# The notion of locality in (Quantum) Physics should be clearly defined

• I
• vanhees71
In summary, the thread about entanglement and Bell tests has been closed prematurely. It has not been clarified what "locality" means. Locality is the property of a relativistic theory that obeys the causality principle of relativistic spacetime. Locality is implemented by construction through the demand that local observables must commute at space-like separated arguments. This means that there cannot be any nonlocal (inter)actions between distant parts of a quantum system. However, in the mostly discussed case of entangled photon pairs you can of course have entangled photon states with the corresponding Bell-inequality violating correlations between the outcomes of measurements on the single photons in the pair at far distant places.
vanhees71
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TL;DR Summary
The notion of locality in (quantum) physics should be clearly defined
Unfortunately one of the threads about entanglement and Bell tests has again been closed prematurely. It has not been clarified what "locality" means.

In the physics community, not involved in philosophical arguments about foundations of QT, it's clearly defined as the property of a relativistic theory that obeys the causality principle of relativistic spacetime, which implies that there cannot be any causal relation between space-like separated events. As far as I know that's also the meaning Bell gives always to this notion in his work on Bell inequalities valid in local (in this meaning!) realistic (which means that all observables always take determined values).

In relativistic QFT this locality principle is implemented by construction through the demand that local observables must commute at space-like separated arguments, i.e., (using the signature ##(+---)## for the Minkowski form)
$$[\hat{A}(x),\hat{B}(y)]_{-}=0 \quad \text{for} \quad (x-y)^2<0,$$
if ##\hat{A}(x)## and ##\hat{B}(x)## are representing local observables (like, e.g., charge-current densities, energy-momentum tensors/intensities, etc.). Since the energy density ##\mathcal{H}(x)## is an observable, this indeed implies that there cannot be any nonlocal (inter)actions between distant parts of a quantum system.

Of course this does not rule out entanglement between far distant parts of quantum systems. In the mostly discussed case of entangled photon pairs you can of course have entangled photon states with the corresponding Bell-inequality violating correlations between the outcomes of measurements on the single photons in the pair at far distant places. All Bell tests are in accordance with standard local QED, which shows that standard relativsitic local QFT, which is local by construction, is able to describe the observed violations of Bell's inequality. That's no contradiction to Bell's derivation of these inequalities, but in addition he has assumed "realism", i.e., that all observables always take determined values, independent of the state of the system. This is, of course, not the case in relativistic local QFTs, which obeys the Heisenberg uncertainty principle, as any QT, which implies that incompatible observables usually do not take determined values, i.e., there are always states, in which one of these observables is determined (or in the case of observables with continues spectra very sharply determined) and the other then is necessarily indetermined (or pretty unsharply determined). The conclusion thus is that Nature behaves according to a local but non-realistic theory, namely relativistic local QFT.

apostolosdt
The conclusions above are of course wrong, but in a very very subtle way.

First, it correctly says that locality is defined precisely as a certain property of events.
They it says that in relativistic QFT locality is implemented as a certain precise property of observables.

But that's the source of error, the category mistake. The observables are not the events. By postulating a locality property of observables, one does not establish a locality property of events. The relation between observables and events is not clear. The standard quantum theory just says that events somehow pop out during the measurement, with probability given by the Born rule. But how exactly it happens? What is the mechanism? Is the mechanism local or nonlocal? Standard quantum theory does not answer such questions. Those are metaphysical questions for standard quantum theory, so it doesn't deal with them. It's OK to not deal with a mechanism, because it's philosophy rather than science, but from having a good reason to not deal with a mechanism it's not valid to conclude that the mechanism is therefore local.

Bell, in his theorem, explicitly deals with events, in a way in which standard theory does not want to deal. It's metaphysics, but formulated mathematically so that a logically convincing analysis is possible. Bell assumes realism, which means that some beables (not all observables!) always take definite values. He does not assume that beables obey deterministic laws, the laws may well be stochastic, but he assumes that one can meaningfully, and mathematically, analyze the values of beables even when they are not measured. The beables, according to Bell, are the missing link between observables and events. More precisely, the events are just the final states of beables, after the process of measurement finishes, while the observables, as abstract mathematical operators in abstract Hilbert space, are just a tool in a computation of the properties of beables. What his theorem shows is that beables, and hence events, violate locality, despite the fact that observables commute over spacelike distances. There is no any contradiction because, as I said, events are not observables. Observables obey a local law, but events don't.

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Structure seeker, Simple question, gentzen and 2 others
Events are of course due to the physical laws. In the context of this discussion an event is most conveniently defined as a "detection event" as the detection of a photon with a detector in the above mentioned Bell experiments. These detection events are of course due to the interactions of photons with matter as described by relativstic QFT. Thus their locality directly follows from the imposed mathematical microcausality constraint of the theory. I don't see, why there's a "category mistake", which however is a philosophical rather than scientific notion to begin with. Here, I'd like to stick to science. Philosophy is for the "interpretations forum"! We also should avoid Bell's metaphysical language like "beables". There's no clear scientific definition of this playful word creations either since Bell did not accept the fact that indeed physics as a natural science indeed is about "observations" and "measurements", not some vague idea of "beables".

vanhees71 said:
Here, I'd like to stick to science. Philosophy is for the "interpretations forum"!
It was you who started talk about Bell's "realism", which is a philosophical concept.

gentzen
No, Bell's "realism" is a clear scientific postulate, i.e., that observables always take determined values. That's the strong part of Bell's work: It translated vague philosophical notions a la EPR, Bohr, et al to a clear scientific notion, which lead to the possible for objective observations allowing for a decision between the predictions of what Bell called a "local realistic theory" (validity of his inequalities) and QT, including local relativistic QFT (violating his inequalities despite being a local theory).

vanhees71 said:
No, Bell's "realism" is a clear scientific postulate, i.e., that observables always take determined values.
No, that's not Bell's realism. And the way you said it is not clear at all, because it's not clear what you mean by "determined".

vanhees71 said:
These detection events are of course due to the interactions of photons with matter as described by relativstic QFT. Thus their locality directly follows from the imposed mathematical microcausality constraint of the theory.
There is no mathematical derivation of detection events from the mathematics of standard relativistic QFT. There can't be such a mathematical derivation, because there is no even a mathematical symbol for a detection event in standard QFT. The absence of such a mathematical derivation is called the measurement problem. Indeed, you always say that measurement is what experimentalists do in the laboratories, and this definition of measurement is not mathematical. Since locality is a mathematical property, without a mathematical derivation of events you cannot say whether the events obey local laws.

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Simple question and WernerQH
Demystifier said:
The standard quantum theory just says that events somehow pop out during the measurement, with probability given by the Born rule.
Some interpretations avoid the postulate that "events somehow pop out during the measurement". So we are squarely in interpretation-dependent territory.
Demystifier said:
But how exactly it happens? What is the mechanism? Is the mechanism local or nonlocal? Standard quantum theory does not answer such questions. Those are metaphysical questions for standard quantum theory, so it doesn't deal with them. It's OK to not deal with a mechanism, because it's philosophy rather than science, but from having a good reason to not deal with a mechanism it's not valid to conclude that the mechanism is therefore local.
Demystifier's (entire) answer is incredibly good. When life gives you lemons, make lemonade! Still, this discussion belongs in the "interpretations forum".

pines-demon, DrChinese, vanhees71 and 1 other person
vanhees71 said:
It has not been clarified what "locality" means.

You know, I usually glance over all of this "problematic" threads, and my impression is that it has been clarified, it's just that other people mean something different than you, and you have a hard time accepting it. Which sometimes look like you just simply ignore that other people mean something different.

DrChinese, Simple question, haushofer and 5 others
Demystifier said:
No, that's not Bell's realism. And the way you said it is not clear at all, because it's not clear what you mean by "determined".
It's simply the assumption that all observable take definite values, no matter whether they are prepared as such or not. That's also very clear from how this assumption is realized in the mathematical description and the derivation of Bell's inequality from the assumption of a local realistic theory.

It was clear that this topic was quickly moved to the interpretations subforum. It's symptomatic that whenever one tries to have a scientific discussion about these topic it inevitably ends up in obscuring philsophy :-(.

weirdoguy said:
You know, I usually glance over all of this "problematic" threads, and my impression is that it has been clarified, it's just that other people mean something different than you, and you have a hard time accepting it. Which sometimes look like you just simply ignore that other people mean something different.
One should clearly distinguish between Kuhn's "two worlds", i.e., science and philosophy. In physics locality has a clear and mathematically well formulated meaning, and one should stick to this, when it comes to discussing science. Unfortunately now that discussion has been moved to the interpretation subforum, and this again opens the entire can of worms with philosophical distortions. It's obviously impossible to discuss these topics in this forum without getting into this rabbit hole of philosophical speculations.

kered rettop and apostolosdt
Demystifier said:
There is no mathematical derivation of detection events from the mathematics of standard relativistic QFT. There can't be such a mathematical derivation, because there is no even a mathematical symbol for a detection event in standard QFT. The absence of such a mathematical derivation is called the measurement problem. Indeed, you always say that measurement is what experimentalists do in the laboratories, and this definition of measurement is not mathematical. Since locality is a mathematical property, without a mathematical derivation of events you cannot say whether the events obey local laws.
So you are saying that QFT doesn't predict what's observed? That's ridiculous given that it provides the very predictions that most accurately fit all observations! There is no measurement problem outside of philosophy. QFT describes all measurements correctly, and from a scientific point of view, there's no problem.

vanhees71 said:
Of course this does not rule out entanglement between far distant parts of quantum systems. In the mostly discussed case of entangled photon pairs you can of course have entangled photon states with the corresponding Bell-inequality violating correlations between the outcomes of measurements on the single photons in the pair at far distant places.
With the usual caveats and stipulations*, quantum mechanics preserves causal locality even as it generalises possible detector correlations to Bell-inequality-violating correlations, as the correlated detection events are timelike separated from the preparation event.

The novelty in the entanglement swap experiment is the presence of Bell-inequality violating correlations in particles with spacelike-separated preparations. This is seen as a challenge to causal locality since, unlike the EPRB case, the correlated detection events are not timelike separated from some preparation event.

However, as I'm sure you know, this is not a challenge to locality as you have laid out because the selection event (the Bell-state measurement) is timelike separated from both preparation events. Like before, we can construct a classical analog, a non-bell-violating correlation swap of detector events (see my Bertlemann's socks example in the other thread) and generalise it to a quantum mechanical entanglement/bell-violating-correlation swap scenario while preserving causal locality.

* The usual caveats and stipulations being the adoption of a minimalist/instrumentalist account, and a clarification of different meanings of locality.

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vanhees71 said:
It was clear that this topic was quickly moved to the interpretations subforum. It's symptomatic that whenever one tries to have a scientific discussion about these topic it inevitably ends up in obscuring philsophy :-(.
It is the "interpretations subforum," not the "philosophy forum". And it will still be the same people discussing with you. So which sort of behavior should we avoid, so that you can have your "scientific discussion" instead of "obscurity"? I mean, the following was posted before the move to the interpretations forum, so being outside of that forum doesn't seem to be an effective protection against "non-scientific discussion" either:
Demystifier said:
Decide, do you want to be a scientist, or a mathematician?
https://www.physicsforums.com/threa...ter-missed-opportunities.1054134/post-6916115
Demystifier said:
Conclusion: You are in the superposition of a mathematical Platonist and a natural scientist. But in your case, this is really a superposition of two versions of a Bohmian. So you are really a Bohmian, but you don't know it because your wave function cannot collapse. You are like a cat who does not know that it is a cat because it is in a superposition of white cat and black cat.

haushofer and Demystifier
vanhees71 said:
TL;DR Summary: The notion of locality in (quantum) physics should be clearly defined

In relativistic QFT this locality principle is implemented by construction.....
In order to specify the meaning of the term "implemented by construction". For example, M. P. Seevinck in “Can quantum theory and special relativity peacefully coexist?” (https://arxiv.org/abs/1010.3714):

"The claim has been made that the principles of quantum theory alone suffice for proofs of the No-Signalling Theorems [13, 14, 26]. The most sophisticated proofs of these theorems are in term of quantum field theory and rely on the notion of microcausality or local commutativity, which means that operators which represent measurements performed on space-like separate parts of a physical system always commute, regardless of whether or not they would commute if operating locally (Peacock, 1991 [25, p. 56]).

The important observation is that this microcausality condition does not follow from some set of quantum principles, but is in fact postulated because it is “the mathematical statement of the fact that no signal can be exchanged between two points separated by a spacelike interval and therefore that measurements at such points cannot interfere” (Schweber, 1961 [27, p. 723]). Indeed, Stapp (1988, [33, p. 88]) admits that “relativistic quantum field theory . . . is constructed to ensure that its predictions do not depend either on the frame of reference or upon the order in which one imagines performing measurements on spacelike separated regions.”

However, “a proof of a result based on a theory which was ‘constructed to ensure’ that result is no proof at all” (Peacock, 1991 [25, p. 70]). This conclusion has been endorsed recently by Mittlestaedt (2008, [19, p. 2]): “The micro-causality condition of relativistic quantum field theory excludes entanglement induced superluminal signals but this condition is justified by the exclusion of superluminal signals. Hence, we are confronted here with a vicious circle, and the question whether there are superluminal EPR-signals cannot be answered in this way.”

DrChinese
vanhees71 said:
In physics locality has a clear and mathematically well formulated meaning, and one should stick to this, when it comes to discussing science.

Well, maybe one should, but others refuse to do it, and they have their right to do it. Those endless and fruitless discussions are often based on the fact, that you ignore that. Words can have different meaning. You perfectly know that others are using "locality" in different way, but yet you come with this QFT-observables-commute mantra like it's gonna change something in the discussion. It won't. And it makes most of those threads hard to read. It looks like you are just copying and pasting your posts. What for?

Motore, Simple question, Demystifier and 1 other person
vanhees71 said:
It's simply the assumption that all observable take definite values, no matter whether they are prepared as such or not.
If you insist on scientific discussion, please cite a scientific reference where this assumption is made. To my knowledge, there is no such reference.

DrChinese and gentzen
vanhees71 said:
So you are saying that QFT doesn't predict what's observed?
I'm not saying it. It predicts, but not in a purely mathematical manner. It talks about measurement without a mathematical definition/description of measurement.

Demystifier said:
I'm not saying it. It predicts, but not in a purely mathematical manner. It talks about measurement without a mathematical definition/description of measurement.
Why should there be a mathematical definition for everything in physics?!

vanhees71 said:
It was clear that this topic was quickly moved to the interpretations subforum. It's symptomatic that whenever one tries to have a scientific discussion about these topic it inevitably ends up in obscuring philsophy :-(.
Do you know any published paper where this is explained in a purely scientific manner, without any philosophy? If you do, why don't you cite it, so that we all can read it? If you don't, why don't you write the first paper that finally explains it without philosophy, and publish it in a scientific journal, so that we all can finally understand this scientifically, without philosophy? That's what a scientist should do.

weirdoguy and Lord Jestocost
martinbn said:
Why should there be a mathematical definition for everything in physics?!
Not for everything. But there should be for measurement, because physicists want to know whether there is something nonlocal about measurement, and the word "nonlocal" has a clear mathematical definition (as @vanhees71 correctly pointed out), so to decide whether measurement involves something nonlocal in a well defined mathematical sense, we must have a mathematical theory of measurement. And by the way, the mathematician von Neumann contributed significantly to the development of such a theory, and concluded that the theory needs a collapse, which is nonlocal.

WernerQH
But Q(F)T describes all observations, including measurements. Measurements use matter consisting of the particles described by QFT, and thus the measured objects interact with the measurement apparatus according to the laws of QFT, i.e., locally.

I don't know, what you think is lacking in the description of measurements. Do you also say classical physics doesn't describe measurement? If not, why not? If yes, what's lacking there?

vanhees71 said:
But Q(F)T describes all observations, including measurements.
Now you are playing with words, like a philosopher. By explaining measurement I mean explaining the process of measurement, not the result of measurement.

GarberMoisha, Simple question, WernerQH and 2 others
vanhees71 said:
Do you also say classical physica doesn't describe measurement?
Classical physics describes measurement, there is no problem in classical physics. The difference is that classical physics does not need the measurement postulate. Instead, measurement is explained from other postulates. In quantum physics, on the other hand, there is the measurement postulate, not derived from other postulates.

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GarberMoisha
Demystifier said:
Not for everything. But there should be for measurement, because physicists want to know whether there is something nonlocal about measurement, and the word "nonlocal" has a clear mathematical definition (as @vanhees71 correctly pointed out), so to decide whether measurement involves something nonlocal in a well defined mathematical sense, we must have a mathematical theory of measurement. And by the way, the mathematician von Neumann contributed significantly to the development of such a theory, and concluded that the theory needs a collapse, which is nonlocal.
This is not philosophy, this is rhetoric.

apostolosdt and vanhees71
martinbn said:
This is not philosophy, this is rhetoric.

DrChinese, Simple question, vanhees71 and 1 other person
Demystifier said:
Classical physics describes measurement, there is no problem in classical physics. The difference is that classical physics does not need the measurement postulate. Instead, measurement is explained from other postulates. In quantum physics, on the other hand, there is the measurement postulate, not derived from other postulates.
What is the measurement postulate in QT? Do you mean Born's rule? How do you think classical physics describes measurement and QT doesn't?

I don't think, it helps if you answer my questions just with new enigmatic statesments.

vanhees71 said:
So you are saying that QFT doesn't predict what's observed?
I would say that QFT predicts what what's observerd by a certain class of observers. This is then used to DEFINE what is meant by an "observable".

But I think this doesn't necessarily mean that "observers" that are more general transormations than poincare transformations are not real. This is where the fuzzy notion of beables may come into play. Either you can say it's "varibles" that can't be observed and aren't observables, or one can maybe imagine that they ARE "observble" but but a class of observer not contained in what QFT is designed for.

/Fredrik

vanhees71 said:
These detection events are of course due to the interactions of photons with matter as described by relativstic QFT. Thus their locality directly follows from the imposed mathematical microcausality constraint of the theory.
QFT predicts conditional probabilities for detection events that can be widely separated in space. But what happens at one of the detectors cannot be completely described as something strictly local. You seem to think of the "biphoton" as a single system, but it distorts the meaning of the word locality to say that you are employing a fully "local" description.

If there were a pair of "magic dice" that show the same face whenever and wherever they are thrown, would you call this an "inseparable" but still "local" system? Would the mystery go away if you explained that the correlations arise because they came from the same factory?

You advertise a meal (relativistic QFT) as "kosher" (local by construction). But you didn't check all ingredients. The Born rule adds distinctive non-local randomness to the stew.

DrChinese, Simple question and gentzen
vanhees71 said:
TL;DR Summary: The notion of locality in (quantum) physics should be clearly defined

It has not been clarified what "locality" means.
I don't understand why you continue to harp on this issue when I have repeatedly pointed out the two different definitions of "locality" that are used in the literature.

(1) "Locality" means spacelike separated measurements commute. (This is the definition you use.)

(2) "Locality" means the Bell inequalities are not violated. (This is the definition many papers in the literature on Bell's theorem use.)

The solution to this "problem" is not to keep complaining about "locality" not being clearly defined, but to stop using the term "locality" whenever there is a question about what meaning is intended. Just use the more technical terminology that says exactly what you mean. Why is this a problem? I don't understand.

DrChinese, Motore and weirdoguy
vanhees71 said:
As far as I know that's also the meaning Bell gives always to this notion in his work on Bell inequalities
No, Bell actually uses "locality" in a third sense which also appears elsewhere in the literature, though not as often:

(3) "Locality" means the joint probability distribution for results of spacelike separated measurements factorizes, so that the result of measurement A is only dependent on the setting of measuring device A, and the result of measurement B is only dependent on the setting of measuring device B.

What confuses many people about Bell-type experiments is that those experiments violate "locality" in the sense of #3 above, and of my #2 in my previous post just now, but do not violate locality in the sense of #1, i.e., the standard QFT sense that you always use the term. That is indeed an issue that gets a lot of discussion, but not having a clearly defined meaning for the term "locality" is not the issue that needs discussion.

Simple question and mattt
vanhees71 said:
What is the measurement postulate in QT? Do you mean Born's rule?
Yes. The Born rule says: When an observable is measured, then the probability is such and such. In classical physics there is no postulate beginning with "When an observable is measured ...".

PeterDonis said:
The solution to this "problem" is not to keep complaining about "locality" not being clearly defined, but to stop using the term "locality" whenever there is a question about what meaning is intended. Just use the more technical terminology that says exactly what you mean. Why is this a problem? I don't understand.
This is a big problem for @vanhees71 because it would imply that there is some notion of locality which is violated, which would contradict his philosophical prejudices, for which he cannot accept that they are philosophical prejudices, because it would ruin his self-picture of a pure scientist who despises philosophy. To preserve his self-picture of a pure scientist, he is forced to use philosophy to argue that it's the others, not himself, who use philosophy. Vicious circle.

DrChinese, Simple question and weirdoguy
PeterDonis said:
but not having a clearly defined meaning for the term "locality" is not the issue that needs discussion.
I agree. So what is it that needs discussion? I fear we can't even agree on that?

I have a feeling some of us here, thinks there is really nothing to be discussed. While others agree that currenty theory describes experiments but does not offer a satisfactory causal explanation of the mechanisms.

Bells "hidden variables" would have been an "explanation", but as it does't work at least in a sensible manner, the quest is still open. But Vanhees as far as I recall, don't see it as a scientific task to "explain" beyond "describe" and consider it a philosophical question?

/Fredrik

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