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

[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.

 

[DarMM]

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).

Let me explain it this way. Tsirelson and Landau showed that the Bell inequality violations come from only the two axes measured by Alice and Bob having actual values. Values along all other axes are undefined as you know. That's why we can have such strong non classical correlations. Intrinsically random variables where after measurement only the variables you measured have well defined values are capable of having stronger correlations than classical theories (even stochastic ones) because there all variables take on well defined values (even if those values are randomly generated).

However many people find this odd because how can nature intrinsically care about "measurement". So they prefer to investigate other ways of generating correlations that strong.

 

[vanhees71]

Well, that's perfectly expressing my statement that we simply have to accept what our observation of nature has told us: She behaves not according to classical theories (even stochastic ones) but according to quantum theory, including the stronger-than-classically-possible correlations described by experiment. You may whine as much as you like about the loss of the "classical confort zone", but nature doesn't care ;-)).

 

[Auto-Didact]

The classical/quantum dichotomy is a red herring: researchers aren't so much calling for a return to the 'classical comfort zone' but for an even further departure away from classicality than QT, but a departure which does have a constructive basis capable of offering an explanation in terms of a mechanism. The reason people make the strawman argument that wanting a mechanism is a call back to classical physics is because classical physics also happened to have such a constructive basis: (real) analysis.

There is no reason whatsoever to think that finding a more comprehensive constructive basis for QT is impossible; on the contrary, the failure to directly formulate GR-based QFT is sufficient evidence that searching for such a more comprehensive constructive basis - more comprehensive than offered by classical physics' real analysis - is not a mere matter of academic luxury, but a logical necessity.

This searching has certainly not been in vain for there have definitely been new offerings of such constructive bases, e.g. non-commutative geometry, n-category theory and the sheaf theoretic characterization of non-locality I have spoken about. The problem is that these constructive bases tend to be too complicated for the average theorist to easily adequately fit them into the correct place during theory construction, especially if the theorist forgoes using foundational research methodology; this leaves theorists stranded, incapable of seeing the forest for the trees.

 

[Demystifier]

if and where and when a photon detection occurs on your screen or CCD cam is random

Is there something random going on when a detection does not occur? I know it's a philosophical question that you find irrelevant, but that is one of the things one wants to understand with a mechanism.

is not magic at all but due to the interaction of the field with the detector electrons, all desrcribed by QFT.

In a similar way, I could introduce a rabbit creation operator that creates a rabbit from the vacuum whenever the magician puts his hand in the previously empty hat. With a little bit of work, I could make this theory compatible with all observation by the spectators in the audience. Would you say that with such a theory there is no magic at all because it is described by the theory?

 

[RUTA]

The Klein-Gordon equation is not QFT!

That’s semantics, you can argue that with Zee