How does QFT handle non-locality?

[PFfan01]

[Split off from https://www.physicsforums.com/threa...ight-quantum-hypothesis.847848/#post-5329824]
As we know, there is a serious contradiction between nonlocal indeterminacy of quantum theory and local reality of special relativity, specifically reflected in the superluminal propagation of quantum states of an entangled electron pair. This problem probably comes from the wave-function assumption: The wave function collapses instantly when a measurement is made. I wonder, how is the problem solved in QFT? The fields of electron and positron disappear instantly when they annihilate?

 

[bhobba]

As we know, there is a serious contradiction between nonlocal indeterminacy of quantum theory and local reality of special relativity,

There is no conflict - except in the half truths of the pop sci press.

The principle QFT is based on is the so called cluster decomposition property which precludes correlations of the EPR type:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/
'It is one of the fundamental principles of physics (indeed, of all science) that experiments that are sufficiently separated in space have unrelated results…'

Its a 'simplistic' statement by Wienberg of the actual property, which is technically more subtle. But the bottom line is the same - EPR type correlations are precluded. And when you think about it its obvious they should be. Put a red slip of paper in an envelope, and a green slip in another. Send one to the other side of the universe and keep the other. Open one and you immediately know the other. Its exactly the same with EPR type correlations - they must be precluded if cluster decomposition is to make sense.

Also relativity is not based on local reality - its based on space-time symmetries. But that is a whole thread in itself for the relativity sub-forum - not the QM sub-forum.

Thanks
Bill

 

[PFfan01]

... experiments that are sufficiently separated in space have unrelated results…

But Fuwa at al claims:
... for the first time, we demonstrate Einstein's "spooky action at a distance" ...
See: http://www.nature.com/ncomms/2015/150324/ncomms7665/full/ncomms7665.html

I assume that Nature Communications reflects main-stream science.

 

[bhobba]

I assume that Nature Communications reflects main-stream science.

Yes - its acceptable - but doesn't make it correct.

Its wrong - and obviously so once you understand QM. You see the formalism of QM does not include collapse - that's only something some interpretations have.

When encountering papers that make grandiose claims like that best to do a search on what people say. Here is what I found:
http://physics.stackexchange.com/qu...nt-really-demonstrated-wave-function-collapse
'The paper doesn't explain how their predictions would differ from those of non-collapse theories. Since the paper doesn't even discuss what would be predicted without collapse, it is difficult to see how it could rule out quantum theory without collapse. Quantum theory without collapse explains all of the predictions commonly attributed to quantum theory with collapse:

http://arxiv.org/abs/1212.3245.

Variations on quantum theory that include collapse, such as the GRW theory, may or may not reproduce the predictions made in the paper, but as this is not discussed it is difficult to tell whether the results are even consistent with such a theory. As such, the title of the paper does not accurately describe its contents.'

We have had a number of similar papers discussed here. Invariably they are a misunderstanding of what's called weak measurements.

Thanks
Bill

 

[vanhees71]

Well, sometimes Nature tends to have quite spectacular headlines, and sometimes I'm a bit worried concerning their review politics. If I'd have had to review an article like this, I'd never let through such a title, let alone the abstract, which I'm able to read and find almost completely wrong! It reads like a bad pop science "explanation" but not like a scietific paper in a referees journal. I've no access to Nature Communications; so I can't say what really has been done; for sure not what's said in title and abtract, because if so, this would mean a clear disproof of very general principles of local microcausal relativistic quantum field theory. If this was really the case, I'd expect to have heard about this and a whole flood of new theory papers should have appeared on arXiv ;-)).

 

[PFfan01]

Yes - its acceptable - but doesn't make it correct.

Its wrong - and obviously so once you understand QM. You see the formalism of QM does not include collapse - that's only something some interpretations have.
...

Einstein's "spooky action at a distance" is the basis of quantum teleportation, which, reportedly, has been well verified experimentally, as Wang et al. claim:

"As well as being of fundamental interest, teleportation has been recognized as an important element in long-distance quantum communication, distributed quantum networks and measurement based quantum computation. There have been numerous demonstrations of teleportation in different physical systems such as photons, atoms, ions, electrons and superconducting circuits."

See: Quantum teleportation of multiple degrees of freedom of a single photon, https://www.researchgate.net/journal/1476-4687_Nature[/URL] (Impact Factor: 41.46). 02/2015; 518 (7540):516-9. DOI: 10.1038/nature14246; [URL]http://www.nature.com/nature/journal/v518/n7540/full/nature14246.html[/URL]

 

[bhobba]

Einstein's "spooky action at a distance" is the basis of quantum teleportation, which, reportedly, has been well verified experimentally, as Wang et al. claim:http://www.nature.com/nature/journal/v518/n7540/full/nature14246.html

Where are you getting this from? That's incorrect.

Once and for all, there is no definite spooky action at a distance - it's simply something some interpretations have. All EPR is, is a correlation. Bell sorted it out ages ago:
https://cds.cern.ch/record/142461/files/198009299.pdf

Thanks
Bill

 

[PFfan01]

Where are you getting this from? That's incorrect.

Once and for all, there is no definite spooky action at a distance - it's simply something some interpretations have. All EPR is, is a correlation. Bell sorted it out ages ago:
https://cds.cern.ch/record/142461/files/198009299.pdf

Thanks
Bill

So you should write a Comment to clarify the confusion.

In addition, I never heard "experiments that are sufficiently separated in space have unrelated results" is a fundamental principle. This statement itself is very ambiguous; "how far separated in space" is "sufficiently separated"?

 

[mfb]

In addition, I never heard "experiments that are sufficiently separated in space have unrelated results" is a fundamental principle. This statement itself is very ambiguous; "how far separated in space" is "sufficiently separated"?

Spacelike separated, so no light ray (or anything slower than light) can go from measurement event A to measurement event B or vice versa.

 

[bhobba]

In addition, I never heard "experiments that are sufficiently separated in space have unrelated results" is a fundamental principle. This statement itself is very ambiguous; "how far separated in space" is "sufficiently separated"?

In SR signals can't go FTL. So separate them by a distance greater than it takes light to travel during the experiment and what is done in one system can't affect the other.

This thread isn't about SR, but there is sufficient confusion about it in the pop-sci press seeing exactly what its about will likely help:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

The FTL stuff associated with EPR you have likely read about doesn't bypass this because it can't be used to send information so clocks can be synchronised.

Thanks
Bill

 

[PFfan01]

In SR signals can't go FTL. So separate them by a distance greater than it takes light to travel during the experiment and what is done in one system can't affect the other.

This thread isn't about SR, but there is sufficient confusion about it in the pop-sci press seeing exactly what its about will likely help:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

The FTL stuff associated with EPR you have likely read about doesn't bypass this because it can't be used to send information so clocks can be synchronised.

Thanks
Bill

1. "Experiments that are sufficiently separated in space have unrelated results" is your reasoning from special theory, and it cannot be sais to be a fundamental principle. In fact, you failed to provide a reference from master journals.

2. What you are trying to say is that the instant propagation of quantum states is not consistent with special theory, as I mentioned in Post #12.

3. Repeatedly, I would like to have the question of Post #12 for you: "As we know, there is a serious contradiction between nonlocal indeterminacy of quantum theory and local reality of special relativity, specifically reflected in the superluminal propagation of quantum states of an entangled electron pair. This problem probably comes from the wave-function assumption: The wave function collapses instantly when a measurement is made. I wonder, how is the problem solved in QFT? The fields of electron and positron disappear instantly when they annihilate?"

Thanks a lot.

 

[bhobba]

1. "Experiments that are sufficiently separated in space have unrelated results" is your reasoning from special theory, and it cannot be sais to be a fundamental principle. In fact, you failed to provide a reference from master journals.

Its from THE master textbook on QFT - written by the master field theorist - Wienberg - Quantum Theory Of Fields
https://www.amazon.com/dp/0521670535/?tag=pfamazon01-20

Its the textbook those that aspire to mastery of QFT work towards. Its beyond my current level - although I own them.

The level I am at is:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

The fields of electron and positron disappear instantly when they annihilate?"

Quantum fields are there all the time. They reside in a Fock Space:
https://en.wikipedia.org/wiki/Fock_space

Its in a superposition of zero particles, one particle etc etc. There is one field for photons, one for electrons and positions etc etc. As in ordinary QM all that happens is the state changes.

QED contains two interacting fields - the electron-positron field and the photon field. An electron-positron disappears the electron field changes and so does the photon field. Note - its not instantaneous but happens very very fast and like so much in QT modeled as a perturbation.

Thanks
Bill

 

[PFfan01]

Its from THE master textbook on QFT - written by the master field theorist - Wienberg - Quantum Theory Of Fields
https://www.amazon.com/dp/0521670535/?tag=pfamazon01-20
...
Bill

I do not have access to Weinberg book with the statement "Experiments that are sufficiently separated in space have unrelated results" as a fundamental principle, but I don't think it is the main-stream view, because Einstein's "spooky action at a distance" is the basis of quantum teleportation, which, reportedly, has been well verified experimentally, as Wang et al. claim:

"As well as being of fundamental interest, teleportation has been recognized as an important element in long-distance quantum communication, distributed quantum networks and measurement based quantum computation. There have been numerous demonstrations of teleportation in different physical systems such as photons, atoms, ions, electrons and superconducting circuits." See: Quantum teleportation of multiple degrees of freedom of a single photon, Nature (Impact Factor: 41.46). 02/2015; 518 (7540):516-9. DOI: 10.1038/nature14246; http://www.nature.com/nature/journal/v518/n7540/full/nature14246.html

There are thousands of papers in Physical Review and Nature, which support Einstein's "spooky action at a distance". Are they all wrong? Only Weinberg is correct? Why does Weinberg not write papers to rebut those "wrong" papers?

Note: You probably misunderstood the meaning of "master" in my post. I was told that Physics Forum accepts citations from journals only in Master Journal List: http://ip-science.thomsonreuters.com/mjl/

 

[bhobba]

There are thousands of papers in Physical Review and Nature, which support Einstein's "spooky action at a distance". Are they all wrong? Only Weinberg is correct? Why does Weinberg not write papers to rebut those "wrong" papers?

I gave the link to Bells paper that gives the detail of the situation. If any paper says different its WRONG - simple as that. While refereed papers are not perfect, by and large they are correct so what is more likely is you are misinterpreting it.

Note: You probably misunderstood the meaning of "master" in my post. I was told that Physics Forum accepts citations from journals only in Master Journal List: http://ip-science.thomsonreuters.com/mjl/

Obviously quotes from well respected standard texts are acceptable references.

Thanks
Bill

 

[PFfan01]

I gave the link to Bells paper that gives the detail of the situation. If any paper says different its WRONG - simple as that. While refereed papers are not perfect, by and large they are correct so what is more likely is you are misinterpreting it.

[Mentor's note: Copy-and-paste of copyrighted material removed]
http://www.iflscience.com/physics/einsteins-spooky-action-distance-confirmed-new-quantum-experiment

 

[PFfan01]

Obviously quotes from well respected standard texts are acceptable references.

I agree that "quotes from well respected standard texts are acceptable references", but I don't agree that they must be correct. This paper [Can. J. Phys. 93: 1470–1476 (2015)] picked out some mistakes in Weinberg's book, claiming: "It is found in the paper that the Landau–Lifshitz version of Laue’s theorem ... and Weinberg’s version of Laue’s theorem ... are both flawed, ...".

 

[PFfan01]

Chinese Physicists Measure Speed of “Spooky Action At a Distance”
Einstein railed against the possibility of spooky action at a distance because it violates relativity. Now Chinese physicists have clocked it traveling more than four orders of magnitude faster than light
http://www.technologyreview.com/view/512281/chinese-physicists-measure-speed-of-spooky-action-at-a-distance/

 

[bhobba]

Einstein railed against the possibility of spooky action at a distance because it violates relativity. Now Chinese physicists have clocked it traveling more than four orders of magnitude faster than light
http://www.technologyreview.com/view/512281/chinese-physicists-measure-speed-of-spooky-action-at-a-distance/

Again I know its wrong because of a theorem called Bells Theorem:
http://www.johnboccio.com/research/quantum/notes/paper.pdf

The theorem states: If QM is correct then you can't have both counter-factual definiteness and locality. You can have one or the other but not both. If you want locality then you can't have counter-factual definiteness. If you want counter-factual definiteness then you need FTL influences - but only if you want counter-factual definiteness. The paper claiming to have measured FTL influences is claiming to have shown that QM must have the property of counter-factual definiteness, which the formalism most definitely does not require. In other words they would have proven QM as it currently stands incomplete - which was Einstein's position. That would be BIG - no VERY BIG news earning the discoverer an instant Nobel prize.

How did it get by the referees process - well you already have had examples of that.

Again it almost certainly is a misunderstanding of so called weak measurements.

I see a pattern in your posts. You are told by me and other science advisor's you have misconceptions. Instead of taking it on board you squirm and post this paper or that paper that supposedly supports your position. Some of those science advisors are high powered Phd's in physics who have written textbooks on it. I am not in that category, but if I said anything that was incorrect rest assured they would have picked me up on it instead of liking my posts.

This is not the way to learn. If you keep it up I won't respond because its a waste of my time.

Thanks
Bill

 

[bhobba]

I agree that "quotes from well respected standard texts are acceptable references", but I don't agree that they must be correct. This paper [Can. J. Phys. 93: 1470–1476 (2015)] picked out some mistakes in Weinberg's book, claiming: "It is found in the paper that the Landau–Lifshitz version of Laue’s theorem ... and Weinberg’s version of Laue’s theorem ... are both flawed, ...".

Can I ask your level of training in QFT? Do you have the background to understand Weinberg? Its a very advanced text not for the faint of heart. Unless you are at that level then there is no way to tell who is correct. I am not at that level - Weinberg is currently beyond me.

In science, especially in advanced esoteric areas, there is sometimes disagreement. But that in no way changes things that are very well known, things like Bells Theorem. If they are proved wrong it would be big news - not simply a disagreement on some fine point of advanced theory.

Thanks
Bill

 

[vanhees71]

Well, but standard relativistic QFT is a very well-established part of physics and is in no way esoteric (it becomes only esoteric when one adds the esoteric ideas of some socalled "interpretations" of quantum theory, of which QFT is one specific formulation that go beyond the empirically testable and indeed very well tested minimal interpretation). The Standard Model describes all so far discovered particles with an astonishing precision (some quantities like the anomalous magnetic moment of the electron or the Lamb shift of the hydrogen-atom energy levels are of the most precise agreement between theory and experiment ever). Weinberg's books are just the most comprehensive treatment of relativistic QFT, starting from the very fundamental concepts as special-relativistic spacetime structure, the representation theory of the Poincare group, and S-matrix theory, showing that the assumption of locality, microcausality, and boundedness of the energy spectrum from below are sufficient conditions for the linked-cluster principle to hold. Without this principle it is hard to believe that natural science as we know it was possible at all. If every local experiment, accessible to human observation, would be strongly correlated with long-distant objects, we'd hardly have the control over our experimental setups as we have, which is obvious from the last 118 years of elementary particle physics (I count 1897, the year of the discovery of the electron as the first elementary particle (lepton) as the birth year of elementary-particle physics).

QFT in this well-established sense, as any formulation of QT, includes the possibility of socalled entangled states which includes the possibility of strong correlations, going beyond the possible correlations within any local deterministic theory, between observables of long-distant parts of a single quantum system. The astonishing thing is not that there seem to be "spooky actions at a distance" (as is the case in that flavor of the Copenhagen interpretation that assumes a collapse as an additional hypthesis and as was rightfully pointed out in the famous Einstein-Podolsky-Rosen paper) but that the strong correlations are explainable by QFT and thus compatible with the locality of interactions and that the linked-cluster principle is not violated either. Particularly, within standard QFT there is no possibility to use entanglement for faster-than-light communication and, to the contrary, the empirical verification of the long-range correlations require the exchange of "classical information" in terms of the measurement protocols done at the distant places, which can be transmitted at most with the speed of light in vacuo.

 

[mfb]

There are thousands of papers in Physical Review and Nature, which support Einstein's "spooky action at a distance". Are they all wrong? Only Weinberg is correct? Why does Weinberg not write papers to rebut those "wrong" papers?

Not the papers are wrong, your interpretation of them is wrong.

The formalism of quantum field theory is completely local. Take the commutator of spacelike separated points in spacetime: it is always zero.
Unfortunately, we cannot directly measure the fields of quantum field theory. We are limited to measurements that involve macroscopic systems, and QFT does not have concepts of "measurements". That's where the interpretations come in. Some of them describe nature with spooky actions at a distance - within those interpretations you can prove that the action has to be superluminal. Others interpretations have different descriptions without nonlocal effects.

 

[zonde]

The formalism of quantum field theory is completely local.

I would like to ask how would you argue that Fock space is local?
I am asking this because as I understand Fock space combines single particle Hilbert spaces in nontrivial way i.e. it restricts multiparticle states to symmetrized or anti-symmetrized combinations. And if two particles are distant when some manipulations are performed with individual particles (say rotation of polarization) Fock space seems to restrict resulting two particle states.

 

[atyy]

[Split off from https://www.physicsforums.com/threa...ight-quantum-hypothesis.847848/#post-5329824]
As we know, there is a serious contradiction between nonlocal indeterminacy of quantum theory and local reality of special relativity, specifically reflected in the superluminal propagation of quantum states of an entangled electron pair. This problem probably comes from the wave-function assumption: The wave function collapses instantly when a measurement is made. I wonder, how is the problem solved in QFT? The fields of electron and positron disappear instantly when they annihilate?

QFT solves the problem by not having local reality. If there is a reality to QFT, then QFT is nonlocal.

QFT has collapse, exactly the same as quantum mechanics.

While QFT conflicts with local reality, it does not permit superluminal transfer of infornation, so it is still consistent with special relativity in the operational sense.

 

[atyy]

I do not have access to Weinberg book with the statement "Experiments that are sufficiently separated in space have unrelated results" as a fundamental principle, but I don't think it is the main-stream view, because Einstein's "spooky action at a distance" is the basis of quantum teleportation, which, reportedly, has been well verified experimentally, as Wang et al. claim:

Weinberg's book is wrong on this point.

You should be aware that the "spooky action at a distance" has only been proven if we also assume that reality exists.

 

[mfb]

If there is a reality to QFT, then QFT is nonlocal.

Where exactly is the nonlocal interaction of fields?

QFT has collapse, exactly the same as quantum mechanics.

Where exactly is the equation describing this collapse?

 

[vanhees71]

I would like to ask how would you argue that Fock space is local?
I am asking this because as I understand Fock space combines single particle Hilbert spaces in nontrivial way i.e. it restricts multiparticle states to symmetrized or anti-symmetrized combinations. And if two particles are distant when some manipulations are performed with individual particles (say rotation of polarization) Fock space seems to restrict resulting two particle states.

I don't understand the question. In which sense should a Hilbert space be "local" or "nonlocal"?

 

[vanhees71]

Weinberg's book is wrong on this point.

You should be aware that the "spooky action at a distance" has only been proven if we also assume that reality exists.

Of course not. Weinberg is correct. It's a clear mathematical statement about local QFT and it's an entire chapter in his book, explaining it very well! There are sometimes claims that "spooky action at a distance" is "observed", even in highly reputated journals like Nature, but it's not very convincing. All these terms of proving some esoteric idea that clearly contradicts basic facts about local QFTs can as well be interpreted in the standard way without the esoterics. If not, that would mean a scientific revolution probably comparable to the discovery of quantum theory itself!

 

[atyy]

Where exactly is the nonlocal interaction of fields?

The collapse is nonlocal.

Where exactly is the equation describing this collapse?

The equation describing the collapse is in Weinberg's QFT text, Volume 1, Eq 2.1.7. This is neither the most general nor the most modern way of stating the collapse postulate. One can find the modern way in http://arxiv.org/abs/0706.3526 Eq 3 and 4.

 

[atyy]

Of course not. Weinberg is correct. It's a clear mathematical statement about local QFT and it's an entire chapter in his book, explaining it very well! There are sometimes claims that "spooky action at a distance" is "observed", even in highly reputated journals like Nature, but it's not very convincing. All these terms of proving some esoteric idea that clearly contradicts basic facts about local QFTs can as well be interpreted in the standard way without the esoterics. If not, that would mean a scientific revolution probably comparable to the discovery of quantum theory itself!

Weinberg is wrong (more likely sloppy, but in the context of this thread where he is being quoted as stating some fundamental postulate of QFT, the presentation of his statement is wrong). Weinberg is wrong because distant experiments can be correlated.

 

[Demystifier]

Of course not. Weinberg is correct.

Weinberg is slightly wrong, but not seriously wrong. See
https://www.physicsforums.com/threads/cluster-decomposition-and-epr-correlations.409861/
especially posts #5 and #7.

 

[atyy]

What Weinberg should have written as the English corresponding to cluster decomposition was "Classical information cannot be transmitted faster than light."

 

[Demystifier]

QFT does not have concepts of "measurements".

Any QFT text that relates the theory with its measurable predictions has some (explicit or implicit) notion of measurement.

 

[Demystifier]

Typically, particle physicists don't understand non-locality of quantum theory. It has been nicely pointed out by Scott Aaronson (an expert in classical and quantum computation theory) in
http://www.scottaaronson.com/democritus/lec9.html
where he writes:
"For example, I've had experts in quantum field theory -- people who've spent years calculating path integrals of mind-boggling complexity -- ask me to explain the Bell inequality to them. That's like Andrew Wiles asking me to explain the Pythagorean Theorem."

(For those who don't know, Andre Wiles is the mathematician who proved the Fermat's last theorem.)

 

[mfb]

The collapse is nonlocal.

But a collapse is not part of the framework of QFT. See below.

The equation describing the collapse is in Weinberg's QFT text, Volume 1, Eq 2.1.7. This is neither the most general nor the most modern way of stating the collapse postulate. One can find the modern way in http://arxiv.org/abs/0706.3526 Eq 3 and 4.

That is outside the scope of QFT already, it is bound to an interpretation. Busch let's an unspecified measurement process happen and assume this "collapses" the wave function. Equation 3 considers the state after this magic collapse.

Any QFT text that relates the theory with its measurable predictions has some (explicit or implicit) notion of measurement.

Yes, because every relation to measurable predictions happens via an interpretation. Some interpretations are nonlocal. No one ever doubted that. Other interpretations are local. If QFT would be inherently nonlocal, there would be no local interpretations.

 

[vanhees71]

Typically, particle physicists don't understand non-locality of quantum theory. It has been nicely pointed out by Scott Aaronson (an expert in classical and quantum computation theory) in
http://www.scottaaronson.com/democritus/lec9.html
where he writes:
"For example, I've had experts in quantum field theory -- people who've spent years calculating path integrals of mind-boggling complexity -- ask me to explain the Bell inequality to them. That's like Andrew Wiles asking me to explain the Pythagorean Theorem."

(For those who don't know, Andre Wiles is the mathematician who proved the Fermat's last theorem.)

To the contrary, HEP theorists (also HE nuclear physicists ;-)) have an everyday insight into relativistic local QFT, and that's why it is hard for us to understand claims of nonlocality of interactions, because it's at the heart of the theory by construction to not make such a causility violating "action at a distance" possible. That's why local operators that represent observables commute at space-like separated arguments by construction.

There are long-ranged correlations described by entanglement also in relativistic local QFT, but this has nothing to do with action at a distance or non-local interactions. As atyy stated there's no classical signal propagation faster than light possible. If you don't use classical information exchange between the far-distant observers they cannot find the long-ranged correlations and that's why entanglement is compatible with the locality of interactions and that's the content of the cluster-decomposition principle as explained in Weinberg's Quantum Theory of Fields vol. I. I haven't found any mistake in this chapter. Could you point to precisely where you think there's something wrong there?

 

[HomogenousCow]

I've always found it weird that textbooks motivate by QFT by showing that particles have a non-zero probability of traveling outside their light cones in NRQM, but then after they're done with the quantization of the KG Lagrangian they completely forget about this issue, instead what they only show is that observables at different events commute with others outside of their light cones. I don't find it obvious that this alone preserves causality.

 

[zonde]

I don't understand the question. In which sense should a Hilbert space be "local" or "nonlocal"?

And I don't understand your's. I was asking about Fock space not single particle Hilbert space.

 

[atyy]

But a collapse is not part of the framework of QFT. See below.That is outside the scope of QFT already, it is bound to an interpretation. Busch let's an unspecified measurement process happen and assume this "collapses" the wave function. Equation 3 considers the state after this magic collapse.
Yes, because every relation to measurable predictions happens via an interpretation. Some interpretations are nonlocal. No one ever doubted that. Other interpretations are local. If QFT would be inherently nonlocal, there would be no local interpretations.

My comments are within the standard interpretation. Other interpretations that are able to be local are nonstandard and must state their assumptions.

Eg. Weinberg uses the standard interpretation when he write his collapse equation. So it is not only Busch. So do Landau and Lifshitz, Cohen-Tannoudji, Nielsen and Chuang. All have collapse.

 

[mfb]

My comments are within the standard interpretation. Other interpretations that are able to be local are nonstandard and must state their assumptions.

What is a "standard" interpretation?
If an interpretation is adding something like nonlocal effects, you should not claim that the theory is nonlocal: it is not. Your favorite interpretation of the local theory is nonlocal, that is a completely different statement.

Eg. Weinberg uses the standard interpretation when he write his collapse equation. So it is not only Busch. So do Landau and Lifshitz, Cohen-Tannoudji, Nielsen and Chuang. All have collapse.

The Copenhagen interpretation is widely used in descriptions, but that does not make it part of the theory.

 

[atyy]

What is a "standard" interpretation?
If an interpretation is adding something like nonlocal effects, you should not claim that the theory is nonlocal: it is not. Your favorite interpretation of the local theory is nonlocal, that is a completely different statement.

The Copenhagen interpretation is the standard interpretation. To avoid the Bell theorem, one needs something like MWI. I think it's pretty fair to say that MWI is nonstandard, eg. all outcomes occur.

 

[zonde]

Yes, because every relation to measurable predictions happens via an interpretation. Some interpretations are nonlocal. No one ever doubted that. Other interpretations are local. If QFT would be inherently nonlocal, there would be no local interpretations.

Considering what you say the best you can claim is that QFT is consistent with locality given there is scientifically sound local interpretation.

You see, if you use relative descriptions for distant things then the model is non-local. It might be consistent with locality if you can convert relative descriptions into absolute descriptions.

 

[Demystifier]

the cluster-decomposition principle as explained in Weinberg's Quantum Theory of Fields vol. I. I haven't found any mistake in this chapter. Could you point to precisely where you think there's something wrong there?

Please see the link in post #30.

 

[vanhees71]

I've always found it weird that textbooks motivate by QFT by showing that particles have a non-zero probability of traveling outside their light cones in NRQM, but then after they're done with the quantization of the KG Lagrangian they completely forget about this issue, instead what they only show is that observables at different events commute with others outside of their light cones. I don't find it obvious that this alone preserves causality.

Well, that's the point! We construct QFT such that it has this feature of microcausality. You are right, it's not enough to have this feature to prove causality. For that you need the Poincare covariance of the S-matrix elements, and one can show that the construction of microcausal local QFTs is sufficient for that. As far as I know, it's not clear whether it is also necessary. Pragmatically you can say that so far the paradigm of this kind of relativistic QT is very successful.

Of course, it's not complete in several aspects: First of all it's not mathematically rigorous, i.e., it is not clear whether QFT really is a mathematical solid theory beyond the perturbative techniques or lattice gauge theory (usually applied to QCD) we use to evaluate it. Second, it's not complete concerning also the physical aspects. The Standard Model of Particle physics (updated to incorporate neutrino mass and oscillations) does not describe dark matter, and last but not least there's no consistent description of gravity yet.

 

[vanhees71]

Please see the link in post #30.

Well this doesn't refer to the linked-cluster principle as explained in Weinberg, let alone pointing out a mathematical error in his treatment. If I find the time, I'll read this chapter again carefully over the weekend.

 

[mfb]

Considering what you say the best you can claim is that QFT is consistent with locality given there is scientifically sound local interpretation.

You see, if you use relative descriptions for distant things then the model is non-local. It might be consistent with locality if you can convert relative descriptions into absolute descriptions.

If you also introduce magical fairies, you have magical fairies. Does that mean QFT has magical fairies? Do we have to say "QFT is consistent with the nonexistence of magical fairies", or can we just say "QFT does not have magical fairies"?

 

[zonde]

If you also introduce magical fairies, you have magical fairies. Does that mean QFT has magical fairies? Do we have to say "QFT is consistent with the nonexistence of magical fairies", or can we just say "QFT does not have magical fairies"?

Physical reality is a must for physics theory while magical fairies are not.
If you have mathematical model and when you establish correspondence with physical reality you attribute the same mathematical object to two distant things then it's non-local as a physics theory. Establishing correspondence with physical reality is a must for mathematical model if we view it as physics theory. Establishing correspondence with magical fairies on the other hand is not required.

 

[atyy]

Well, that's the point! We construct QFT such that it has this feature of microcausality. You are right, it's not enough to have this feature to prove causality. For that you need the Poincare covariance of the S-matrix elements, and one can show that the construction of microcausal local QFTs is sufficient for that. As far as I know, it's not clear whether it is also necessary. Pragmatically you can say that so far the paradigm of this kind of relativistic QT is very successful.

Of course, it's not complete in several aspects: First of all it's not mathematically rigorous, i.e., it is not clear whether QFT really is a mathematical solid theory beyond the perturbative techniques or lattice gauge theory (usually applied to QCD) we use to evaluate it. Second, it's not complete concerning also the physical aspects. The Standard Model of Particle physics (updated to incorporate neutrino mass and oscillations) does not describe dark matter, and last but not least there's no consistent description of gravity yet.

Microcausality is not local reality.

Weinberg's error is not mathematical, but in his English explanation of the mathematics. The correct explanation of the linked cluster principle is that no superluminal transmision of classical information is allowed (ie. spacelike observables commute), and that time evolution preserves the inability for superluminal communication (linked cluster principle).

 

[ddd123]

Isn't the Aharonov-Bohm effect nonlocal too? What does QFT say about that?

 

[mfb]

Physical reality is a must for physics theory while magical fairies are not.
If you have mathematical model and when you establish correspondence with physical reality you attribute the same mathematical object to two distant things then it's non-local as a physics theory. Establishing correspondence with physical reality is a must for mathematical model if we view it as physics theory. Establishing correspondence with magical fairies on the other hand is not required.

You are combining one specific interpretation with QFT, and you call both together "theory". The interpretations are called interpretations instead of theories for a good reason. QFT delivers amplitudes (in a broad sense) and nothing else. The calculation to get those amplitudes are local. Everything beyond that is interpretation, and there are both local and nonlocal interpretations. Yes, you need interpretations to perform experiments and to test QFT, but you do not need nonlocal interpretations.

Isn't the Aharonov-Bohm effect nonlocal too? What does QFT say about that?

It is local, and it works as local effect in all interpretations.

 

[vanhees71]

Microcausality is not local reality.

Weinberg's error is not mathematical, but in his English explanation of the mathematics. The correct explanation of the linked cluster principle is that no superluminal transmision of classical information is allowed (ie. spacelike observables commute), and that time evolution preserves the inability for superluminal communication (linked cluster principle).

But that's all you need to make QT consistent with relativistic causality. As I said, I'm not sure whether microcausality is necessary for the linked-cluster principle to be valid. It's, however, sufficient, and that's nicely shown in Weinberg's book. I guess, I have to read the chapter again to see what may be wrong with the wording around it.

In the same sense you can say, the assumption of a collapse is just words. The difference is that the linke-cluster principle is essential for QFT being compatible with the relativistic space-time structure (and causality) while the collapse is simply not needed for anything and makes the theory inconsistent with relativistic causality. In a sense it is a contradiction to the linked-cluster principle.