to have similar implications for FTL-nonlocality if we can.

 

[Lord Jestocost]

Can we infer, from the spatially separated detection events, that the quantum system is also spatially extended? Or do such concepts not apply to the quantum system.

What means a "spatially extended quantum systems"?

 

[Lynch101]

What means a "spatially extended quantum systems"?

I'm asking if we can infer that the quantum system is spatially extended by virtue of the fact that measurements of it occur in spatially separated locations?

So, the measurement events are spatially separated, does this imply that the quantum system is extended in space?

 

[vanhees71]

Sure, why not?

 

[gentzen]

Murray Gell-Mann puts it in “The Quark and the Jaguar” in the following way:
...
Franck Laloë in “Do We Really Understand Quantum Mechanics?”:
...

Both are certainly nice references, and the quoted parts are relevant to the discussed topic and the points were confusion can arise. I wasn't even aware of Franck Laloë's book, and I am a huge fan of Quantum Mechanics: Volume III: Fermions, Bosons, Photons by Claude Cohen-Tannoudji, Bernard Diu, and Frank Laloë. I was aware of Gell-Mann's book, but I never made any serious effort to read it. I did read (what I believe to be) the last paper coauthored by Gell-Mann, and it has had a huge impact on my thinking about probability. I am quite familiar with the consistent histories framework (from articles and books by Roland Omnès and Robert Griffiths), but less familiar with the related decoherent histories interpretation by Gell-Mann and Hartle.

It's clearly an error in thinking.

I assume that you did read carefully what Gell-Mann wrote before quoting him. But I have the impression that you did not read carefully what I have written. Or maybe you cared most about giving a relevant reference, and less about whether it supported your statement.

The quoted passage from Gell-Mann (and also the wider context in which it appeared in his book) doesn't contradict what I wrote. I highlighted the importance of "the absence of faster than light signaling", and so does Gell-Mann. The "error in thinking" would be to deduce that type of nonlocality from "correlations between spatially separated events". So his complaint about "an abuse of language" for that sort of misconception is fully compatible with my claim that the word "local" is not the problem.

 

[Lynch101]

Sure, why not?

Instead of thinking in terms of two separate systems we can think of a single spatially extended system. If the measurement outcomes on either 'end' of the system are not pre-determined but measurement on one 'end' instantly determines the measurement outcome at the other 'end', this would equate to an FTL influence. Wouldn't it?

This is assuming we can consider the system spatially extended.

 

[Lord Jestocost]

Both are certainly nice references, and the quoted parts are relevant to the discussed topic and the points were confusion can arise. I wasn't even aware of Franck Laloë's book, and I am a huge fan of Quantum Mechanics: Volume III: Fermions, Bosons, Photons by Claude Cohen-Tannoudji, Bernard Diu, and Frank Laloë. I was aware of Gell-Mann's book, but I never made any serious effort to read it. I did read (what I believe to be) the last paper coauthored by Gell-Mann, and it has had a huge impact on my thinking about probability. I am quite familiar with the consistent histories framework (from articles and books by Roland Omnès and Robert Griffiths), but less familiar with the related decoherent histories interpretation by Gell-Mann and Hartle.I assume that you did read carefully what Gell-Mann wrote before quoting him. But I have the impression that you did not read carefully what I have written. Or maybe you cared most about giving a relevant reference, and less about whether it supported your statement.

The quoted passage from Gell-Mann (and also the wider context in which it appeared in his book) doesn't contradict what I wrote. I highlighted the importance of "the absence of faster than light signaling", and so does Gell-Mann. The "error in thinking" would be to deduce that type of nonlocality from "correlations between spatially separated events". So his complaint about "an abuse of language" for that sort of misconception is fully compatible with my claim that the word "local" is not the problem.

Maybe, there is some misunderstanding.
To my mind, words like "local" or "non-local" are problematic in conjuction with quantum theory. They can over and over again trigger people to think about quantum phenomena with classical ideas (this I meant with "error in thinking").

 

[Demystifier]

To my mind, words like "local" or "non-local" are problematic in conjuction with quantum theory. They can over and over again tirigger people to think about quantum phenomena with classical ideas.

Interesting! Can you substitute them with better words?

And can you really talk about quantum phenomena without classical ideas? For example, what about macroscopic measurement outcomes?

 

[vanhees71]

Instead of thinking in terms of two separate systems we can think of a single spatially extended system. If the measurement outcomes on either 'end' of the system are not pre-determined but measurement on one 'end' instantly determines the measurement outcome at the other 'end', this would equate to an FTL influence. Wouldn't it?

This is assuming we can consider the system spatially extended.

Indeed, two entangled photons are a single system by definition. They are not separable. Nevertheless there are two photons which can be detected at far distant places.

 

[Lord Jestocost]

And can you really talk about quantum phenomena without classical ideas? For example, what about macroscopic measurement outcomes?

To be honest: I personally try avoid to think about quantum phenomena with classical ideas and concepts. I have the feeling that it merely leads down a rabbit hole.

Regarding observations (measurement outcomes): We can never be certain whether appearances in our mind can be thought "classically" as experiences of an outer world and are not mere imagining. The possibility of thinking of appearances as experiences of “something outer” allows us to talk about measurement outcomes in a conventional classical way.

 

[Lynch101]

Indeed, two entangled photons are a single system by definition. They are not separable. Nevertheless there are two photons which can be detected at far distant places.

Can we therefore conclude that this single system is spatially extended?

 

[Lynch101]

To be honest: I personally try avoid to think about quantum phenomena with classical ideas and concepts. I have the feeling that it merely leads down a rabbit hole.

If all our measurements of quantum systems are at the classical level, are are we not then forced to at least consider classical ideas? Surely we have to explain how quantum systems give rise to classical observables?

Also, wasn't it consideration of classical ideas that led to the EPR paper, which in turn led to Bell's theorem, so there can be some benefit to doing it, no?

Regarding observations (measurement outcomes): We can never be certain whether appearances in our mind can be thought "classically" as experiences of an outer world and are not mere imagining. The possibility of thinking of appearances as experiences of “something outer” allows us to talk about measurement outcomes in a conventional classical way.

It's possible to follow the implications of both scenarios. In general we tend to start with the assumption that there is an 'outer world', but we could equally explore the idea that there isn't. I don't think it would change much however, because ultimately it all boils down to describing our observations.

 

[vanhees71]

Can we therefore conclude that this single system is spatially extended?

Sure, why not? All there is are, however, the probabilities or probability distributions for the outcome of measurements.

 

[Lynch101]

Sure, why not? All there is are, however, the probabilities or probability distributions for the outcome of measurements.

It's more to do with the use of the term 'quantum non-separability' instead of 'quantum non-locality' (FTL-nonlocality).

It's clearly an error in thinking. Murray Gell-Mann puts it in “The Quark and the Jaguar” in the following way:

“The label ‘nonlocal’ applied by some physicists to quantum-mechanical phenomena like the EPRB effect is thus an abuse of language. What they mean is that if interpreted classically in terms of hidden variables, the result would indicate nonlocality, but of course such a classical interpretation is wrong.” [bold by LJ]

If we can infer the spatial extension of the quantum system then it isn't necessarily a classical interpretation in terms of hidden variables that indicates FTL-nonlocality. If the measurement on one 'end' of the system immediately determines the outcome at the other, spatially separated 'end' of the system, this too would imply FTL-nonlocality.

 

[Demystifier]

All there is are, however, the probabilities or probability distributions for the outcome of measurements.

But measurements are macroscopic. So on the microscopic level, where measurements don't exist, there are no even probabilities. In a theoretical universe containing only one hydrogen atom there would be nothing at all, not even probabilities. Is it what you are saying?

What I am asking is, are the probabilities of measurement outcomes there when there are no measurements?

 

[vanhees71]

If there were only a single hydrogen atom there'd be nobody to bother about its state and the meaning of this state.

Of course the probabilities are there when nobody measures. If the measurement is done you don't need any probabilities anymore.

 

[Demystifier]

If there were only a single hydrogen atom there'd be nobody to bother about its state and the meaning of this state.

Of course the probabilities are there when nobody measures. If the measurement is done you don't need any probabilities anymore.

So probabilities of measurement outcomes are only relevant when there are no measurement outcomes?

 

[gentzen]

Maybe, there is some misunderstanding.
To my mind, words like "local" or "non-local" are problematic in conjuction with quantum theory. They can over and over again trigger people to think about quantum phenomena with classical ideas (this I meant with "error in thinking").

I see. I never had to teach students, so the problem that my words would trigger ideas that make it harder for them to learn quantum theory never happened to me. For me personally, it was rather the absence of the concept of density matrix that initially prevented me from understanding quantum mechanics (in my QM course at university).

After I learned a similar concept in statistical optics later in my job, I guessed that it was this concept that had been missing for me before. Much later a new job forced me to really learn and understand QM. Today I have the impression that most of classical physics remains valid, and the tricky part is rather to convince others that taking quantum corrections (like exchange effects, quantum surface transmission, channeling contrast, quantum moment conservation) into account is both possible and required for reproducing certain effects seen in experimental data, despite the fact that Monte Carlo simulations seem to be based entirely on classical concepts. A correction for exchange effects or for channeling contrast can feel badly non-local. To convince others, it helps to dig a bit into where the non-locality came from. Typically two or more electrons became indistinguishable for some specific reason. I don't think that the word "non-local" itself ever played a role is such discussions, neither positive nor negative.

 

[physika]

The same holds for "reality", which is even harder to define. For me reality is objective, reproducible observability, i.e., what can be tested by experiments.

...for others, have pre-defined values

 

[physika]

if the measurement on one 'end' of the system immediately determines the outcome at the other, spatially separated 'end' of the system, this too would imply FTL-nonlocality.

not necessarily.

 

[vanhees71]

I see. I never had to teach students, so the problem that my words would trigger ideas that make it harder for them to learn quantum theory never happened to me. For me personally, it was rather the absence of the concept of density matrix that initially prevented me from understanding quantum mechanics (in my QM course at university).

After I learned a similar concept in statistical optics later in my job, I guessed that it was this concept that had been missing for me before. Much later a new job forced me to really learn and understand QM. Today I have the impression that most of classical physics remains valid, and the tricky part is rather to convince others that taking quantum corrections (like exchange effects, quantum surface transmission, channeling contrast, quantum moment conservation) into account is both possible and required for reproducing certain effects seen in experimental data, despite the fact that Monte Carlo simulations seem to be based entirely on classical concepts. A correction for exchange effects or for channeling contrast can feel badly non-local. To convince others, it helps to dig a bit into where the non-locality came from. Typically two or more electrons became indistinguishable for some specific reason. I don't think that the word "non-local" itself ever played a role is such discussions, neither positive nor negative.

Sure, in "bread-and-butter physics" dealing with the description of observable phenomena, there's only one meaning of "locality", namely the impossibility to transmit information with any "faster-than-light signal" within any theory which is consistent with any theory within the (special-)relativistic (!) spacetime model. In relativistic QFT this is implemented from the very beginning by the microcausality principle for local observables, from which all the fundamental properties derivable from the so realized local relativsitic QFTs follow: unitarity and Poincare invariance of the S-matrix/optical theorem/dispersion relations, relation between spin and statistics (half-integer spin=fermions; integer spin=bosons), CPT symmetry.

What's often confusingly called "non-locality" in the more quantum-foundations inclined community refers to long-ranged correlations between "entangled parts" of a quantum system. It would help tremendously to call this "inseparability" as Einstein did. The trouble seems to be that Einstein's much clearer written paper of 1948 has been mostly ignored in comparison to the unfortunate EPR paper of 1935, and thus the confusing lingo of the EPR paper and the even more confusing answer by Bohr prevailed.