How does QFT handle non-locality?

[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.

 

[atyy]

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.

Why but? Weinberg is simply wrong. That's all.

 

[ShayanJ]

Now that we're talking about Weinberg's mistakes, I want to mention something I've always wanted to mention but haven't found the opportunity.
Weinberg defines a ray as(sect. 2.1, page 49, end of the page):

A ray is a set of normalized vectors (i.e., $(\Psi,\Psi)=1$) with $\Psi$ and $\Psi'$ belonging to the same ray if $\Psi'=\xi \Psi$, where $\xi$ is an arbitrary complex number with $|\xi|=1$.

But as I understand it(which I'm pretty sure is correct), $\xi$ doesn't have to be unit-norm and it can be any complex number. Its just that even after choosing a particular vector on the ray, we still have the freedom to multiply it by a unit-norm complex number.
I just want to provide an example of simple mistakes that even Weinberg can make so maybe its not too bold to say he's wrong on something else too.

 

[zonde]

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.

You mean that I implied collapse? But I didn't, my statement was very general.
And you have to square amplitudes to establish minimum correspondence to physical reality (experimentally observed relative frequencies). I suppose that this operation is present in any interpretation.

The calculation to get those amplitudes are local.

Calculations to get single particle amplitudes can be local, that's clear. But how would you argue that you can get by local calculations amplitudes that give you coincidence rates of distant entangled particles?

Yes, you need interpretations to perform experiments and to test QFT, but you do not need nonlocal interpretations.

I don't understand this. You don't need interpretation to take module squared of probability amplitude. And that's enough to perform experimental tests of QFT, right?

 

[atyy]

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.

This is wrong. Collapse is not a contradiction to the linked cluster principle. The linked cluster principle and the commutation of spacelike observables means "no superluminal signalling". However, although collapse is inconsistent with the reality of relativistic spacetime causality, it is not inconsistent with "no superluminal signalling". One way to see that you are wrong is that the "no signalling" set is bigger than the "relativistic spacetime causality" or "local" sets, eg. Fig 2 of http://arxiv.org/abs/1303.2849.

 

[mfb]

@zonde: squares of local things are still local.
The coincidence is not a physical event. You can have observers note this coincidence - but only with a time- or lightlike connection. See how the local interpretations handle this: it works.

 

[zonde]

squares of local things are still local.

Pure math is not local or non-local. Local or non-local are terms that describe physical reality not math. So you have to establish at least minimal correspondence with physical reality to speak about locality. With that on mind your statement is upside down: if squares (that represent relative frequencies of local detection events) are local you can argue that amplitudes should be considered local too. Unless of course you propose to establish direct correspondence between amplitudes and physical reality.

The coincidence is not a physical event.

Coincidence is not physical event but it is a physical observation. And my argument is based on how apparent FTL speeds of neutrinos in Opera experiment were perceived. It was considered that if FTL results of Opera experiment would be confirmed it would violate SR. And exactly for that reason it was considered so unbelievable and thoroughly investigated. Opera experiment looked at coincidences between emission and detection events and results of such analysis are considered physical as it takes physical observation to falsify physics theory (SR in this case).
But of course coincidence is not a basic physical observation. Basic physical observation is detection records with time tags. But derivations of coincidences and subsequent relative coincidence rates are external to QM so that results should be taken as physical observation by QM.

See how the local interpretations handle this: it works.

This thread is not about interpretations but about QFT instead. So please don't try to drag this discussion into discussion about interpretations.
But as you made the argument please name these interpretations. Then I could ask questions about these interpretations in another thread.

 

[vanhees71]

This is wrong. Collapse is not a contradiction to the linked cluster principle. The linked cluster principle and the commutation of spacelike observables means "no superluminal signalling". However, although collapse is inconsistent with the reality of relativistic spacetime causality, it is not inconsistent with "no superluminal signalling". One way to see that you are wrong is that the "no signalling" set is bigger than the "relativistic spacetime causality" or "local" sets, eg. Fig 2 of http://arxiv.org/abs/1303.2849.

Sure, it's inconsistent with "no superluminal signalling", because if you assume that the measurement of A's photon's polarization in the usual polarization-entangled biphoton state, leads to a collapse of the two-photon state, the polarization of B's photon is instantaneously determined, while before A's measurement it's maximally (in the sense of information theory) undetermined.

I've still to carefully read Brunner et al's RMP, but as long as quantum correlations are a subset of no-signalling correlations, everything is fine, right? But then one must abandone (at least the naive) collapse hypothesis.

 

[atyy]

Sure, it's inconsistent with "no superluminal signalling", because if you assume that the measurement of A's photon's polarization in the usual polarization-entangled biphoton state, leads to a collapse of the two-photon state, the polarization of B's photon is instantaneously determined, while before A's measurement it's maximally (in the sense of information theory) undetermined.

Let's suppose the initial state is |uu>+|dd>

When A measures u, then the state will immediately collapse to |uu>, so B will measure u with certainty. But can B tell that A made a measurement? He cannot, because if A always measures before B, A will collapse the state to |uu> half the time and to |dd> the other half of the time. But if A measures after B, then B will measure u half the time and d half the time. So although taking collapse as reality will violate relativistic causality as something real, collapse does not lead to any superluminal communication. This is why collapse is consistent with "no superluminal signalling".

I've still to carefully read Brunner et al's RMP, but as long as quantum correlations are a subset of no-signalling correlations, everything is fine, right? But then one must abandone (at least the naive) collapse hypothesis.

The quantum correlations are a subset of no-signalling, and the relativistic causality correlations are a subset of the quantum correlations. Quantum mechanics including collapse violates relativistic causality as something real, but it does not violate no signalling.

 

[vanhees71]

Let's suppose the initial state is |uu>+|dd>

When A measures u, then the state will immediately collapse to |uu>, so B will measure u with certainty. But can B tell that A made a measurement? He cannot, because if A always measures before B, A will collapse the state to |uu> half the time and to |dd> the other half of the time. But if A measures after B, then B will measure u half the time and d half the time. So although taking collapse as reality will violate relativistic causality as something real, collapse does not lead to any superluminal communication. This is why collapse is consistent with "no superluminal signalling".

Sure, but still the state change assumed by the collapse is instaneously acting over a long distance. Your argument of unobservability of the collapse is a perfect argument to just abandon the postulate of collapse.

It's clear that Alice get's the correct result about what Bob will find, assuming that after her measurement the state is $|uu \rangle$, but it doesn't apply that anything happens instantaneously to B's particle due to A's local spin measurement. So what you call a "collapse" here is just the adaption of A's description of the system after she made her measurement, it's not a statement of some physical process acting instantaneously on B's particle.

The quantum correlations are a subset of no-signalling, and the relativistic causality correlations are a subset of the quantum correlations. Quantum mechanics including collapse violates relativistic causality as something real, but it does not violate no signalling.

This I don't understand. If the collapse is taken as a real physical phenomenon then it violates relativistic causality. If it's taken as something non-real, you can just forget about it. I don't know of any example of the application of quantum theory where you need to assume the collapse as a real physical process, and that's why I don't understand, why it is still used today (or after 1935, when EPR pointed out that it's contradicting relativistic causality).

 

[Demystifier]

This I don't understand.

This only confirms my note in #33.
Now seriously, I am trying to understand what exactly you don't understand. Do you know what is signal locality and do you understand why is collapse compatible with signal locality?