The general structure of relativistic QFTs

In summary, the conversation discusses the concept of "locality" in quantum physics, specifically in the context of relativistic quantum field theories (QFTs). It is pointed out that the only successful realization of relativistic QFTs is through local interactions, which are necessary to ensure Poincare covariance and the cluster-decomposition principle. The spin-statistics theorem is also mentioned, which states that fields with half-integer spin must be quantized as fermions, while those with integer spin must be quantized as bosons. This local formulation of QFT is able to describe all known particles and their interactions with high precision. Additionally, it is shown that this formulation allows for the existence of entangled states and long-range correlations,
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vanhees71
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TL;DR Summary
I try to clarify some misunderstandings about the general structure of relativistic QFT. Particularly the important defining property of "locality"
In a recent thread about Bell tests etc. it has been claimed my point of view of "locality" where "non-mainstream physics". Of course, I cannot give a complete summary of the foundations in a forum posting, as demanded by @DrChinese there. The most clear treatment, particularly emphasizing the pivotal role the principle of "microcausility" and thus "locality" plays in the QFT formulation of relativistic QT, can be found in

S. Weinberg, The Quantum Theory of Fields, vol. 1, Cam. Uni. Press (1995)

The first step in the construction of a relativistic QT is the analysis of the unitary (ray) representations of the underlying spacetime symmetry, i.e., the proper orthochronous Poincare group, which is a semidirect product of space-time translations and proper orthochronous Lorentz transformations. Instead of this group, its covering group is relevant in QT, i.e., the proper orthochronous Lorentz group is substituted by its covering group, ##\text{SL}(2,\mathbb{C})##. There are non non-trivial central extensions (in contradistinction to the analog case of the Galiei group in non-relativistic QT), i.e., one can concentrate on the unitary irreducible representations.

As it turns out the corresponding analysis (Wigner 1939) leads to two big classes of representations, i.e., the "massive and massless representations", that admit a causal description of the quantum dynamics. The single-particle states (i.e., free-particle states) are characterized by the mass Casimir operators ##m^2 \geq 0## and "spin" ##s##. For massive representations ##s \in \{0,1/2,1,\ldots \}## characterizes the irreducible representation of the rotation group for the "particles at rest", i.e., ##\vec{p}=0## (and since ##p \cdot p=m^2##, ##p^0 \in \{\pm m \}##). For massless representations there is only helicity, i.e., except for ##s=0##, where there is no polarization degree of freedom, there are only two polarization states, ##h=\pm s##, where the helicity is the component of the total angular momentum of the particle in direction of its momentum, and ##p^0 \in \{\pm |\vec{p}| \}##.

As it further turns out, so far the only successful realization of relativistic QT is in terms of local (sic!) relativistic quantum field theories (QFTs), i.e., one realizes the unitary irreps. of the Poincare group, described above with local field operators ##\hat{\psi}_{\sigma}(x)##, which transform according to a finite-dimensional representation of the proper orthochronous Lorentz goup characterized by two numbers ##(k,k')## with ##k,k' \in \{0,1/2,1,\ldots \}##. This representation then contains all the representations of the rotations with ##j \in \{|k-k'|,|k-k'|+1,\ldots k+k' \}##, and the field equations of motion thus must "project out" all the "unwanted" representations except the representation ##j## of the rotation group one likes to describe a particle with this spin, ##j##. This leads to the usual well-known field equations like Klein-Gordon, Dirac (where one puts together ##(1/2,0) \oplus (0,1/2)## to also represent space reflections in addition to the proper orthochronous Lorentz transformations), and massless spin-1 particles (which are necessarily "gauge fields" in order to have only two helicity polarization degrees of freedom rather than some continuos polarization degrees of freedom corresponding to more general representations of the socalled "little group" of the massless representations, which is ISO(2) rather than SO(3) in the massive case).

Then to implement interactions one realizes that to get a well-defined unitary scattering matrix, that is Poincare covariant and fulfilles the cluster-decomposition principle one has to implement the microcausality constraint, i.e., the Hamilton density ##\hat{\mathcal{H}}(x)## must commute with any local observable ##\hat{mathcal{O}}(y)## at space-like distances of their arguments:
$$[\hat{\mathcal{H}}(x),\hat{\mathcal{O}}(y)]=0 \quad \text{for} \quad (x-y)^2<0.$$
It turns out that the local fields corresponding to spin ##s## must be quantized as fermions (bosons) if ##s## is half-integer (integer), which is the famous spin-statistics theorem. In addition for these "locality" properties to hold each field is to be composed of the two possible representations for given ##m^2>0## with ##p^0>0## and ##p^0<0##, i.e., for each "particle state" there's also a correspondin "anti-particle state", both with positive energy ##E=\sqrt{\vec{p}^2+m^2}>0## (by using the "Feynman Stueckelberg trick" to have the ##p^0>0## modes with annihilation and the ##p^0<0## modes with creation operators in the mode decomposition of the free-field operators, which also is necessary to have fields transforming locally under Poincare transformations). Then one can show that also the CPT symmetry holds for any such (interacting) QFT, and the original goal is also achieved: One has a unitary Poincare-covariant S-matrix, fulfilling the cluster-decomposition principle, the latter being the very property demanded as "locality" in this standard sense of relativistic quantum physics.

As Weinberg stresses, it might not be the only way to build a QFT with these properties, but so far there is no example for an alternative construction, and so far these standard formulation with local QFTs describe all the known particles and their interactions with high precision.

Last but not least it also describes all the Bell tests with photons correctly, i.e., it is a way to have "locality" on the one hand, i.e., a theory, within which it is impossible to have causal effects between space-like separated events due to the microcausality constraint, but on the other hand as any QT also relativistic QFT implies the existence of entangled states and the corresponding long-range correlations described by them, which can be used for all the successful Bell tests.

Partiucularly there is no contradiction between the "locality" of the QFT in the above described sense and the possibility to prepare entangled photon pairs of before uncorrelated photon pairs via "entanglement swapping" as described in the other thread based on the work by Zeilinger et al,

Jian-Wei Pan, Dik Bouwmeester, Harald Weinfurter, and Anton Zeilinger, Experimental Entanglement Swapping: Entangling Photons That Never Interacted, PRL 80, 3891 (1998)

The entanglement of photons 1 and 4 for the subensemble selected by a projective Bell measurement of photon 2 and 3 is due to the original preparation of the entangled pair of photons 1 and 2 as well as photons 3 and 4 (where the pairs (12) and (34) themselves are uncorrelated). Both the creation of these original entangled pairs as well as the selection process through coincidence measurements on photons (23) are explained by local interactions of the em. field with the various "devices" used to manipulate them (parametric down conversion in BBO crystals, beam splitters, mirrors, lenses, etc. etc.), i.e., by standard QED. The selection through the measurement on the pair (23) and the measurements on photons 1 and 4 to establish their entanglement for the corresponding subensemble can be space-like seperated, excluding any causal influence of the measurement event with the pair (23) on photon 1 and/or photon 4. This is also what is meant in the paper, when they say the photons 1 and 4 "never interacted with one another or which have never been dynamically coupled by any other means":

We experimentally entangle freely propagating particles that never physically interacted with one
another or which have never been dynamically coupled by any other means. This demonstrates that
quantum entanglement requires the entangled particles neither to come from a common source nor to
have interacted in the past. In our experiment we take two pairs of polarization entangled photons and
subject one photon from each pair to a Bell-state measurement. This results in projecting the other two
outgoing photons into an entangled state. [S0031-9007(98)05913-4]

So the results of this and other experiments with entangled states is in full accordance with both "locality" of interactions and the long-ranged correlations described by the "inseparability" of far distantly observed parts of an entangled system, leading to the specific correlations contradicting the predictions of all "local realistic" theories in Bell's sense, and afaik also Bell uses "local" in this standard sense of relativistic physics, i.e., that space-like separated events cannot be causally connected.
 
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I think you should post this (except for the introduction) as an Insight article, so that it does not get lost in the mass of postings!
 
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vanhees71 said:
Summary: I try to clarify some misunderstandings about the general structure of relativistic QFT. Particularly the important defining property of "locality"

which transform according to a finite-dimensional representation of the proper orthochronous Lorentz goup characterized by two numbers (k,k′) with k,k′∈{0,1/2,1,/ldots}.
you should fix the latex in the quoted portion above as well in the follow (near the middle of the post)
vanhees71 said:
Summary: I try to clarify some misunderstandings about the general structure of relativistic QFT. Particularly the important defining property of "locality"

i.e., the Hamilton density H^(x) must commute with any local observable mathcalO^(y) at space-like distances of their arguments:
$$[\hat{\mathcal{H}}(x),\hat{\mathcal{O}(y)]=0 \quad \text{for} \quad (x-y)^2<0.$$
 
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  • #4
Thanks for pointing out the typos. I've corrected it.
 
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vanhees71 said:
The entanglement of photons 1 and 4 for the subensemble selected by a projective Bell measurement of photon 2 and 3 is due to the original preparation of the entangled pair of photons 1 and 2 as well as photons 3 and 4 (where the pairs (12) and (34) themselves are uncorrelated). Both the creation of these original entangled pairs as well as the selection process through coincidence measurements on photons (23) are explained by local interactions of the em. field with the various "devices" used to manipulate them [...]
My take on this is that QFT achieves "locality" through propagators reaching into the backward light cone, leading to some kind of retro-causation. Events involving photons with the "wrong properties" (e.g. wrong polarization) could never happen. Nature's book keeping is always consistent!
 
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What do you mean by "retro-causation"?
 
  • #7
A "cause" being in the future of the "effect". Of course we are habituated to label an event A happening before event B as the cause, and B as its effect. The propagators ensure that any events A and B are always consistent.
 
  • #8
This wouldn't be acausality. QFT is to the contrary one way to assure that exactly such acausalities don't occur in relativistic QT (in contradistinction to the historical attempts to formulate relativistic QT in "1st-quantized form").
 
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vanhees71 said:
This wouldn't be acausality.
Of course not. I'm not worried about causality.
If one radioactive atom is surrounded by several detectors, how do you explain that at most one of the detectors will register the decay? Wouldn't all detectors be sensitive to the quantum field? How can you avoid that two detectors trigger, if evolution can only be forward in time? It is obvious that there is some dependence of earlier events on the available final states (events). I'd rather avoid the term causation, and talk about consistency of our description.
 
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  • #10
vanhees71 said:
the principle of "microcausility" and thus "locality"
In other words, you think "locality" means "microcausality". But not everyone agrees with this definition of words.

I emphasize (again, since this has come up in mutiple threads) that this is not a dispute about physics. Nobody has disputed anything about the physics you are describing. The issue is purely one of words: you keep insisting that the word "locality" has to mean what you want it to mean, i.e., "microcausality", but not everyone agrees with that. The word "locality" is used in the literature to mean multiple different things.

Aside from the insistence on one particular meaning of "locality", what you present in the OP of this thread is useful information and would not be disputed by anyone.

vanhees71 said:
it has been claimed my point of view of "locality" where "non-mainstream physics"
To be specific, the claim is that your insistence on one particular definition of "locality" is "non-mainstream physics", since, as noted above, there are multiple different definitions of that term in the literature. But, as noted above, that is a dispute about words, not about physics. Nobody has disputed any of the physics you are describing. Nobody disputes that quantum field theory has the properties and makes the predictions that you say it does. The only thing that is disputed is your unwillingness to acknowledge that there are other definitions of "locality" in the literature besides the one you prefer.
 
  • #11
I think this indeed is what physicists mean when they talk about locality. The problem in fact is that people use the same word with other meanings, and this leads to confusion, including the claim it was no mainstream physics. It has indeed repeatedly claimed that this mainstream physics is under dispute and that it were necessary to introduce a violation of locality in this sense to understand the findings in experiments realizing entanglement swapping, delayed-choice/quantum-eraser phenomena, teleportation etc. That's all I wanted to clarify.
 
  • #12
vanhees71 said:
I think this indeed is what physicists mean when they talk about locality.
Yes, we know that's your opinion.

vanhees71 said:
It has indeed repeatedly claimed that this mainstream physics is under dispute
No, it hasn't. The dispute is over your use of the word "locality". Nobody has ever disputed the physics you have presented.

If you disagree, please give a specific reference to a specific example.

vanhees71 said:
and that it were necessary to introduce a violation of locality in this sense to understand the findings in experiments realizing entanglement swapping, delayed-choice/quantum-eraser phenomena, teleportation etc.
Nobody has claimed that QFT, with all of the properties you state, does not predict the correct results for these experiments. The only dispute is over your use of the word "locality", which others do not agree is an appropriate word to use to describe such experimental results. But, as I have already noted, that is a dispute over words, not over physics.
 
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  • #13
It was in the thread you just closed ,before I could answer the claim that my "point of view" were not "mainstream physics". It's at least mainstream physics terminology in the HEP and nuclear physics as well as the quantum optics community. I just opened this thread to set this record straight. That's all.
 
  • #14
vanhees71 said:
It was in the thread you just closed ,before I could answer the claim that my "point of view" were not "mainstream physics".
That claim was about the use of the word "locality". I don't think there was any dispute about the actual physics.

vanhees71 said:
It's at least mainstream physics terminology in the HEP and nuclear physics as well as the quantum optics community.
That may indeed be the case, but those still are not the same as the entire quantum physics community as a whole. It would be nice if all of the different specialties within quantum physics would get together and agree on terminology, but unfortunately I don't expect that to happen any time soon. When there is any possibility of confusion, my recommendation is always to not use the problematic term at all and to instead refer to the actual underlying condition in the theory (for example, say "spacelike separated measurements commute" instead of "locality" for QFT).
 
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vanhees71 said:
Bell uses "local" in this standard sense of relativistic physics, i.e., that space-like separated events cannot be causally connected.
But Bell concludes that quantum theory is not local in that sense, while a minimal interpretation concludes that it is local. How would you explain this discrepancy?

My answer: Bell assumes that some events exist even without measurement, while minimal interpretation is based on the idea that unmeasured event is a nonsense.
 
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Demystifier said:
But Bell concludes that quantum theory is not local in that sense, while a minimal interpretation concludes that it is local. How would you explain this discrepancy?

My answer: Bell assumes that some events exist even without measurement, while minimal interpretation is based on the idea that unmeasured event is a nonsense.
I don't think "event" is the right word here. May be "value of an observable".
 
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martinbn said:
I don't think "event" is the right word here. May be "value of an observable".
Bell would say "value of a beable". For him, it is very important to distinguish the notion of beable from the notion of observable.
 
  • #18
Demystifier said:
Bell would say "value of a beable". For him, it is very important to distinguish the notion of beable from the notion of observable.
What is the difference in this context? If the value of an observable exists, then isn't that observable a beable?
 
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martinbn said:
What is the difference in this context? If the value of an observable exists, then isn't that observable a beable?
Conceptually, yes. But technically, observable is a self-adjoint operator and it's not clear what is the "value" of an operator. Eigenvalue? Mean value? Weak value? Something else?
 
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  • #20
PeterDonis said:
That claim was about the use of the word "locality". I don't think there was any dispute about the actual physics.
Then @DrChinese should not make such claims!
PeterDonis said:
That may indeed be the case, but those still are not the same as the entire quantum physics community as a whole. It would be nice if all of the different specialties within quantum physics would get together and agree on terminology, but unfortunately I don't expect that to happen any time soon. When there is any possibility of confusion, my recommendation is always to not use the problematic term at all and to instead refer to the actual underlying condition in the theory (for example, say "spacelike separated measurements commute" instead of "locality" for QFT).
That's why we always get into useless disputes about words. I strongly recommend to stick to the terminology of the "main-stream physics community". Then we could concentrate on the really interesting things and not always discuss what the one or the other metaphysicist understands under "locality", "reality", and all that. It was my hope that one could strictly shuffle all this non-physics stuff to the "interpretation forum", but it's obviously not possible, because it seems that even very clear experimental real-world setups are discussed in a way which leads into the philosophical abyss of imprecisely defined "words".
 
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  • #21
Demystifier said:
But Bell concludes that quantum theory is not local in that sense, while a minimal interpretation concludes that it is local. How would you explain this discrepancy?
This I don't understand. Where does Bell say this? I'm pretty sure that Bell was very well aware of the standard conception of the microcausality constraint underlying the very fundamentals of local (sic!) relativistic QFT.
Demystifier said:
My answer: Bell assumes that some events exist even without measurement, while minimal interpretation is based on the idea that unmeasured event is a nonsense.
I thought Bell only assumes this for his "realistic HV models". It's clearly contradicting basic (minimally interpreted) QT, and that's the very point: He derives from the assumptions of locality (which is a feature of both is "local realistic HV models" and local relativistic QFT AND "realism", i.e., that also unprepared observables take certain values. I think it's important to keep in mind that the state describes the preparation of the system rather than what's measured, and this is very important in our context too, because the preparation is in the very beginning of the here discussed kinds of Bell tests. In the entanglement-swapping experiment it's the state described by two uncorrelated photon-pair Bell states. Everything that comes later is the measurement, and you just select (or even post-select) subensembles based on (filter) measurements of the pair mixing one photon from each of the uncorrelated pair states (Photons 2+3 in the description of the paper). Only then, using the measurement protocoll for photons 1+4 you can check that now indeed photons 1+4 within each of the four subensembles is in the predicted entangled state. It's of course true that photons 1+4 have never interacted with each other or locally with any equipment. This entanglement of the subensemble is, however, not due to some "non-local interaction" but due to the selection of the states based on the local measurements on the phons 2+3, given the initially prepared entagled photon pairs (1+2) and (3+4). So the preparation of the pair 1+4 in an entangled state by selections based on the preparation of the pairs 1+2 and 3+4 in the very beginning, and also this preparation procedure does at no place violate locality in the sense of relativistic QFTs.

The important point of Bell's work for me is that the brought the vague alternative idea by EPR ("local realistic hidden variable theories") into the realm of science by finding an experimentally testable prediction of this class of models contradicting the predictions of local relativistic QFT. It may be that Bell himself was sympathising with local realistic HV theories as an alternative to Q(F)T, but the empirical facts have clearly disproven it.
 
  • #22
Demystifier said:
Bell would say "value of a beable". For him, it is very important to distinguish the notion of beable from the notion of observable.
"beable" is one of these buzzwords, I don't know what they are good for. I'd simply state that according to standard QT (no matter, whether relativistic or non-relativistic) it depends on the preparation of the system under consideration whether an observable takes a determined value or not and if not, how probable any possible outcome of a measurement of this observable is predicted to be.
 
  • #23
Demystifier said:
Conceptually, yes. But technically, observable is a self-adjoint operator and it's not clear what is the "value" of an operator. Eigenvalue? Mean value? Weak value? Something else?
An observable is described by a self-adjoint operator in the formalism. Physically it's a measurement procedure. Making "sharp measurements" (von Neumann measurements) the observables are predicted to take on values given by the spectrum of its describing self-adjoint operator, and the probability, given the state the system is prepared in when measured, is then given by Born's rule, for the general case as
$$P_A(a|\hat{\rho})=\sum_{b} \langle a,b|\hat{\rho}|a,b \rangle,$$
where ##|a,b \rangle## denotes an orthonormal set of eigenvectors of ##\hat{A}## with eigenvalue ##a##.

Of course you can generalize this in the more modern way with POVMs, which is more flexible realistic in being able to also include, e.g., the uncertainties of the measurement device itself (like temporal/spatial resolution of detectors etc.), but I don't think that the fundamental questions we discuss here are much affected by those refinements of the quantum theory of measurements.
 
  • #24
vanhees71 said:
This I don't understand. Where does Bell say this? I'm pretty sure that Bell was very well aware of the standard conception of the microcausality constraint underlying the very fundamentals of local (sic!) relativistic QFT.
See 2nd edition of his book, last chapter "La nouvelle cuisine".
In Sec. 6 he says: "Could the no-superluminal-signalling of ‘local’ quantum field theory be regarded as an adequate formulation of the fundamental causal
structure of physical theory? I do not think so."
In sec. 8: "However it has turned out that quantum mechanics cannot be
‘completed’ into a locally causal theory, at least as long as one allows,
as Einstein, Podolsky and Rosen did, freely operating experimenters."
 
  • #25
Demystifier said:
But Bell concludes that quantum theory is not local in that sense
Bell never claims that spacelike separated measurements do not commute. "Causally connected" in this sense means "do not commute".

Demystifier said:
My answer: Bell assumes that some events exist even without measurement, while minimal interpretation is based on the idea that unmeasured event is a nonsense.
Interpretation discussions are off topic in this forum. If you want to discuss interpretations, please start a new thread in the interpretations subforum.
 
  • #26
Demystifier said:
In Sec. 6 he says: "Could the no-superluminal-signalling of ‘local’ quantum field theory be regarded as an adequate formulation of the fundamental causal
structure of physical theory? I do not think so."
In sec. 8: "However it has turned out that quantum mechanics cannot be
‘completed’ into a locally causal theory, at least as long as one allows,
as Einstein, Podolsky and Rosen did, freely operating experimenters."
Bell's definition of "a locally causal theory" here is not the same as the one @vanhees71 is using. Bell was not disagreeing on any physics.
 
  • #27
vanhees71 said:
Then @DrChinese should not make such claims!
If you keep insisting on one meaning to a word that has multiple meanings in the literature, you are going to keep getting pushback.

vanhees71 said:
That's why we always get into useless disputes about words. I strongly recommend to stick to the terminology of the "main-stream physics community".
But your terminology is not "the terminology of the mainstream physics community", because there is no such thing in this case. There is not one "mainstream" terminology or one "mainstream" physics community involved here.

I have already given my recommendation for avoiding useless disputes about words: stop using the words that are causing the problem. In this case, that means stop using the word "locality" altogether and say what you actually mean. If what you actually mean is "spacelike separated measurements commute" then say that. If what you actually mean is "the Bell inequalities are violated" then say that. (And I would make the same recommendation to @DrChinese.)
 
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  • #28
Maybe, it might be helpful to listen to Don Howard who makes the following remark in his paper "EINSTEIN ON LOCALITY AND SEPARABILITY" :

Given their importance in what follows, the separability and locality principles should be clearly distinguished. To repeat: separability says that spatially separated systems possesses separate real states; locality adds that the state of a system can be changed only by local effects, effects propagated with finite, subluminal velocities. There is no necessary connection between the two principles, though they are frequently stated as if they were one. Some theories conform to both principles, general relativity being an example of such a separable, local theory. Other theories conform to just one or the other. Quantum mechanics is, on my interpretation, a non-separable, local theory. Examples of the opposite sort, namely, of separable, non-local theories, are to be found among the non-local hidden-variable theories.
 
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  • #29
Demystifier said:
See 2nd edition of his book, last chapter "La nouvelle cuisine".
In Sec. 6 he says: "Could the no-superluminal-signalling of ‘local’ quantum field theory be regarded as an adequate formulation of the fundamental causal
structure of physical theory? I do not think so."

Interesting. It would be even more interesting if he would have come up with a viable alternative. Maybe it could be a more satisfactory theory than relativistic QFT, which has its problems from a mathematical point of view.
Demystifier said:
In sec. 8: "However it has turned out that quantum mechanics cannot be
‘completed’ into a locally causal theory, at least as long as one allows,
as Einstein, Podolsky and Rosen did, freely operating experimenters."
Of course, Bell was well aware of this. Since the experiments by Aspect it was pretty clear that the EPR idea is ruled out by experiment.
 
  • #30
PeterDonis said:
If you keep insisting on one meaning to a word that has multiple meanings in the literature, you are going to keep getting pushback.But your terminology is not "the terminology of the mainstream physics community", because there is no such thing in this case. There is not one "mainstream" terminology or one "mainstream" physics community involved here.
This is what you claim. I don't know, why you insist on using unclear language in physics discussions. Usually you always want peer-reviewed references for claims. So now, I'd like to see one for the claim there is another meaning of "locality" in the physics (!) literature.
PeterDonis said:
I have already given my recommendation for avoiding useless disputes about words: stop using the words that are causing the problem. In this case, that means stop using the word "locality" altogether and say what you actually mean. If what you actually mean is "spacelike separated measurements commute" then say that. If what you actually mean is "the Bell inequalities are violated" then say that. (And I would make the same recommendation to @DrChinese.)
If we are not allowed to use standard physics terminology, how should we discuss physics at all?
 
  • #31
Demystifier said:
See 2nd edition of his book, last chapter "La nouvelle cuisine".
In Sec. 6 he says: "Could the no-superluminal-signalling of ‘local’ quantum field theory be regarded as an adequate formulation of the fundamental causal
structure of physical theory? I do not think so."
Hm, so Bell insists on his own definition. Sounds a bit like @vanhees71. 😉
 
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  • #32
PeterDonis said:
Bell never claims that spacelike separated measurements do not commute. "Causally connected" in this sense means "do not commute".
The point is that by construction the Hamilton density commutes with any local operator that represents and observable at space-like separated arguments. This means that space-like separated events can NOT by causally connected.
PeterDonis said:
Interpretation discussions are off topic in this forum. If you want to discuss interpretations, please start a new thread in the interpretations subforum.
This is well within the minimally interpreted realm of Q(F)T. It has nothing to do with interpretation. It's well-defined mathematical property of QFT and has the clear physical interpretation, given above.
 
  • #33
Lord Jestocost said:
Maybe, it might be helpful to listen to Don Howard who makes the following remark in his paper "EINSTEIN ON LOCALITY AND SEPARABILITY" :

Given their importance in what follows, the separability and locality principles should be clearly distinguished. To repeat: separability says that spatially separated systems possesses separate real states; locality adds that the state of a system can be changed only by local effects, effects propagated with finite, subluminal velocities. There is no necessary connection between the two principles, though they are frequently stated as if they were one. Some theories conform to both principles, general relativity being an example of such a separable, local theory. Other theories conform to just one or the other. Quantum mechanics is, on my interpretation, a non-separable, local theory. Examples of the opposite sort, namely, of separable, non-local theories, are to be found among the non-local hidden-variable theories.
[emphasis put in by me]

Thanks for posting this! That makes the point utmost clear. I hope we can stick to this clear language rather than insisting on the use of confusing mixing different concepts, which in my opinion only occur in the popular-science literature and, maybe, in some circles of the "philosophy-of-science" community.
 
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  • #34
PeterDonis said:
Bell's definition of "a locally causal theory" here is not the same as the one @vanhees71 is using. Bell was not disagreeing on any physics.
How do you come to the conclusiion that Bell used the term in a different way I did? In the quote he explicitly spoke about "local quantum field theory":
See 2nd edition of his book, last chapter "La nouvelle cuisine".
In Sec. 6 he says: "Could the no-superluminal-signalling of ‘local’ quantum field theory be regarded as an adequate formulation of the fundamental causal
structure of physical theory? I do not think so."
That he believes that local quantum field theory was not a satisfactory description of physics, is another point. I'd be keen to learn, which alternatives Bell had to offer. Unfortunately I don't have the quoted book at hand.
 
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vanhees71 said:
That he believes that local quantum field theory was not a satisfactory description of physics, is another point. I'd be keen to learn, which alternatives Bell had to offer.
He thought that some Bohmian version of QFT is what we need, without fundamental Lorentz invariance, but still with Lorentz invariant measurable predictions in the FAPP sense. Something very much in spirit with what I talk about in https://arxiv.org/abs/2205.05986
 
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