Undergrad Murray Gell-Mann on Entanglement

[atyy]

Yes, I disagree with this statement. Correct is: If A's photon passes the h-polarization filter she associates the state $hh \rangle$ to the two photons. However, her measurement has no instantaneous influence on B's photon, i.e., there must not be a collapse if the interpretation should be consistent with the very construction of QED as a local relativistic QFT, and you don't need it!Well, I'm also against the use of the word quantum jumps, but I guess Peres has the right thing in mind when he states this, and he is right that the temporal sequence for space-like separated "interventions" is frame dependent, which implies that one intervention cannot have a causal influence on the other space-like separated intervention. That's the whole point of our disagreement. In my (and if I understand him right also Peres's) notion of the state as epistemic (particularly the "update" or if you wish to call it with another unsharp word "quantum jump" of the state after a "filtering intervention" as in our example here) there is no tension between causality and relativistic QFT whatsoever, and that's so by construction of the QFT, and Peres's argument in the paper is just another very convincing argument for why (at least) the Hamilton density operator has to commute at spacelike separation of the arguments, i.e., if $(x-y) \cdot (x-y)<0$ (west-coast convention of the metric) you must have $[\hat{\mathcal{H}}(x),\hat{\mathcal{H}}(y)]=0$. Usually one assumes even more, i.e., that any two local operators commute at spacelike separation of their arguments.

Well, whatever it is you need the mathematics, and it is true that the state is assigned to spacelike surface, and the "update" takes place instantaneously on that surface.

 

[zonde]

I don't know, what you mean by measuring A's photon at different angle.

Let's say A measured her photon with polarizer at an angle $\alpha_1$. B measured his photon at an angle $\beta_1$ and got result "+".
Now what it means to say that "it's totally irrelevant for B what A does with her photon"?
I propose such meaning: if A would have measured her photon with polarizer at an angle $\alpha_2$ then B measuring his photon at the same angle $\beta_1$ could still get result "+".

Or do you have on mind different meaning for "it's totally irrelevant for B what A does with her photon"?

 

[Demystifier]

But that interpretation contradicts the locality of the interaction between A's photon and her polarization measurement apparatus.

But according to the minimal ensemble interpretation (MEI), quantum theory says nothing about the interaction between an individual photon and an individual apparatus. It only talks about a large ensemble of interacting photon-apparatus pairs. At the level of ensemble the interactions are local, but there is no guarantee that interactions are local even at the individual level. It could be that individual interactions contain a non-local part, but that these non-local parts cancel-up in the average at the ensemble level. This is a logical possibility that does not contradict known facts about quantum theory (including relativistic QFT) in the MEI form.

 

[Ken G]

It seems to me that "holistic" and "nonlocal" might mean the same thing, here.

I think there's an important difference. "Nonlocal" still implies an influence of sorts, merely one that is not constrained by the speed of light. "Holistic" takes the mathematics at face value-- the system is a single entity, not made of parts that "influence" each other. If there are not parts, there is not any issue with propagation of influences, either slower or faster than c. One simply rejects the concept of a part influencing another part, and poof, nothing "nonlocal" there, it's just a single thing. That's what the mathematics is, after all-- a single thing, with all the correlations built in.

By the way, the simplest way to think of the state as a "single thing" is to treat it as information, rather than a physical entity. One can imagine there is a physical entity out there if one likes, but that's not what the scientist deals in, the scientist deals in information and using information to make and test predictions. We all create a sense of something "physical" during that process, of course, but we needn't mistake our intuitive imaginings for any part of what we are actually doing when we carry out a test. Above all, we don't tell the mathematical entities we manipulate that they must be subservient to our intuitive pictures-- we must train our intuition to the mathematics that works, not the other way around.

 

[stevendaryl]

I think there's an important difference. "Nonlocal" still implies an influence of sorts, merely one that is not constrained by the speed of light.

I think that nonlocal doesn't necessarily imply FTL influences. Local to me means that the most complete description of the universe "factors" into descriptions of small regions of spacetime, and that the evolution of one region depends only on what's true in neighboring regions. Quantum mechanics is not local in this sense, because in the case of distant entangled systems, the most complete description of the universe does not factor into a bunch of local descriptions. For example, in EPR for photons, the most complete description for Alice's photon is that for any orientation of a polarizing filter, the photon has a 50% chance of passing through that filter. The most complete description for Bob's photon is the same. But the most complete description for Alice, together with the most complete description for Bob doesn't add up to the most complete description for the Alice/Bob system, since it doesn't include the perfect correlation between their results when their filters are aligned.

Classical probabilities can be nonlocal in this sense, as well, but in that case, there is a more complete description that is local.

 

[Ken G]

Let me add to my previous point about the difference between "nonlocal" and "holistic." A lot is made of entanglement as being "spooky", but for some reason I never hear the term "spooky" in the context of the Pauli exclusion principle. Why not? Is not the PEP just as "nonlocal" as EPR? For example, we have stellar remnants the size of planet Earth called "white dwarfs" which can cool to the point that they are completely degenerate, in principle. By then, the star is still the size of Earth, it contains some 10⁵⁷ electrons, and each of those electrons has some ghastly kinetic energy equivalent to a billion Kelvin if they weren't degenerate. Yet with all those electrons zinging around with all that kinetic energy, not a single collision is allowed to occur, and not a single photon is allowed to be emitted (in the idealized limit). Talk about entanglement! The identical nature of those Fermions is such that if you think that is a "system of parts" that are "nonlocally influencing" each other, each electron must be influenced by all the others so that it can "know" it is not allowed to enter a previously occupied state-- across an object the size of Earth. Why isn't that "spooky action at a distance"? If one wants EPR to be a "nonlocal influence," then a black dwarf is the mother of all nonlocal influences. To me, it just makes more sense to think a black dwarf is all one thing, and the information we have about that thing tells us it cannot emit light-- without any "parts" talking to any other "parts." It just isn't made of parts any more, our naive notion that matter is "made of particles" breaks down when the particles are identical and degenerate. One can imagine that a proton is "made of quarks and virtual gluons", but what sense does it make to say something is made of virtual things? We should just accept that our concept of what it means to be "comprised of" tiny pieces is simply not a general description of reality that should work in all situations.

 

[stevendaryl]

Let me add to my previous point about the difference between "nonlocal" and "holistic." A lot is made of entanglement as being "spooky", but for some reason I never hear the term "spooky" in the context of the Pauli exclusion principle. Why not? Is not the PEP just as "nonlocal" as EPR?

I think that they're very closely related. The nonlocality of EPR is due to having nonfactorable composite wave functions, and the Pauli exclusion principle is a constraint on such wave functions.

 

[Ken G]

I think that nonlocal doesn't necessarily imply FTL influences. Local to me means that the most complete description of the universe "factors" into descriptions of small regions of spacetime, and that the evolution of one region depends only on what's true in neighboring regions. Quantum mechanics is not local in this sense, because in the case of distant entangled systems, the most complete description of the universe does not factor into a bunch of local descriptions.

I agree that you are using "nonlocal" in the way I mean "holistic," and that's probably because you are not buying off on the idea that nonlocality must be enforced by "influences" that happen "instantaneously" in an EPR setup. But for those who do wish to maintain a sense of fractured locality, a "pieceness" or "discreteness" to systems that are cobbled together from smaller entities plus influences between those entities, they need a concept of "nonlocal" that does not violate their "discreteness" concept. It's for them that a distinction between nonlocal and holistic must be made.

In other words, to me "holistic" differs from "nonlocal" in the sense that when the ancient Greeks wondered if matter was continuous or comprised of discrete "atoms", they left out a third possibility: it could be analyzed in terms of discrete bits in some situations, continuous fluids in others, and still in others, it could not be thought of either as discrete local bits-and-influences, nor as a continuum maintained by either propagating or nonlocal influences, but instead, a system could be all one thing. I don't think they even imagined that possibility, so how amazing is it that we have come to it with the mathematics of quantum mechanics-- we should embrace that fascinating new possibility, rather than fight it because it is outside our expectations.

For example, in EPR for photons, the most complete description for Alice's photon is that for any orientation of a polarizing filter, the photon has a 50% chance of passing through that filter. The most complete description for Bob's photon is the same. But the most complete description for Alice, together with the most complete description for Bob doesn't add up to the most complete description for the Alice/Bob system, since it doesn't include the perfect correlation between their results when their filters are aligned.

Yes exactly, but notice the significance of how you've built up this scenario-- the "merging" that happened to create the holistic system was a merging of Alice's and Bob's information, more so than a merging of their photons. They don't even possesses their own photons, any more than a white dwarf possesses separate distinguishable electrons. What is holistic is the information, when we treat it together, or about individual photons, when we treat it that way. The system is happening at the level of how we are treating the information, not the sum of two individual electrons and their experimental outcomes. A photon doesn't own its own experimental outcome, a scientist owns that.

 

[Nugatory]

But Gell-Mann said: "People say loosely ,crudely, wrongly that when you measure one of the photons it does something to the other one. It doesn't."
He's not agnostic. He's strongly denying any causative link.

I'm not sure that's a fair assessment of Gell-Mann's claim, because it's not clear exactly what's being denied when we're dealing with a denial of something that has been stated "loosely, crudely". Or as Bhobba said:

Yes - but its for a lay audience. I think a bit of latitude is reasonable.

 

[A. Neumaier]

it is true that the state is assigned to spacelike surface, and the "update" takes place instantaneously on that surface.

No. This is a noncovariant, observer-specific view.
See https://www.physicsforums.com/threads/states-in-relativistic-quantum-field-theory.885079/

 

[Ken G]

I think that they're very closely related. The nonlocality of EPR is due to having nonfactorable composite wave functions, and the Pauli exclusion principle is a constraint on such wave functions.

Right, exactly, they are indeed very closely related. So we need an approach to both that resolves the same issues. But no one talks about spooky action at a distance when they say the ground state of an atom has higher energy levels, or when they talk about white dwarfs. No one says that an excited electron in an atom can only drop down to unoccupied states because "nonlocal influences" from the other electrons collapse its state. I think that's because it sounds local to say you cannot sit in a chair if someone else is already there, but that's not why the PEP works, it works because the exchange antisymmetry is holistic. The actual reason an electron cannot go into an occupied state is not because another electron is already there, that very language suggests electrons have their own identities-- it can't do it expressly because it does not have its own identity, the system is holistic.

 

[ddd123]

Holism sounds pretty much like nonlocality to me, since a system like that is extended in space.

 

[Ken G]

Holism sounds pretty much like nonlocality to me, since a system like that is extended in space.

Is an iron atom in its ground state extended in space? The holistic elements are outside of spatial considerations, in general.

 

[ddd123]

Well it is extended in space. I don't understand the second sentence.

 

[Ken G]

My point is that the PEP has nothing to do with spatial extent, it works for the completely overlapping wavefunctions of the two electrons in the ground state of Helium, and it works for a white dwarf the size of Earth. It is about a system not being "made of parts", which is what I mean by holism. Not being made of parts is a much more fundamentally different way to think about a system than simply spatially extended and subject to superluminal influences as a result. I'm saying it makes more sense to say that EPR type effects come from the holism of the Bell state, and don't care at all about spatial extent.

 

[atyy]

Right, exactly, they are indeed very closely related. So we need an approach to both that resolves the same issues. But no one talks about spooky action at a distance when they say the ground state of an atom has higher energy levels, or when they talk about white dwarfs. No one says that an excited electron in an atom can only drop down to unoccupied states because "nonlocal influences" from the other electrons collapse its state. I think that's because it sounds local to say you cannot sit in a chair if someone else is already there, but that's not why the PEP works, it works because the exchange antisymmetry is holistic. The actual reason an electron cannot go into an occupied state is not because another electron is already there, that very language suggests electrons have their own identities-- it can't do it expressly because it does not have its own identity, the system is holistic.

Xiao-Gang Wen does apply the term "nonlocal" to fermions on p144: "Fermions are weird because they are non-local objects".
https://www.amazon.com/dp/019922725X/?tag=pfamazon01-20

 

[ddd123]

I don't find the EPR example any weirder than the white dwarf one, the latter isn't just used as a typical example of nonlocality but it could be. The holism property isn't related with spatial extension in both cases but in both cases the perceived weirdness comes from the fact that they're spatially extended. I don't see the point here: even if spatial extension doesn't play a particular role in the construction of such states, it doesn't mean that they cease to have that property.

 

[Ken G]

Xiao-Gang Wen does apply the term "nonlocal" to fermions on p144: "Fermions are weird because they are non-local objects".
https://www.amazon.com/dp/019922725X/?tag=pfamazon01-20

Yet what is non-local about the two electrons in the ground state of helium? Their spatial wavefunctions couldn't possibly overlap more, but change the spin, and poof-- all heck breaks loose. What is the "nonlocal influence" that prevents a spin flip there?

 

[stevendaryl]

Yet what is non-local about the two electrons in the ground state of helium? Their spatial wavefunctions couldn't possibly overlap more, but change the spin, and poof-- all heck breaks loose. What is the "nonlocal influence" that prevents a spin flip there?

Well, I take "nonlocal influence" as any influence that is NOT local. There is nothing local about the Pauli exclusion principle.

 

[Ken G]

I don't find the EPR example any weirder than the white dwarf one, the latter isn't just used as a typical example of nonlocality but it could be. The holism property isn't related with spatial extension in both cases but in both cases the perceived weirdness comes from the fact that they're spatially extended. I don't see the point here: even if spatial extension doesn't play a particular role in the construction of such states, it doesn't mean that they cease to have that property.

The point is I have heard people talk about the PEP in white dwarfs many times, but rarely heard anyone say there is a "nonlocal influence" that acts on those electrons. They just say the electron "isn't allowed" to do various things, that's it, no imagined influences propagating superluminally the width of the white dwarf. Yet in the EPR situation, which we all agree is fundamentally similar, all of a sudden we get these nonlocal influences. Take Gell-Mann's statement, and replace mention of entanglement with mention of the PEP-- does anyone object to it now?

 

[atyy]

But that interpretation contradicts the locality of the interaction between A's photon and her polarization measurement apparatus. Also if Alice measures something else of her photon after it has passed the polarization filter, say directed to let through H-photons (which with utmost accuracy can indeed be made a v Neumann filter measurement!), all the outcomes of further measurements on her photon are described by associating the polarization state $|H \rangle$ with it. For A it's totally irrelevant what's the state of B's photon, as is for B whatever A does with her photon. The correlations due to the entanglement, which itself is due to the production of the entangled photon pair in the very beginning, can, however be observed by comparing the measurement protocols with accurate timestamps of each single-photon detection event by A and B. From this point of view (the minimal statistical interpretation) there is not need for assuming a collapse at all, and that prevents this interpretation from leading to inconsistency with the very foundations of relativistic QFT!

I made another reply above in post #91.

Here is another question: aren't the "foundations" and "local interactions" of relativistic that you are considering classical relativistic causality? After all, one way to state them is to use the action - that is the tool we typically use to enforce locality in QFT. For a bosonic QFT, the action has identical form to a classical field theory. So I think you are just hankering after classical relativistic causality.

 

[ddd123]

The point is I have heard people talk about the PEP in white dwarfs many times, but rarely heard anyone say there is a "nonlocal influence" that acts on those electrons. They just say the electron "isn't allowed" to do various things, that's it, no imagined influences propagating superluminally the width of the white dwarf. Yet in the EPR situation, which we all agree is fundamentally similar, all of a sudden we get these nonlocal influences. Take Gell-Mann's statement, and replace mention of entanglement with mention of the PEP-- does anyone object to it now?

You keep shifting between "nonlocal" and "nonlocal influence" as if they meant the same thing, but for me they aren't the same (as I said in the first post in the thread).

 

[Ken G]

You keep shifting between "nonlocal" and "nonlocal influence" as if they meant the same thing, but for me they aren't the same (as I said in the first post in the thread).

Yet you have not answered my question: what is spatially nonlocal about the spins of the two electrons in the ground state of the helium atom? Yet the reason they cannot be the same is a holistic property of the exchange antisymmetry. So holism is different from nonlocality, and what happens in a white dwarf is all about exchange antisymmetry and not at all about spatial nonlocality.

 

[stevendaryl]

You keep shifting between "nonlocal" and "nonlocal influence" as if they meant the same thing, but for me they aren't the same (as I said in the first post in the thread).

As an analogy, you could consider differential geometry. Curvature is a local property, because you can talk about the curvature at a single point (or the average curvature in a small region). Topology (whether the space is infinite, or is a sphere, etc.) is nonlocal, because no amount of information within a single region can tell you anything about the topology. But there is no sense in which topology implies nonlocal influences.

 

[ddd123]

Yet you have not answered my question: what is spatially nonlocal about the spins of the two electrons in the ground state of the helium atom? Yet the reason they cannot be the same is a holistic property of the exchange antisymmetry. So holism is different from nonlocality, and what happens in a white dwarf is all about exchange antisymmetry and not at all about spatial nonlocality.

In the case of the helium atom the consequences of spatial extension of a holistic system aren't evident, but in general they can be.

 

[Ken G]

Gell-Mann is talking about nonlocal influences, he is saying something happening to one particle does not reach out and touch the other. So the only kind of nonlocality that is relevant to the discussion is nonlocal influences. Indeed, the spatial nonlocality is a red herring, because EPR experiments are not more surprising if the particles are spatially separated-- they are just as surprising if they aren't! That should be obvious-- does anyone really find Bell inequality violations to be perfectly understandable as long as the measurements are not spacelike separated? It's utterly irrelevant if they are spacelike separated, we have no way of understanding EPR in terms of "influences" either way, and Gell-Mann's quote applies just as well if they are not spatially separated or if they are. People just find it more surprising if they are spacelike separated, but they shouldn't because we'd need new physics if the EPR came out differently based on separation! Think what a crisis that would be-- no one ever mentions that part!

 

[Ken G]

In the case of the helium atom the consequences of spatial extension of a holistic system aren't evident, but in general they can be.

So which is the more general issue: spacelike separation, or holism? The latter, clearly. After all, it's the only one that actually appears in the mathematics of the Bell state, whereas spatial separation is irrelevant.

 

[ddd123]

Gell-Mann is talking about nonlocal influences, he is saying something happening to one particle does not reach out and touch the other. So the only kind of nonlocality that is relevant to the discussion is nonlocal influences.

Not exactly, as I said I agree with Gell-Mann on the nonexistence of nonlocal influences. But OP asked about agreement with Gell-Mann, and since Gell-Mann goes beyond that to declare that nonlocality itself is wrong, discussing whether nonlocality can mean something different is relevant to the discussion...

 

[ddd123]

So which is the more general issue: spacelike separation, or holism?

It's just a matter of description, you can restrict the meaning of "nonlocal" the way you do, but you're arguing over terms. I don't say that the way I mean nonlocality reflects a general, fundamental property, I just say that it describes consequences of certain things, which, sure, are secondary in a sense.

 

[Ken G]

Not exactly, as I said I agree with Gell-Mann on the nonexistence of nonlocal influences. But OP asked about agreement with Gell-Mann, and since Gell-Mann goes beyond that to declare that nonlocality itself is wrong, discussing whether nonlocality can mean something different is relevant to the discussion...

Perhaps you are extending the discussion to other remarks by Gell-Mann outside of the quote in the OP. That's fine, but what I'm talking about is that quote. Some hold that you need nonlocal influences, I'm saying that to have nonlocal influences you first have to think the system is "made of parts" that could be the subject and object of those influences, but the mathematics does not say the system is made of parts, it says the system is holistic. That's all true independent of spatial separation, I just don't think spatial separation has anything to do with EPR physics, it only has to do with the awkward picture of insisting that a system must be comprised of distinct parts which must then propagate influences between them. What I mean by holism is the rejection of that awkward picture, a picture that does not even dovetail with the very mathematics of a Bell state.