The general structure of relativistic QFTs

[vanhees71]

I thought it was obvious that an operator describing photon polarization at two detectors (at different locations!) must be a non-local operator. Is it not?

Let's not waste our time on the "standard" or "proper" meaning of words. Obviously I should have added more details. I think that QFT is better viewed as a theory of isolated events, points in spacetime, and what is classically called a field is correlations between (microscopic) events. This idea should feel quite natural for someone who applies QFT in condensed matter physics. It is not a priori necessary to assume something physical to exist between those events. They need not be "immersed" in some kind of medium (aether, vacuum, field, ...) that is continuous. There's a theory of point processes, or random point fields, describing this. It would give physical meaning to the actual graininess of quantum fields.

I still do not know, what you mean. To describe the coincidence experiments when measuring photon polarization states on different places you need, of course, the two-point correlation (two-photon Green's) function of the (electromagnetic) field. Of course, it's all about correlations. What else?

 

[Lord Jestocost]

In the book „Elegance and Enigma The Quantum Interviews” (edited by Maximilian Schlosshauer), some of the key terms appearing in the book are defined in the glossary list. Under the entry 'nonlocality', one finds:

"In the context of quantum mechanics, this term chiefly has two meanings.
(1) The impossibility of describing correlations between outcomes of local measurements, performed at two different locations, in terms of a local hidden-variables model.
(2) Actual physical action-at-a-distance, where the physical situation in one region instantaneously influences the physical situation in another, arbitrarily distant region.

I hope there is no misunderstanding. To my mind, these definitions of nonlocality simply mean that it would be an abuse of language if the adjective “nonlocal” is used as a description of quantum or quantum field theory. Quantum or quantum field theory are non-separable, local theories.

 

[PeterDonis]

it would be an abuse of language if the adjective “nonlocal” is used as a description of quantum or quantum field theory.

Not with definition (1) that you quoted, since that definition is equivalent to saying that the Bell inequalities are violated, and QFT does violate the Bell inequalities.

 

[Lord Jestocost]

Bell's inequality is derived from the assumption of separability. Separability, as Don Howard puts in his paper “Einstein on locality and separability”, means:

“The separability principle operates on a more basic level as, in effect, a principle of individuation for physical systems, a principle whereby we determine whether in a given situation we have only one system or two. If two systems are not separable, then there can be no interaction between them, because they are not really two systems at all.”

[Edit]You can use definition (1) in the context of conversation about quantum mechanics, but when using the term 'nonlocal' as an adjective for the noun 'quantum mechanics', one only muddies the waters.

 

[PeterDonis]

Bell's inequality is derived from the assumption of separability.

Haven't I asked someone (possibly you) to point out exactly where in Bell's papers the "separability" assumption is made?

 

[Lord Jestocost]

My point is merely the following:

Even if observed quantum-mechanical phenomena appear to us as human beings to be ‘nonlocal’, physicists should avoid to use the label ‘nonlocal’ as an adjectival term in regard to quantum theory. The impossibility of describing correlations between outcomes of local measurements in terms of a local hidden-variables model, has at the end nothing to do with quantum theory. In discussions about quantum theory, vague terminology is indeed a big problem.

 

[PeterDonis]

physicists should avoid to use the label ‘nonlocal’ as an adjectival term in regard to quantum theory.

I would say physicists should avoid both "nonlocal" and "local" as terms when discussing quantum theory. Instead, as I have posted before, they should state explicitly what specific criterion they are talking about. For example, if it's spacelike separated measurements commuting, say that.

 

[gentzen]

Nicolas Gisin’s short book Quantum Chance nicely explains how the paradox arises that quantum mechanics is local and nonlocal at the same time: The randomness itself is nonlocal, and it must be really random, because otherwise this non-locality could be used for instantaneous signal transmission. At the same time, however, the randomness also becomes less problematic, because it is now clear in the sense of which idealization it must be perfect. After all, there is probably no such thing as mathematically perfect true randomness.

I don't think that the word "nonlocal" here is problematic. You might disagree that there is a paradox at all, and if you replace "nonlocal" by "inseparable", it might get easier to argue against there being a paradox. Or you might find the quote incomprehensible. But I doubt that the word "nonlocal" is responsible for that.

 

[vanhees71]

Not with definition (1) that you quoted, since that definition is equivalent to saying that the Bell inequalities are violated, and QFT does violate the Bell inequalities.

True, but it's not due to a violation of locality but of "reality", i.e., the concept that all observables take determined values, which are only unknown to us in full detail, so that we describe them statistically, i.e., via probability distributions of some hidden variable(s). That's of course what is not fulfilled according to any QT, including local relativistic QFT. Of course, I use the physical notion of "locality" in the sense of standard relativistic QFTs.

 

[vanhees71]

I don't think that the word "nonlocal" here is problematic. You might disagree that there is a paradox at all, and if you replace "nonlocal" by "inseparable", it might get easier to argue against there being a paradox. Or you might find the quote incomprehensible. But I doubt that the word "nonlocal" is responsible for that.

It is, in my opinion, mandatory to use "inseparable" rather than "nonlocal", because locality and thus also its negation have a precise mathematical meaning in relativistic local (sic!) QFTs, namely that the Hamilton density commutes with all local observable operators at space-like separated arguments, which excludes faster-than-light propagation of (causal) effects, i.e., space-like separated events cannot be causally connected also within relativistic local QFTs by construction.

 

[Lord Jestocost]

I completely agree with @vanhees71 point of view in comment #70. On ‘mathpages.com’ one reads, for example, the following:

“People sometimes think that the lack of separability implies ‘action at a distance’, but that's a misunderstanding. Everyone agrees that quantum mechanics does not entail any action at a distance, because no information or energy propagates faster than light. Nevertheless, the entangled parts of a quantum system are not separable, and this is precisely what the violations of Bell's inequality demonstrate. It’s true that in the classical context the only way things could not be separable would be by action at a distance, but the peculiar feature of quantum mechanics is that things can be non-separable without implying any action at a distance. The non-separability is subtle, but it represents a profoundly non-classical aspect of the world.”

Entry: “Quantum Mechanics and Separability” (https://www.mathpages.com/home/kmath731/kmath731.htm)

 

[martinbn]

I completely agree with @vanhees71 point of view in comment #70. On ‘mathpages.com’ one reads, for example, the following:

“People sometimes think that the lack of separability implies ‘action at a distance’, but that's a misunderstanding. Everyone agrees that quantum mechanics does not entail any action at a distance, because no information or energy propagates faster than light. Nevertheless, the entangled parts of a quantum system are not separable, and this is precisely what the violations of Bell's inequality demonstrate. It’s true that in the classical context the only way things could not be separable would be by action at a distance, but the peculiar feature of quantum mechanics is that things can be non-separable without implying any action at a distance. The non-separability is subtle, but it represents a profoundly non-classical aspect of the world.”

Entry: “Quantum Mechanics and Separability” (https://www.mathpages.com/home/kmath731/kmath731.htm)

I think this is the main reason for the endless discussions. Not whether QM is local or not, but the insistence that "quantum nonlocality" implies some sort of action/interaction/influence and so on at a distance.

 

[CoolMint]

True, but it's not due to a violation of locality but of "reality", i.e., the concept that all observables take determined values, which are only unknown to us in full detail, so that we describe them statistically, i.e., via probability distributions of some hidden variable(s). That's of course what is not fulfilled according to any QT, including local relativistic QFT. Of course, I use the physical notion of "locality" in the sense of standard relativistic QFTs.

This is way too subtle for most experts to note the subtle difference, imo. Even when they claim that quantum systems don't have definite values at all times, they go on and act and argue as if they had forgotten what they have claimed earlier.
Classicaility is just too overwhelming as a concept to remove completely from thought.

 

[WernerQH]

To describe the coincidence experiments when measuring photon polarization states on different places you need, of course, the two-point correlation (two-photon Green's) function of the (electromagnetic) field. Of course, it's all about correlations. What else?

One cannot arrive at observable consequences of QFT without using Born's rule in one form or another. But Born's rule breaks locality (in the sense of physical continuity between "cause" and "effect"). In its most spectacular applications QFT involves products of local operators at widely separated points in space and time, and applying Born's rule is then a decidedly non-local operation. There is a vestige of continuity in the fields and the operators that describe them, but this continuity applies only to statistical ensembles. Bell's theorem precludes any kind of causal continuity in the individual system.

We share a distaste for quibbling about mere words, and I don't think that our views of QFT are radically different. But I think calling QFT "causally local" causes misperceptions. The epithet "local" applies only to its "deterministic" side. Insisting on locality you are ignoring the vital stochastic (statistical) part of QFT.

 

[martinbn]

I completely agree with @vanhees71 point of view in comment #70. On ‘mathpages.com’ one reads, for example, the following:

“People sometimes think that the lack of separability implies ‘action at a distance’, but that's a misunderstanding. Everyone agrees that quantum mechanics does not entail any action at a distance, because no information or energy propagates faster than light. Nevertheless, the entangled parts of a quantum system are not separable, and this is precisely what the violations of Bell's inequality demonstrate. It’s true that in the classical context the only way things could not be separable would be by action at a distance, but the peculiar feature of quantum mechanics is that things can be non-separable without implying any action at a distance. The non-separability is subtle, but it represents a profoundly non-classical aspect of the world.”

Entry: “Quantum Mechanics and Separability” (https://www.mathpages.com/home/kmath731/kmath731.htm)

Also from there

Now, it’s well known that no energy or information propagates faster than light according to quantum mechanics, and yet some people still have the vague idea that quantum entanglement implies action at a distance. This may be partly due to lack of clarity about the technical meaning of the word “action” in physics, but also partly due to the fact that the non-separability of quantum mechanics is subtle, involving distant correlations but not communication. People often use sloppy language, saying things like “one electron is affected by the measurement of the other”, but they are really referring to the existence of correlations, not to any action at a distance. Even Bell himself, who evidently yearned for a return to a Lorentzian world view, admitted that instantaneous action at a distance is inconsistent with the well-established Lorentz invariance.

 

[vanhees71]

One cannot arrive at observable consequences of QFT without using Born's rule in one form or another. But Born's rule breaks locality (in the sense of physical continuity between "cause" and "effect"). In its most spectacular applications QFT involves products of local operators at widely separated points in space and time, and applying Born's rule is then a decidedly non-local operation. There is a vestige of continuity in the fields and the operators that describe them, but this continuity applies only to statistical ensembles. Bell's theorem precludes any kind of causal continuity in the individual system.

We share a distaste for quibbling about mere words, and I don't think that our views of QFT are radically different. But I think calling QFT "causally local" causes misperceptions. The epithet "local" applies only to its "deterministic" side. Insisting on locality you are ignoring the vital stochastic (statistical) part of QFT.

It's correlations, not causal effects, that's described by the correlation functions. That's the important point of the whole debate! You evaluate the joint probability for registering a photon pair at two space-like separated events. This has nothing to do with non-local interactions.

 

[WernerQH]

It's correlations, not causal effects, that's described by the correlation functions.

How do correlations arise, if not through causal effects?

 

[PeterDonis]

it's not due to a violation of locality but of "reality"

Again you are insisting on your preferred definitions of words. Some people use "locality" to mean "the Bell inequalities are not violated". Certainly that is the usage implied by item (1) in the post that I responded to. I understand you don't like this usage, but that's beside the point. Not everyone uses words the way you would like them to be used.

It is, in my opinion, mandatory to use "inseparable" rather than "nonlocal", because locality and thus also its negation have a precise mathematical meaning in relativistic local (sic!) QFTs,

In my opinion, as I've already stated, we should stop using vague ordinary language words altogether. "Inseparable" is vague ordinary language; that word can have multiple meanings, just like "locality". Instead of saying "inseparable", state the precise mathematical condition you are referring to (just like saying "spacelike separated measurements commute" instead of "locality"). Then we all know what we are talking about and we can stop having pointless arguments over words and discuss physics instead.

 

[vanhees71]

Do I have to follow your opinion that I should not use the standard meaning of words and instead use some imprecise and confusing language? What should this be good for? Is PF now a philosophy forum rather than a physics forum? That'd be a pity...

 

[PeterDonis]

Do I have to follow your opinion that I should not use the standard meaning of words

The whole point is that there is not a single "standard meaning" for the words that are creating these problems. I have said this again and again and you continue to ignore it.

and instead use some imprecise and confusing language?

I said no such thing. I said you should explicitly give the precise mathematical condition you are using instead of using imprecise and confusing language. For example, instead of saying "inseparable" you should say the precise mathematical condition that you are referring to with that word.

 

[vanhees71]

I did this repeatedly. It's impossible to get any further if one only repeats the same well-known definitions again and again.

 

[PeterDonis]

I did this repeatedly.

Where have you given the precise mathematical condition that you are using the term "inseparable" to refer to?

 

[PeterDonis]

It's impossible to get any further if one only repeats the same well-known definitions again and again.

You are missing the point. Nobody has ever disputed the fact that QFT has the mathematical property you say it has (that spacelike separated measurements commute).

However, the argument you continue to insist on making is that QFT is "local" because it has that mathematical property. That argument is nonsense as an argument; it's a definition of the term "local", not an argument for why QFT is "local". And it's also a pointless argument, since what we are supposed to be discussing is the physics, not the definitions of words.

 

[vanhees71]

Then you should finally tell me what you think the word "local" means in the context of relativistic QFT. I use the word in the standard sense used in all modern textbooks about the subject, and I've summarized it in #1 of this thread. The details fill the first few chapters of Weinbergs QT of fields vol. 1. It's impossible to understand and communicate about an exact science, if it is not allowed to use the standard definitions and terminology of the vast majority of the science community. You are also usually a proponent of this rule for PF. So I'm very surprised that particularly you are fighting my attempt to clarify this confusion by pointing to the standard meaning of the word "locality".

BTW: A bipartite quantum system is called separable, if it's state can be written in the form
$$\hat{\rho}=\sum_j p_j \hat{\rho}_j^{(A)} \otimes \hat{\rho}_j^{(B)}$$
with $p_j>0$ and $\sum_j p_j=1$.

 

[PeterDonis]

Then you should finally tell me what you think the word "local" means in the context of relativistic QFT.

I have already done that in multiple posts, but I'll summarize again here. The "relativistic QFT" one is "spacelike separated measurements commute", which is the definition you've been using. The other one I've referred to multiple times is "the Bell inequalities are not violated". Bell's original paper got more specific about the latter and used "locality" to describe the factorizability condition on the joint probability distribution for measurement results (equation 2 in his original paper).

It's impossible to understand and communicate about an exact science, if it is not allowed to use the standard definitions and terminology of the vast majority of the science community.

The "relativistic QFT" community is not the same as "the vast majority of the science community". It would be very nice if the entire "science community" agreed on one definition for the word "locality". But it hasn't. The fact that you only recognize one definition as "standard" does not mean all your beliefs about that definition are correct.

A bipartite quantum system is called separable, if it's state can be written in the form
$$\hat{\rho}=\sum_j p_j \hat{\rho}_j^{(A)} \otimes \hat{\rho}_j^{(B)}$$
with $p_j>0$ and $\sum_j p_j=1$.

Is this equivalent to saying that a "separable" system is not entangled, and vice versa?

 

[PeterDonis]

You are also usually a proponent of this rule for PF. So I'm very surprised that particularly you are fighting my attempt to clarify this confusion by pointing to the standard meaning of the word "locality".

Your repeated posts have not clarified any confusion, because nobody is confused about the actual physics involved. All your repeated posts have done is caused pointless arguments because other posters here, including ones with considerable knowledge of the subject matter under discussion, do not use the word "locality" the same way you do and object to your talking as if your preferred usage was the only one that exists.

 

[PeterDonis]

Thread closed for moderation.

 

[Doc Al]

This thread can remain closed. I think we've beat this topic to death (at least for the time being). This thread demonstrates that the meaning of "local" is context-dependent. To avoid wheel spinning over terminology. it behooves us to be explicit about what we mean when using the term.