A How do entanglement experiments benefit from QFT (over QM)?

[DrChinese]

Its inaccurate to talk about a pair of photons traveling. What travels is a single quantun system in an entangled 2-photon state. In QFT it is impossible to separate this system into two photons. This is called inseparability.

I couldn't agree more. Although it's common practice to reference each as subsystems (or components) simply for shorthand purposes (since they eventually result in 2 particles).

However, you eventually have the combined system breaking out into what becomes 2 independent single particle systems (for example an entangled pair of electrons becomes 2 unentangled electrons). We don't know exactly when or how that happens (from experimental considerations), just that at some later time, that's what we find.

[entangled system with particle number=2] -> [independent particle A] + [independent particle B]

But while it is an inseparable system: it has both spatial and/or temporal extent... and therefore it should not be thought of as a localized quantum object. And clearly, the nature of an observation on one of the components somehow affects the other - or vice versa. Or it is mutual. I don't know. But clearly trying to describe it initially as 2 independent components can't be right (as you rightfully object); and trying to describe the correlated results as independently arrived at also can't be right (as Bell would object).

So I again ask: if we start with an entangled system which has spatial extent, and we measure one of the components A: how does the other B come into being with some observable strongly correlated to the A component?

And of course, I am asking how QFT would handle that, as vanhees71 asserts it offers an explicit local mechanism. (And I don't think it does, because of Bell.)

 

[bhobba]

Its inaccurate to talk about a pair of photons traveling. What travels is a single quantun system in an entangled 2-photon state. In QFT it is impossible to separate this system into two photons. This is called inseparability.

Its responsible for why its not like the classical green and red slip discussion in articles on EPR. The slips are always separate objects - in QM if entangled that's not true - they are inseparable, but of course you can still observe each part - but the observable is different to the observable if that part was a single system - it acts on the whole entangled system. Its also the usual starting point of discussions on decoherence even though by itself is not quite what we think of as decoherence which usually includes an environment as well.

Thanks
Bill

 

[DarMM]

Well in a sense inseperability isn't that odd or shocking. Classical statistical theories have inseparability as well since in general the distribution for two observables does not factor, i.e. $p(a,b) \neq p(a)p(b)$. However pure states would always factor.

If the classical theory has an epistemic limit then we would have the interesting feature that there can be pure states do not factor, just like quantum theory.

Thus inseparability is not unique to QM.

It's really the violation of the CHSH inequalities (or generalizations thereof) by a subset of entangled states that's the "shocking" part of QM.

 

[bhobba]

So I again ask: if we start with an entangled system which has spatial extent, and we measure one of the components A: how does the other B come into being with some observable strongly correlated to the A component?

That's axiom 1 in Ballentine. Why is the outcome an eigenvalue, and why is it the particular eigenvalue that is observed. We do not know, or even if its an in issue to worry about. By construction the particular observation of this single system is |a>|b> or |b>|a>. How the entangled system is prepared ensures |a> and |b> are correlated,

As I have mentioned my view is correlated systems is difficult to include in discussions of locality because by construction they always have a certain relationship.

Thanks
Bill

 

[DrChinese]

As I have mentioned my view is correlated systems is difficult to include in discussions of locality because by construction they always have a certain relationship.

No issue there. And I would call that relationship "quantum nonlocal". It certainly shouldn't be called "local" (or anything that implies that c is respected in the process of the entangled system evolving into 2 independent particles in a Product State). Obviously, the distance between a) the measurement that terminates the entanglement; and b) the other now independent partner; is too great for that.

 

[A. Neumaier]

No issue there. And I would call that relationship "quantum nonlocal". It certainly shouldn't be called "local" (or anything that implies that c is respected in the process of the entangled system evolving into 2 independent particles in a Product State). Obviously, the distance between a) the measurement that terminates the entanglement; and b) the other now independent partner; is too great for that.

The 2-particle systen is already nonlocal, so it shouldn't be surprising that it generates nonlocal effects. The intuitive problems come solely from treating the system as two separate entities - which it never is. Only the recorded events are separate things.

 

[DennisN]

Interesting discussion going on here!

The intuitive problems come solely from treating the system as two separate entities - which it never is. Only the recorded events are separate things.

With "recorded events" I assume you mean when the detectors detect the events, or? If so, is an entangled photon pair (system) a nonseparate entity after one (or the other) photon passes a polarizer? I'm a bit confused .

 

[DrChinese]

Interesting discussion going on here!

With "recorded events" I assume you mean when the detectors detect the events, or? If so, is an entangled photon pair (system) a nonseparate entity after one (or the other) photon passes a polarizer? I'm a bit confused .

That is a tough question to answer. The general thinking has long been that polarizer outputs (for A) could be recombined to restore the original entangled system (of A+B). And regardless of that, it is not clear whether the OTHER part of the entangled system (B) changes when a final measurement is made on A or only when B itself is measured. I think all of that is interpretation dependent, lacking experimental clarity.

 

[DrChinese]

A previous reference posted by someone related to this thread (I forget who) says:

Relativistic causality =
No signaling = "...the local probability distributions of one experimenter (marginal probabilities) are independent of another experimenter’s choices."

Their definition more or less matches the microcausality of vanhees71. And they reference:

https://arxiv.org/abs/quant-ph/9508009Daniel Rohrlich and Sandu Popescu (1995)

"Quantum mechanics and relativistic causality together imply nonlocality: nonlocal correlations (that violate the CHSH inequality) and nonlocal equations of motion (the Aharonov-Bohm effect) "

So this is what I deduce from above:

a) We have a theory (QFT) that embeds relativistic causality (no signaling) explicitly.
b) There is (traditional) quantum nonlocality within that theory, as relates entanglement and some other effects.

The result is a theory that respects "no signaling" but reproduces the Entangled State statistics of QM. That would explain (to some extent) why vanhees71 insists there is microcausality in QFT, but why I insist that quantum nonlocality is a generally accepted feature of generally accepted quantum theories. You could even say we are both correct.

 

[A. Neumaier]

A previous reference posted by someone related to this thread (I forget who) says:

Relativistic causality =
No signaling = "...the local probability distributions of one experimenter (marginal probabilities) are independent of another experimenter’s choices."

Their definition more or less matches the microcausality of vanhees71. And they reference:

https://arxiv.org/abs/quant-ph/9508009Daniel Rohrlich and Sandu Popescu (1995)

"Quantum mechanics and relativistic causality together imply nonlocality: nonlocal correlations (that violate the CHSH inequality) and nonlocal equations of motion (the Aharonov-Bohm effect) "

So this is what I deduce from above:

a) We have a theory (QFT) that embeds relativistic causality (no signaling) explicitly.
b) There is (traditional) quantum nonlocality within that theory, as relates entanglement and some other effects.

The result is a theory that respects "no signaling" but reproduces the Entangled State statistics of QM. That would explain (to some extent) why vanhees71 insists there is microcausality in QFT, but why I insist that quantum nonlocality is a generally accepted feature of generally accepted quantum theories. You could even say we are both correct.

If quantum nonlocality is defined as the possibility of violation of Bell inequalities then causality and quantum nonlocality coexist in relativistic QFT.

 

[A. Neumaier]

That is a tough question to answer. The general thinking has long been that polarizer outputs (for A) could be recombined to restore the original entangled system (of A+B). And regardless of that, it is not clear whether the OTHER part of the entangled system (B) changes when a final measurement is made on A or only when B itself is measured. I think all of that is interpretation dependent, lacking experimental clarity.

A polarizer is a dissipative instrument, hence such a recombination is impossible. A recombination is in principle possible, however, for passing a Stern-Gerlach magnet, which is a unitary process.

 

[A. Neumaier]

Interesting discussion going on here!

With "recorded events" I assume you mean when the detectors detect the events, or? If so, is an entangled photon pair (system) a nonseparate entity after one (or the other) photon passes a polarizer? I'm a bit confused .

Yes, events are detection events. What happens at an event is interpretation dependent.

In interpretations where the state represents knowledge, different observers continue with different states. For the analysis of the complete nonlocal experiment, the perspective of the observer having the complete information is relevant. It's view of the state involves nonlocal information in its past light cone only, hence is fully compatible with relativity.

In the Bohmian interpretation, nothing at all happens to the state when a detectors detects an event. The detector simply records a particle at its position.

 

[Cthugha]

However, you eventually have the combined system breaking out into what becomes 2 independent single particle systems (for example an entangled pair of electrons becomes 2 unentangled electrons). We don't know exactly when or how that happens (from experimental considerations), just that at some later time, that's what we find.

[entangled system with particle number=2] -> [independent particle A] + [independent particle B]

Personally, I find this an odd way of labeling it. You have a spatially extended field and a measurement puts it into an eigenstate corresponding to the measurement. This is not really different for entanglement compared to standard qm in spatially extended systems. If you have a spatially extended wavefunction for an electron, which spans from here to the moon and perform a measurement on it and find it here on earth, you also immediately know that the probability to detect it on the moon at the same time will be 0. Here, you also can assume non-local influences if you consider the wavefunction to be an real or you can assume that the wavefunction is a bookkeeping device representing knowledge that is not "real" and do not need non-local influences. These basic options do not change when considering entanglement.

For some reason some people started calling any violation of Bell inequalities non-locality at some point, which is somewhere between odd and unwarranted because it favors one of this alternatives over the other without any experimental evidence. From my point of view, it is perfectly okay to claim that inside a realist interpretation, violation of Bell inequalities equate non-locality, but people rarely care to mention that this logical step depends on the interpretation used.

 

[vanhees71]

I agree in the case of classifying mechanisms for entanglement. For other foundational issues I would say it does matter since it changes the structure of the state space quite a bit. Although I realize your remarks were only about entanglement mechanisms.

What do you mean by "mechanisms for entanglement"? It's all explained by QT, and there are several ways to prepare entangled states (of course you have to mention which observables are entangled to be concrete).

One example is the preparation of entangled states via local interactions (and all intereactions are local within relativistic QFT!): E.g., in the original Michelson Morley experiment the decay of an unstable "particle" into two particles leads to the creation of an (asymptotic free) two-particle state, where energies, momenta, and angular momenta/spin are entangled due to the validity of conservation laws.

More common today are the ubuiquitously used biphotons produced via parametric down conversion, where again the same principle of dynamically generated entangled state holds.

Another way is "entanglement swapping". Here you prepare two independent entangled systems (e.g., two biphotons) and perform a filter measurement on partial systems of each of these systems. The subensemble(s) passing the filter(s) are entangled, and indeed here far distant parts of the two systems that have never been in any causal contact with each other are entangled, but the selection of the subensemble is due to bringing two independent local measurement processes in coincidence. Also here no violations of relativsitic causality is needed to explain the correlations encoded in the descxription by entangled state: Everything is due to the initial preparation in (partially) entangled states.

I guess, there might be more prepration procedures for entangled states, which is how I'd translate the sloppy term "mechanism for entanglement" into more precise language, but as long as all results are consistent with relativistic QFT there's no faster-than-light causal effects necessary to explain them.

 

[vanhees71]

Before I dig into the meat of your post, I'd like to address your kind comment.

I am not asking anyone to take sides with me against vanhees71, and I certainly respect almost everything vanhees71 adds to this forum. While his and my interactions of late seem acrimonious on some levels, I can assure you that I am truly interested in hearing the other side of opinions, viewpoints, perspectives, etc. I am perfectly happy to adjust my own perspective as I gain new knowledge. Please don't feel you need to sugarcoat anything on my behalf.

I've no problems with this. Only claiming, another poster provides "minority opinions" goes too far, particularly given the fact that your conclusion of acausality and non-locality based on an alternative model (local deterministic hidden-variable theory a la Bell) which is, according to the opinion of the vast majority of physicists working in the field, disproven with the plethora of Bell tests having been performed (and nearly every day you find new papers on this elucidating various aspects of the issue). That's why my answers also got sharper with the time, but indeed it's all about understanding the science!

 

[DarMM]

What do you mean by "mechanisms for entanglement"?

Explanations for what is occurring to generate the correlations in entangled particles as classified by which assumption of Bell's theorem they reject. It has nothing to do with you are discussing, i.e. preparations of entangled states and thus isn't a "sloppy term" for that concept.

local deterministic hidden-variable theory

I think it's pretty clear @DrChinese isn't saying that.

 

[vanhees71]

I guess it's best to do this an idea at a time.

You said earlier on the one hand: that entangled pairs evolve such that neither it affected by a measurement of the other. To me, that says they evolve independently. Any pair of anything that evolve causally independently of each other would have Product State statistics, and could not have Entangled State statistics.

On the other hand: you just stated that the distant subsystems are inseparable (which of course I agree with). There is no useful meaning to your description of that single entangled system as "inseparable" unless a measurement on one component of the system affects another component of that system (regardless of actual mechanism). Of course, we call that effect "quantum nonlocality" and it cannot be limited to a forward looking light cone (as you imply).

So how are distant parts of an entangled system considered inseparable, while measurements on those parts are made locally without some kind of distant impact? Bell has something to say about that, and you seem to skip past that at every turn.

The distant parts are inseparable due to the preparation in an entangled state. The correlations are implied by this initial (!) state preparation and not caused by local measurements on one part.

Bell has discovered a way to check the question, whether there are local deterministic hidden-variable theories that can explain the observed facts we are discussing here. The important point is that this entire class leads to a conclusion, Bell's inequality, which contradicts the predictions of QT. Thus you can check one theory against the other with objective experiments, and all experiments done so far with an astonishing precision and statistical significance (since both the HV theory and QT make probabilistic statements, you need statistical significance) disprove the local deterministic HV theories and confirm standard Q(F)T. The very construction of standard relativistic QFT rules out that there is the possibility of causal effects between space-like separated measurements, i.e., non-local interactions.

I prefer to use clear language, and I use Einstein's term, because it's more precise: There are correlations between measurement outcomes on far-distant parts of entangled systems. This is inseparability. There are no non-local interactions in standard relativistic QFT by construction. In this sense this theory is local. There's no contradiction in these two statements.

Bell was ingenious in inventing this possibility to check vague metaphysical or even philosophical issues. There's no question about this. I must admit, however, that I find his writing not always very clear, and I prefer to stick to the experimental papers which clearly state what was how prepared and what was measured and what came out of these measurements.

 

[vanhees71]

Explanations for what is occurring to generate the correlations in entangled particles as classified by which assumption of Bell's theorem they reject. It has nothing to do with you are discussing, i.e. preparations of entangled states and thus isn't a "sloppy term" for that concept.

Then I don't understand what you mean by "mechanisms" at all. Entanglement is a property of quantum states. Quantum states describe preparation procedures (in a broad sense of course). So all there is necessary to understand entanglement is to understand how entanglement comes about. I've just given some (for sure not exhaustive) examples. If it's not answering your question about "mechanisms of entanglement", I didn't understand what you mean by "mechanism".

 

[DarMM]

Then I don't understand what you mean by "mechanisms" at all. Entanglement is a property of quantum states. Quantum states describe preparation procedures (in a broad sense of course). So all there is necessary to understand entanglement is to understand how entanglement comes about. I've just given some (for sure not exhaustive) examples. If it's not answering your question about "mechanisms of entanglement", I didn't understand what you mean by "mechanism".

I didn't have a question about entanglement, all the stuff in your post is known to me.

I'm referring to what physical fact/explanation is responsible for the breaking of the CHSH inequalities, a fairly standard topic in Quantum Foundations.

 

[vanhees71]

And your answer to that question is? Isn't it just a general consequence of the standard formalism? Physicswise there's no quibble in the standard minimal statistical interpretation (often called "orthodox interpretation" to distinguish it from several other flavors of Copenhagen interpretations).

 

[Demystifier]

If it's not answering your question about "mechanisms of entanglement", I didn't understand what you mean by "mechanism".

The mechanism that one would really want to know here is not so much the mechanism of entanglement, but the mechanism by which observables attain their definite values. Even if one accepts that it is random, it still doesn't answer the question. How the interacting system knows that it is not just any interaction, but an interaction that corresponds to a "measurement"? That's the question on which the minimal interpretaion of QM does not have an answer, that's the thing on which one would like to know the mechanism.

 

[DarMM]

The mechanism that one would really want to know here is not so much the mechanism of entanglement, but the mechanism by which observables attain their definite values

Yes, that's more accurate. It's often presented in Foundation papers as concerning entanglement, but really it's a general issue.

 

[vanhees71]

The mechanism that one would really want to know here is not so much the mechanism of entanglement, but the mechanism by which observables attain their definite values. Even if one accepts that it is random, it still doesn't answer the question. How the interacting system knows that it not just any interaction, but an interaction that corresponds to a "measurement"? That's the question on which the minimal interpretaion of QM does not have an answer, that's the thing on which one would like to know the mechanism.

Take photons: They are measured using a detector usually functioning using the interaction of the em. field with the bound electrons in the detector material, i.e., the well-known photoeffect. In this way you measure the distribution of the photons as a function of space and time since these are all local interactions of the radiation field with a bound electron which has a position determined up to the usual position uncertainty of the bound state in the atom/molecule in the detector material.

There's nothing special here except that the photoelectron is multiplied somehow to get a measurable signal. All this works with the known physical laws in terms of local interactions described on the fundamental level by the standard model of elementary particle physics. There's nothing special only because these interactions are used to do measurements.

 

[Demystifier]

Take photons: They are measured using a detector usually functioning using the interaction of the em. field with the bound electrons in the detector material, i.e., the well-known photoeffect. In this way you measure the distribution of the photons as a function of space and time since these are all local interactions of the radiation field with a bound electron which has a position determined up to the usual position uncertainty of the bound state in the atom/molecule in the detector material.

There's nothing special here except that the photoelectron is multiplied somehow to get a measurable signal. All this works with the known physical laws in terms of local interactions described on the fundamental level by the standard model of elementary particle physics. There's nothing special only because these interactions are used to do measurements.

I don't see any mechanism here. You describe me how the magician's trick looks like from the point of view of the incurious spectator (just pull up the rabbit from the hat that looks empty, what's the big deal?), while I want to know how it looks like from the point of view of the magician.

 

[vanhees71]

Which magic trick are you referring to? It's just the interaction between the em. field and electrons bound in an atom/molecule/solid. Of course, if and where and when a photon detection occurs on your screen or CCD cam is random with probabilities given by the prepared photon states, but that there are "definite outcomes", i.e., registration events (or sometimes also no event at all, depending on the efficiency of the detector) is not magic at all but due to the interaction of the field with the detector electrons, all desrcribed by QFT.

 

[DarMM]

That's the detection event, not the correlations.

 

[RUTA]

QM is just the non-relativistic limit of QFT (Zee has a nice derivation of the SE from the KG equation for example). So, if you have an experiment that is properly analyzed using QM, then your experiment has been analyzed using QFT. Thinking that QFT can somehow resolve the mystery of entanglement found in QM is to say, “I think QM can resolve the mystery of entanglement found in QM.”

 

[PeterDonis]

QM is just the non-relativistic limit of QFT (Zee has a nice derivation of the SE from the KG equation for example). So, if you have an experiment that is properly analyzed using QM, then your experiment has been analyzed using QFT.

This is backwards. You can have an experiment that is properly analyzed using QM but incorrectly analyzed using QFT, because your "proper" analysis using QM makes non-relativistic assumptions that are invalid in QFT, but are valid in the non-relativistic approximation.

Or, to put it another way, if your statement were true, it would be impossible to show experimentally that QFT is correct and non-relativistic QM is wrong, because they would have to make the same predictions for all experiments. But that's obviously false; they don't, and experimentally we can show that QFT is correct and non-relativistic QM is wrong by finding experiments whose results depend on relativistic effects.

If you had said that an experiment properly analyzed in QM has been analyzed using QFT in the non-relativistic approximation, that would have been fine; but that's a weaker statement than the one you made.

 

[RUTA]

This is backwards. You can have an experiment that is properly analyzed using QM but incorrectly analyzed using QFT, because your "proper" analysis using QM makes non-relativistic assumptions that are invalid in QFT, but are valid in the non-relativistic approximation.

Or, to put it another way, if your statement were true, it would be impossible to show experimentally that QFT is correct and non-relativistic QM is wrong, because they would have to make the same predictions for all experiments. But that's obviously false; they don't, and experimentally we can show that QFT is correct and non-relativistic QM is wrong by finding experiments whose results depend on relativistic effects.

If you had said that an experiment properly analyzed in QM has been analyzed using QFT in the non-relativistic approximation, that would have been fine; but that's a weaker statement than the one you made.

My statement stands, it is exactly correct. QM is the non-relativistic limit of QFT, so if your experiment has been properly analyzed using QM, it has been properly analyzed using QFT. The same is true of Newtonian mechanics and special relativity (SR). If you analyze an experiment correctly using Newtonian mechanics, then your experiment is amenable to this non-relativistic limit of SR, so you have just used SR to analyze the experiment.

 

[PeterDonis]

If you analyze an experiment correctly using Newtonian mechanics, then your experiment is amenable to this non-relativistic limit of SR

In other words, you are restricting your statement to experiments for which the non-relativistic approximation is valid, i.e., makes predictions which are correct to within the experimental error. But your statement doesn't have that qualifier. It reads like it should apply to any experiment at all, even ones for which the non-relativistic approximation does not make correct predictions. To me, "analyze correctly" means "use the theoretical machinery correctly to generate a prediction"; it does not necessarily imply that the prediction actually matches experiment.

 

[PeterDonis]

you are restricting your statement to experiments for which the non-relativistic approximation is valid

The reason this is important is that if we are talking about foundations, an approximation that's only valid within a limited domain can't possibly be a valid basis for any claim about foundations, because any claim based on that approximation can only be valid in the limited domain in which the approximation is valid.

 

[RUTA]

The reason this is important is that if we are talking about foundations, an approximation that's only valid within a limited domain can't possibly be a valid basis for any claim about foundations, because any claim based on that approximation can only be valid in the limited domain in which the approximation is valid.

We’re talking about experiments done and analyzed accurately using QM, yes, certainly that means the predictions match the experimental outcomes. Only a fool would claim otherwise and I’m not a fool. My statement stands.

 

[PeterDonis]

We’re talking about experiments done and analyzed accurately using QM, yes, certainly that means the predictions match the experimental outcomes.

Yes, but that's only a limited set of all experiments. There are experiments whose outcomes do not match the predictions of non-relativistic QM. You are eliminating these from the scope of your statement by saying that these experiments cannot be "correctly analyzed" using non-relativistic QM. That's fine, but it also means you can't use non-relativistic QM as a basis for any statements about QM foundations.

 

[RUTA]

Yes, but that's only a limited set of all experiments. There are experiments whose outcomes do not match the predictions of non-relativistic QM. You are eliminating these from the scope of your statement by saying that these experiments cannot be "correctly analyzed" using non-relativistic QM. That's fine, but it also means you can't use non-relativistic QM as a basis for any statements about QM foundations.

The experiment Dr. Chinese described in this thread is that for a Bell basis state which falls into the realm of QM, i.e., non-relativistic QFT. My statement stands.

 

[PeterDonis]

The experiment Dr. Chinese described in this thread is that for a Bell basis state which falls into the realm of QM, i.e., non-relativistic QFT.

For that particular experiment, yes, the predictions of non-relativistic QM are accurate. So for studying that particular experiment, I agree that QFT does not add anything.

But this thread has also become a discussion on quantum foundations, and quantum foundations has to cover all experiments, not just that particular one.

 

[RUTA]

For that particular experiment, yes, the predictions of non-relativistic QM are accurate. So for studying that particular experiment, I agree that QFT does not add anything.

But this thread has also become a discussion on quantum foundations, and quantum foundations has to cover all experiments, not just that particular one.

That experiment and any others accurately described by QM are being analyzed by QFT. What do you mean QFT doesn’t add anything? You are using QFT in those experiments when you’re using QM. That’s my point, which as usual, you are missing entirely.

 

[PeterDonis]

What do you mean QFT doesn’t add anything?

QFT beyond the non-relativistic approximation does not add anything to the analysis of that particular experiment, since it doesn't change any of the predictions.

You are using QFT in those experiments when you’re using QM.

You are using QFT in the non-relativistic approximation. You appear to be fine with just calling that "using QFT" unqualified. I personally am not, because I think "using QFT" without qualification implies all of QFT, not just the non-relativistic approximation.

But either way that's a matter of choice of words, not physics. We agree that non-relativistic QM makes correct predictions for that particular experiment.

That’s my point, which as usual, you are missing entirely.

That "as usual" is uncalled for. Please maintain civility.

 

[Haelfix]

Quantum field theory is a special case of quantum mechanics, not viceversa. It is the usual quantum mechanics of a special kind of object, namely fields. This is really manifest when you study the worldline formalism of QFT (which is equivalent to standard perturbative second quantization methods).
https://ncatlab.org/nlab/show/worldline+formalism
To answer the OP. The reason entanglement is rarely discussed in the context of QFT (until about fifteen years ago), was that there were significant technical challenges and the whole formalism manifestly hides most of the entanglement structure. Indeed it might come as quite a shock, but the entanglement between two field modes is, in general, so strong as to be UV divergent in the entanglement entropy. For an introduction:

https://arxiv.org/abs/1803.04993
For the purpose of the endless interpretation and foundations of QM questions, I really don't think there is anything to be gleaned from phrasing things in the more challenging language. Relativistic QFT is, by construction, formulated precisely in such a way as to ensure that field operators commute within spacelike regions. So the dynamical laws must satisfy this constraint. Exactly how and what a 'measurement' does to break this, is of course up to everyone's favorite interpretation, but it's not clear to me what you gain from speaking in the technically more challenging language...

 

[PeterDonis]

Quantum field theory is a special case of quantum mechanics

Just to be clear, "quantum mechanics" as you are using the term here does not mean the same thing as "non-relativistic QM" as I was using the term in my last few posts. "Quantum mechanics" as you are using the term here is a very general term covering all theories that use a certain basic framework. QFT, as you say, is one such theory (more precisely, "QFT" as the term has been used in this thread means something like "relativistic quantum field theory of elementary particles", something like the Standard Model of particle physics). Non-relativistic QM is another such theory, which can be viewed as a non-relativistic approximation to QFT.

 

[Haelfix]

Correct. In fact, people can construct things like non relativistic quantum field theory as well. They're just far more difficult to solve for, as the Euclidean symmetry group is far less constraining than what relativity can yield. Nevertheless it has been done and see's some benefit in condensed matter physics and fringe applications in particle physics.

It is just a bit misleading when one can take a limit of QFT to arrive at the Shroedinger equation. It's a correct derivation but it has the disadvantage of getting the order of generality a bit mixed up.

 

[A. Neumaier]

QM is just the non-relativistic limit of QFT (Zee has a nice derivation of the SE from the KG equation for example). So, if you have an experiment that is properly analyzed using QM, then your experiment has been analyzed using QFT. Thinking that QFT can somehow resolve the mystery of entanglement found in QM is to say, “I think QM can resolve the mystery of entanglement found in QM.”

The Klein-Gordon equation is not QFT!

 

[A. Neumaier]

Quantum field theory is a special case of quantum mechanics, not viceversa. It is the usual quantum mechanics of a special kind of object, namely fields.

Whenever QM and QFT are contrasted, as in this thread, QM refers to the case of finitely many degrees of freedom, while QFT (both relativistic and nonrelativistic) refers to the case of infinitely many degrees of freedom. These differ a lot in their properties. A non-relativistic limit does not change QFT into QM in this sense.

Moreover, many arguments in the foundations depend on things being exact, hence do not survive when limits are involved.

Finally, in QFT, position is a parameter, not an operator, which changes a lot of the foundational aspects. For example, this is the reason why there is no useful QFT version of Bohmian mechanics.

Thus foundations look quite different from the perspectives of QFT and QM.

 

[bhobba]

And the detector too, and the observer :) Which means we have to include the observer in the wave function :) Which means MWI :)

Cheeky boy.. Really enjoying this discussion BTW. But I still think removing correlations from discussions of locality makes things a lot easier. Even in ordinary relativity you have to have some way of handling it for it to make sense. It can't be used to sync clocks so that's one way out, probably others as well. I just think not worrying about locality in the context of correlations is the easiest.

For Bell it doesn't actually change anything except how you look at it. It shows that in QM the statistical nature of correlations is different than classically. But if you want it to be the same you have to introduce the concept of non-locality into correlations. To me doing that is just making a stick to whack yourself with and we end up with a massive amount of dialogue regarding what it means - some valid, but much of it nonsense - even from people that should know better. We get a lot of papers here, proper peer reviewed ones, that are really misunderstandings of weak measurements - that''s probably the main one - but misunderstanding Bell is up there as well. That'''s why I generally link to Bells initial paper with Bertlmann's socks before discussing it.
https://hal.archives-ouvertes.fr/jpa-00220688/document
Keep going - this is really interesting.

Thanks
Bill

 

[vanhees71]

That's the detection event, not the correlations.

Indeed, as I stress for years, the detection event is not the cause of the correlations but the preparation in an entangled state (I guess you refer to the correlations described by entanglement). The preparation in an entangled state in all experiments I know refer finally back to some preparation due to local interactions either, though you can entangle far distant pieces of a larger system that have never locally interacted (entanglement swapping). That's however also due to the selection based on local manipulations of other parts of the system. After all everything causal is somehow due to local interactions, i.e., the same trick that makes classical relativistic physics local, namely the description by fields, makes also the quantum description local, namely through local (microcausal) relativstic QFTs.

 

[vanhees71]

My statement stands, it is exactly correct. QM is the non-relativistic limit of QFT, so if your experiment has been properly analyzed using QM, it has been properly analyzed using QFT. The same is true of Newtonian mechanics and special relativity (SR). If you analyze an experiment correctly using Newtonian mechanics, then your experiment is amenable to this non-relativistic limit of SR, so you have just used SR to analyze the experiment.

Nonrelativistic QT is an approximation of relativstic QFT, valid under certain assumptions. If nonrelativistic QT is applicable, it depends on the accuracy you check it, whether you realize that there are relativistic corrections. E.g., the hydrogen atom spectrum as treated in QM 1 (neglecting relativity as well as the magnetic moment of the electron) is pretty accurate, but you see fine structure, hyperfine structure and radiative corrections like the Lamb shift when looking closer. The relativistic theory so far has not been disproven. To the contrary, it's among the best confirmed theories ever.

 

[vanhees71]

We’re talking about experiments done and analyzed accurately using QM, yes, certainly that means the predictions match the experimental outcomes. Only a fool would claim otherwise and I’m not a fool. My statement stands.

If it comes to the foundations we discuss here, i.e., the compatibility of Einstein causality with QT you must argue with the relativistic theory of course since Einstein causality is for sure invalid in non-relativistic physics (quantum but as well classical). Whenever photon Fock states are involved we also must use at least for them the relativistic theory. There's no non-relativstic descriptions for photons.

Of course you are right that for much of QT it's good enough to use the non-relativistic description like atomic/molecular physics for not too large $Z$ and much of solid-state physics.

 

[vanhees71]

Quantum field theory is a special case of quantum mechanics, not viceversa. It is the usual quantum mechanics of a special kind of object, namely fields. This is really manifest when you study the worldline formalism of QFT (which is equivalent to standard perturbative second quantization methods).
https://ncatlab.org/nlab/show/worldline+formalism
To answer the OP. The reason entanglement is rarely discussed in the context of QFT (until about fifteen years ago), was that there were significant technical challenges and the whole formalism manifestly hides most of the entanglement structure. Indeed it might come as quite a shock, but the entanglement between two field modes is, in general, so strong as to be UV divergent in the entanglement entropy. For an introduction:

https://arxiv.org/abs/1803.04993
For the purpose of the endless interpretation and foundations of QM questions, I really don't think there is anything to be gleaned from phrasing things in the more challenging language. Relativistic QFT is, by construction, formulated precisely in such a way as to ensure that field operators commute within spacelike regions. So the dynamical laws must satisfy this constraint. Exactly how and what a 'measurement' does to break this, is of course up to everyone's favorite interpretation, but it's not clear to me what you gain from speaking in the technically more challenging language...

I don't know whether this is a misunderstanding of words again, but QM is a very small part of QT, namely the non-relativistic first-quantization formalism, i.e., the quantization of non-relativsitic point-particle mechanics, using position, momentum (and spin) as the fundamental operators representing the observable algebra. This also implies that you work with a fixed number of particles.

QFT is most comprehensive. In the non-relativistic case ("second-quantization formalism") with Hamiltonians that do not include particle-number changing interaction terms it's equivalent to the first-quantization formalism. Even in the non-relativistic case QFT is much more versatile in building effective models for many-body systems. If you read a modern condensed-matter textbook, you'll see that the art usually is to find the right effective degrees of freedom (usually describing collective phenomena) and treat them as a weakly interacting gas, leading to a quasi-particle description. Usually the quasi-particle number is not conserved, and that's why you use QFT. An example are lattice vibrations of solids (quasi-particles are called phonons).

In the relativistic case there's so far even only QFT successfully used. The reason is simply that in reactions of particles at relativistic energies you usually open channels where particles can be annihilated and/or new ones created. That's most conveniently described as a QFT.

In this sense QM is a proper subset of QFT, and as Witten stresses in his article entanglement comes automatically, which is also not a surprise since already the necessity of symmetrization/antisymmetrization of product states for indistinguishable bosons/fermions, built into the theory from the very beginning by imposing commutation/anticommutation relations for the field operators. You don't need to go into these very special mathematical details to see this.

Even in non-relativistic QM entanglement is rather the rule than something exceptional. Already the description of two (distinguishable or not doesn't matter) interacting particles lead to entanglement. Disentangled are the center-mass and relative coordinates describing the free motion of the two-body system as a whole and the relative motion in terms of a quasi-particle (with the reduced mass as its mass) moving in an external potential given by the two-body interaction potential. Transforming back to the coordinates of the original particles shows that you have an entangled state with respect to these observables. For the hydrogen atom, this has been nicely discussed in

https://doi.org/10.1119/1.18977https://arxiv.org/abs/quant-ph/9709052

 

[Auto-Didact]

I don't know whether this is a misunderstanding of words again, but QM is a very small part of QT, namely the non-relativistic first-quantization formalism, i.e., the quantization of non-relativsitic point-particle mechanics, using position, momentum (and spin) as the fundamental operators representing the observable algebra.

This isn't a misunderstanding of just words: this is a conceptual difference coming from a difference of approach, namely physics as an empirical science (e.g. the perspective of experimental/applied physics) vs physics as (the purest form of) applied mathematics (e.g. the perspective of theoretical/mathematical physics). Your perspective doesn't require that physical theories also be proper theories within pure mathematics proper.

The world line formalism is the result of a research programme from pure mathematics and/or mathematical physics which directly implies that QFT and string theory are basically different manifestations of the same underlying mathematical theory, with QFT being the limit where a brane is reduced to a single point, i.e. a 0-dimensional particle, and string theory with the string being the 1-dimensional limit of a brane, etc.

 

[vanhees71]

Sure, you can always try to find even more comprehensive theories, of which QFT is again an approximation, but it's clear that QFT is more comprehensive than QM, which is a speciatl case.

The only problem with your claim QFT were simply a special case of string theory is that there seems to be no string theory providing the Standard Model as a limit (or has this changed over the years?).

 

[Auto-Didact]

Important to understand is that what I'm saying about QFT and string theory being different manifestations of the same mathematical theory, isn't a statement from physics, but from mathematics - specifically from a more sophisticated branch of mathematics which underlies both the theory of complex analysis and the theory of partial differential equations.

In other words, the statements are independent of string theory being physics such as reproduction of the Standard Model; in fact the statements are mathematics-based theory-independent statements about physics and as such are statements applicable to all possible (both true and false) physical theories.

To answer your question more directly - being a constructivist - the generalization of the world line formalism into world volumes is evidence to me that (conceptually and therefore mathematically and therefore) actually QFT = string theory, i.e. string theory can at best - exactly as QFT - only be an EFT, and they are therefore both incapable of serving as a foundation of physics. I spoke about this here and more at length in https://www.physicsforums.com/threads/on-fundamental-theories-in-physics.976173/, which unfortunately is not viewable anymore.

The completion of the constructive QFT programme is IMO our only hope forward of finding a new theory capable of dethroning QM as the foundation of physics, as well as unifying GR with QT; the mathematics involved in discovering and formulating string theory definitely indirectly helps theorists to find this new fundamental theory, but string theory itself as a physical theory isn't a solution nor does it directly help to find a solution.