B Why is it assumed communication through entanglement would be FTL?

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vanhees71

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What you are passing on might indeed be the current consensus, but I do not think that is an adequate response to the obvious point that, since non-relativistic QM is just an approximation to QFT, quantum foundation discussions that are solely based on non-relativistic QM--which is basically all of them--are incomplete. Those many top writers have surely heard of QFT, yes, but that doesn't mean their failure to include QFT in their foundations work can simply be ignored.
Where is QFT not included in the work on foundations? Of course, if you discuss non-relativistic approximation nothing prevents "spooky action at a distance" since nothing prevents faster-than-light causal interactions. In non-relativistic physics it's even the usual case since interactions are described by instaneously acting forces (like Newton's gravitational force) rather than retareded interactions as in relativistic (quantum) field theories.

The most real physics work about these foundational questions is made with photons, and there's no non-relativistic theory for photons. Indeed quantum-opticians use relativistic QFT to describe photons. Of course the theory of local interactions of photons with all kinds of equipment often is described with non-relativistic physics (like the theory of photo detection or the linear optics devices like lenses, mirrors, beam splitters etc.), but this is well-justified and doesn't lead to any contradictions with relativistic causality, because in such cases the retardation effects are indeed negligible since it concerns only local interactions between photons and the matter making up these devices. I also don't think that there's a principle problem to also treat these parts fully relativistically. The relativistic QFT is also worked out well for many-body systems (at least in thermal equilibrium, and that's usually what's needed for this purpose).
 

vanhees71

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Here I mean collapse as a physical nonlocal process.

It is not correct to use the microcausality of QFT to object to the nonlocality of collapse, because
(1) microcausality does not refer to physical locality
(2) under appropriate assumptions, any physical variables reproducing the quantum predictions must be nonlocal - it is not possible to save locality by rejecting collapse.
Can you elaborate on both points further?

Microcausality tells us that local observable operators commute at space-like distances of their arguments. Particularly that's valid for any observable operator and the Hamilton density. Due to the commutativity the interactions in standard relativistic QFT (including QED and the entire standard model) are "local" in the sense that there are no causal effects that go faster than light. You also once agreed that there's no FTL communication possible within relatistic standard QFT, and this must be so due to the microcausality principle and the validity of the cluster-decomposition principle and Lorentz invariance of the S matrix.

(2) What's "nonlocal" in QT, and also in non-relativistic QFT I would rather like to call "inseparability" (Einstein had it right from the very beginning!). It refers to the long-range correlations between far-distant parts (or even more precisely between local (!) measurement results at far-distant places) described by entanglement. Of course, nothing in QFT contradicts these findings, and it's very accurately demonstrated that these predictions hold true, while local deterministic HV theories fail.

There's no need for an instaneous collapse with a dynamics somehow outside of the laws of physics to explains all these findings with the utmost relativistic entities we have at hand, i.e., photons!
 

vanhees71

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All that @vanhees71 is saying is that he doesn't see the necessity of collapse as a physical process.

I agree that microcausality of QFT is not an argument against signal-local theories that might be nonlocal in other ways, e.g. Bohmian Mechanics. I'm not sure if @vanhees71 would disagree either as the discussion has been confused by the use of different meanings for "collapse".

I don't think physical variables must be nonlocal to replicate QM predictions, that's just one way of explaining CHSH violations, but not the only one.
Bohmian mechanics is not formulated in a satisfactory way to reinterpret relativistic QFTs. Within non-relativistic QT as in non-relativistic classical mechanics of course non-local interactions are the rule not the exception. Thus you cannot argue with non-relativistic approximations when it comes to the question in which sense Einstein causality is fulfilled (or as claimes not fulfilled) within relativistic microcausal QFTs. In the standard interpretation of relativistic microcausal QFTs, the interactions by construction are local (and realized via assuming the microcausality constraint on local observable operators).

The irony is that most accurate Bell tests are performed with photons, and these are relativistic. All these experiments do not contradict standard QED in any way, and this shows that indeed everything concerning the violations of various forms of Bell's inequaltity (including CHSH) is in full accordance with standard QED, which assumes local interactions (in the sense of microcausality) but at the same time of course does not exclude the entanglement and the corresponding correlations between local (sic!) measurements on far-distant parts of an entangled quantum system (like two or more polarization-entangled photons; note that even the momentum-position EPR "paradox" has recently been tested with photons, and also there nothing contradicts standard QED).

Concerning "collapse", I think it's describing nothing more than the adaption of the state description by an observer after having performed a measurement. It's not a physical process. It is also clear that, as Peres famously wrote (e.g., in his book "Quantum Theory: Concepts and Methods"), within this minimal statistical interpretation there cannot be contradictions between the different descriptions of a situation depending on what's locally known about one part of an entangled system. E.g., with photon pairs prepared in the polarization-singlet state, when A measures the polarization in z-direction to be horizontal, she immediately knows that B's photon will be found to be vertically polarized (concerning the same z-direction). Nothing changes for B. He'll simply find randomly (with probability 50%) a vertically polarized photon. The correlations due to the entanglement can only be revealed when comparing the measurement protocols by A and B. It's indeed not possible to be revealed by the local measurements on the single photons alone, and that's why A and B cannot FTL communicate using polarization-entangled photons nor can there be any contradictions between A's and B's description of their local single-photon measurement's outcomes: Both simply find perfectly (maybe the most perfectly possible) unpolarized photons.
 

DarMM

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Bohmian mechanics is not formulated in a satisfactory way to reinterpret relativistic QFTs.
I agree, it's just that there's currently no proof something like Bohmian Mechanics won't eventually be able to. So my response to @atyy that microcausality doesn't technically rule out such theories.
 

vanhees71

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I agree, it's just that there's currently no proof something like Bohmian Mechanics won't eventually be able to. So my response to @atyy that microcausality doesn't technically rule out such theories.
That's of course true, but I think it's so hard to find a satisfactory Bohmian reinterpretation of relativistic QFT precisely to this "tension" between Einstein causality and non-locality. It's really a quite subtle mathematical way, relativistic microcausal QFT manages to make local interactions compatible with the strong non-local correlations described by entanglement, and indeed, as Weinberg stresses, microcausality is only a sufficient but (maybe) not necessary condition for a relativistic QFT. So far, however, nobody has found a working non-local relativistic QFT without some flaws. E.g., afaik there's no working theory including interacting tachyons ;-).
 

Demystifier

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That's of course true, but I think it's so hard to find a satisfactory Bohmian reinterpretation of relativistic QFT precisely to this "tension" between Einstein causality and non-locality.
It depends on what one means by "satisfactory". Are you familiar with the presently existing approaches and what exactly do you find unsatisfactory with them?
 

atyy

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All that @vanhees71 is saying is that he doesn't see the necessity of collapse as a physical process.

I agree that microcausality of QFT is not an argument against signal-local theories that might be nonlocal in other ways, e.g. Bohmian Mechanics. I'm not sure if @vanhees71 would disagree either as the discussion has been confused by the use of different meanings for "collapse".

I don't think physical variables must be nonlocal to replicate QM predictions, that's just one way of explaining CHSH violations, but not the only one.
I agree that nonlocal physical variables are not the only way of explaining the CHSH violations.

With regards to @vanhees71, in the context of this thread, I think @DrChinese basically gave a correct answer - one could quibble with word choice, and maybe not stating exactly the other "outs" apart from physical nonlocality - but he was basically on target answering the OP - and @vanhees71 seems to have substantial problems with it, making @DrChinese's correct and simple reply to the OP lost. I don't think the OP has been served.
 

vanhees71

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What precisely do you think is correct in @DrChinese 's answer? He is always arguing in terms of fictitious local HV theories, which are not QT and then claims that my standard interpretation using QFT were a minority statement, though it's the opposite way: The majority of physicists, particularly quantum opticians, interprete the fact that Bell tests prove local deterministic HV theories wrong, while they confirm standard Q(F)T, and indeed there's no contradiction between any experiment and this standard relativistic QFT.
 

DarMM

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I agree that nonlocal physical variables are not the only way of explaining the CHSH violations.

With regards to @vanhees71, in the context of this thread, I think @DrChinese basically gave a correct answer - one could quibble with word choice, and maybe not stating exactly the other "outs" apart from physical nonlocality - but he was basically on target answering the OP - and @vanhees71 seems to have substantial problems with it, making @DrChinese's correct and simple reply to the OP lost. I don't think the OP has been served.
I agree that @DrChinese 's answer is correct and a simple exposition of the answer to OP's question.

I think @vanhees71 mistook @DrChinese 's statement regarding a lower bound for nonlocal influence velocity in a nonlocal hidden variable theory as a statement that there had been observed violations of Relativity and that was when the discussion moved off.

@vanhees71 I also don't think @DrChinese is advocating local classical hidden variables, he was just commenting on the experimental bounds on nonlocal hidden variable theories.
 

vanhees71

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Well, then @DrChinese and I have a mutual misunderstanding for a long time :-((.

The experimental bounds on nonlocal HV theories are utmost tight. It's among of the most accurate precision decisions between any two physical theories ever!
 

DrChinese

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The problem is that @vanhees71 is claiming that QFT is local in a way that is excluded by the Bell inequality violations.

No one is contesting that QFT is local in the sense of not allowing superluminal communication.
I agree with this entirely. QFT cannot possibly be classically local causal in a relativistic sense as ALL such theories are excluded by Bell, plus the thousands of experiments that exclude local realism. And of course, there are no known superluminal signals known at this time, and they are also excluded by all currently accepted theory.
 

DrChinese

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1. Where does he state that about QFT? Bear in mind that I am not asking what he says about quantum foundations; I've read plenty of what he's written about quantum foundations, and none of it says a thing about QFT; all of his writings on the subject that I have read, like all the other quantum foundations literature that I have read, uses non-relativistic QM as its framework. So the fact that it all talks about states of spatially separated systems does not at all answer the question I am asking, because of course non-relativistic QM assigns states to spatially separated systems. Nobody is disputing that. But that does not mean that QFT does so too. To establish that you need to show me a reference about QFT.

More generally, your argument appears to be that, since all of these well-known scientists are using non-relativistic QM instead of QFT to discuss quantum foundations, QFT must make no difference to quantum foundations. I think that is a weak argument. At the very least, if it really is true that everybody working in the field believes that, it would be nice to see a reference to a textbook or paper where they explain why; I have never seen one, and while I have not read the entire literature in the field, I have spent some time looking since it seems so obvious to me that there should be such an argument if everyone in QM foundations is simply going to ignore QFT. Every time someone posts a link to a new QM foundations paper here at PF, I look at it just to see if QFT is mentioned. So far it never has been.

2. Again, you need to define what you mean by "quantum nonlocality". If it means "correlations that violate the Bell inequalities", then of course you are correct, and nobody has disputed that. Nobody is disputing the actual experimental results. The only disputes are about what kind of story you want to tell in ordinary language about the experimental results, and whether you need to pay attention to QFT in order to tell such a story.

If you mean something else by "quantum nonlocality", then you're going to have to explain what, because at that point "quantum nonlocality" no longer means the thing that is "established by perhaps a thousand experiments", but some other theory-dependent claim.

3. My position, as should be obvious from the above, is that "quantum nonlocality" in the sense of correlations between spacelike separated measurements that violate the Bell inequalities, is an obvious experimental fact. QFT predicts this experimental fact, so QFT is perfectly consistent with quantum nonlocality in this sense.

4. QFT is also "locally causal" in the sense that spacelike separated measurements commute.

5. I would rephrase this as: the need to explain how measurements on entangled systems at macroscopic spacelike separations can show correlations that violate the Bell inequalities. That makes it precise exactly what experimental facts you are referring to.

This is not an experimental fact but a theory-dependent statement. The experimental fact is correlations that violate the Bell inequalities.
1. Seriously, I cannot fathom what you intend here. To say an author espousing the existence of quantum nonlocality is referring to theory OTHER than QFT makes no sense whatsoever. If there were some caveat about QFT, they would say so. It's not like QM is quantum nonlocal and QFT is not. And yet again you ask me to prove what you say, not what I say - which I have demonstrated by quote after quote and could do for as many as needed. And yet... where is a single quote from an author saying QFT is local causal and/or Bell doesn't apply?

And if I'm wrong: What element of QFT renders a substantially different prediction for Bell inequalities than garden variety QM?


2. Seriously, after referencing a 2019 book titled Quantum Nonlocality and presenting multiple quotes from top sources? Okay:

Vaidman: Given entangled particles placed at a distance, a measurement on one of the particles instantaneously changes the quantum state of the other, from a density matrix to a pure state."

Weinberg [minor paraphrasing]: "A measurement in one subsystem can change the state of a distant isolated subsystem faster than c."


3. I agree with this. :smile:

You skirt the edge of things by saying that they are correlations though, and not something more. In my example, I show how Alice steers Bob, and that occurs in ALL reference frames. Of course, if there is retrocausality then perhaps it is Bob that steers Alice (and I am not asserting that). Outside of that, I would have to say that Alice is in the driver's seat and is the causal agent of the steering of Bob's state. After all, she can steer Bob to any state she likes. Just to be clear: there is nothing Bob sees that indicates *by itself* what that new state is. There is no signal embedded via steering alone, of course you would need to know what Alice did to be convinced that steering occurred.

So I just don't see how you can miss that Alice causes Bob's state to change exactly according to what she measures. Cause, not just correlation. Forget QFT, this confirmed experimental fact supercedes theory.


4. I'm not gonna touch this. How this is meaningful in light of every evidence of the HUP at work is beyond my understanding. I think we already settled that I do not understand how your statement is correct AND yet non-commuting observables in an entangled QM system DO commute in an entangled QFT system.


5. Again, you are watering down what everyone else is saying. See the quotes for 2 above, which indicate Alice is steering.

But even if Alice was NOT the causal agent, I would still say that there is some type of nonlocal connection. A and B do not "happen" to end up in the same state, out of an infinite number of such states. The measurement choice is a CRITICAL piece of the overall context.

@PeterDonis Thanks for continuing the discussion.-DrC
 

DrChinese

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I don't think physical variables must be nonlocal to replicate QM predictions, that's just one way of explaining CHSH violations, but not the only one.
I agree with this, because no one understands the underlying mechanisms at work.

Ditto with whether or not collapse is physical. Certainly, in my example, which is basically the original EPR example: it LOOKS as if collapse is physical and involves action exceeding c. But that is before you consider the interpretations of QM, which seek to clarify/simplify things.
 

DrChinese

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What precisely do you think is correct in @DrChinese 's answer? He is always arguing in terms of fictitious local HV theories
[I said I wouldn't respond to Vanhees71, and now I am... :smile: ]

Just to clarify the glaring (and completely wrong) item about me: I am in no way advocating local hidden variable theories. Either we live in an observer dependent world (one that is contextual, there are no hidden variables); or we live in a world where there are nonlocal influences; or both. We know this after Bell. Any theory that does not follow Bell is excluded; and to the extent any theory denies both contextuality and nonlocality, it is excluded too. If anyone says that QFT denies both contextuality and nonlocality: then either their understanding of QFT is wrong, or QFT is wrong.
 
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To say an author espousing the existence of quantum nonlocality is referring to theory OTHER than QFT makes no sense whatsoever.
Sure it does. The authors talking about quantum nonlocality all talk about the Schrodinger Equation. The Schrodinger Equation is not QFT. It's non-relativistic QM.

It's not like QM is quantum nonlocal and QFT is not.
I have never made this claim so I don't understand why you bring it up.

All I am saying is that if all these authors talk about the Schrodinger Equation when they talk about quantum nonlocality, they are not talking about QFT.

What element of QFT renders a substantially different prediction for Bell inequalities than garden variety QM?
I have never claimed that it does. In fact I explicitly said the opposite, that QFT predicts Bell inequality violations, just as non-relativistic QM does.

after referencing a 2019 book titled Quantum Nonlocality and presenting multiple quotes from top sources?
None of which use QFT as their framework. Neither do the two quotes you give here.

I show how Alice steers Bob, and that occurs in ALL reference frames.
This can't be right since in some frames Bob's measurement occurs before Alice's if their measurements are spacelike separated. The non-relativistic language you and the authors you quote are using ignores this issue, but that doesn't mean it's not an issue.

this confirmed experimental fact supercedes theory.
There is no confirmed experimental fact that "Alice steers Bob". The confirmed experimental fact is that their measurement results show correlations that violate the Bell inequalities. You are confusing experimental facts with theory-dependent claims.

I do not understand how your statement is correct AND yet non-commuting observables in an entangled QM system DO commute in an entangled QFT system.
What non-commuting observables are you talking about? All "Alice" observables commute with all "Bob" observables (the observables being discussed here are all spin measurements). That is just as true in non-relativistic QM as it is in QFT. And for any pair of entangled particles, there is one "Alice" observable and one "Bob" observable.

The only non-commuting observables involved are multiple "Alice" observables in different directions, and multiple "Bob" observables in different directions. But there are never multiple "Alice" observables or multiple "Bob" observables involved for a single entangled pair. Each "Alice" particle only gets measured in one direction, and each "Bob" particle only gets measured in one direction.

See the quotes for 2 above, which indicate Alice is steering.
This is an argument from authority and it does not convince me. Either these authors are being sloppy in their language, or they don't mean what you are claiming they mean by that language, or they simply have not thought through what they're saying. It seems obvious that since the Alice and Bob measurements commute, neither can "steer" the other, since the results do not depend on the order in which the measurements are made. And the experimental evidence does not show that either one "steers" the other; all it shows is correlations that violate the Bell inequalities.

You appear to agree that nobody knows what underlying mechanism produces those correlations; but your claim about "steering" is a claim that we do know what the mechanism is--"steering" is precisely such a mechanism.

even if Alice was NOT the causal agent, I would still say that there is some type of nonlocal connection
I agree that it seems like there must be some underlying mechanism that produces the correlations that violate the Bell inequalities, and "nonlocal connection" is as good a name for this unknown mechanism as any. But the fact remains that the mechanism is unknown (and even our belief that there must be some such mechanism might possibly be wrong).
 

vanhees71

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But that's the point! QFT is of course NOT a local deterministic HV, but completely in accord with Einstein causality, including the impossibility of FTL communication, and all observations, including the violation of Bell's inequalities.

What's shown concerning Bell is that local deterministic HV theories are ruled out. Relativistic QFT is not such a theory and is in full accordance with all findings concerning the violation of Bell inequatlities and there's nothing nonlocal that is not allowed to be nonlocal: The interactions are local (the microcausality constraint is fulfilled), the cluster-decomposition principle is valid. The "nonlocal correlations" (though "nonlocal" is a misleading term here! Einstein's term "inseparability" is a far better term for it) described by entanglement is of course there and must be in order to be consistent with the findings on Bell's inequality. What's excluded in fact IS Bell's local realistic HV theories. What's confirmed by the experiments is QT and particularly also relativistic local (microcausal) QFT! I think this is the point, where we cannot agree upon, but the experimental facts speak for themselves: It's simply a fact that Bell's inequalities are violated in all Bell measurements done so far, and at the same very high confidence levels the predictions of relativistic QFT are confirmed!

I'm not sure what you mean by "contextuality" here: It's of course clear that the specific correlations seen in Bell experiments depends on what's measured and which subensembles are considered. That's the key issue with entanglement swapping, as we have discussed recently in this forum too. In this sense of course QFT is "contextual" as any QT.
 

DrChinese

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1. I agree that @DrChinese 's answer is correct and a simple exposition of the answer to OP's question.

2. I think @vanhees71 mistook @DrChinese 's statement regarding a lower bound for nonlocal influence velocity in a nonlocal hidden variable theory as a statement that there had been observed violations of Relativity and that was when the discussion moved off.

3. @vanhees71 I also don't think @DrChinese is advocating local classical hidden variables, he was just commenting on the experimental bounds on nonlocal hidden variable theories.
1. Thanks for saying so!!

2. I am unaware of any experimental violation of either special or general relativity. Like many, I am confused as to how to reconcile these theories to the vast experimental evidence of Quantum Nonlocality; but I don't see the conflict between these as direct. It's more of an implied conflict, which is why the quantum interpretations exist.

3. As an advocate of the importance of Bell's Theorem, I say: No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.
 
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I don't think "ontology" is the right word here. In particular, in the path-integral formulation of QFT there are no field operators at all, but ontology should not depend on the formulation.
This is a fair point. Neither formulation has states for spatially extended systems, though, so those aren't part of the ontology either.
 

Cthugha

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I agree with this entirely. QFT cannot possibly be classically local causal in a relativistic sense as ALL such theories are excluded by Bell, plus the thousands of experiments that exclude local realism.
I do not see how the assumption that QFT as outlined by @vanhees71 is classically local causal is warranted. Essentially, it boils down to Mermin's tongue-in-cheek statement (American Journal of Physics 66, 753-767 (1998) , https://arxiv.org/abs/quant-ph/9801057):

"My complete answer to the late 19th century question “what is electrodynamics trying to tell us” would simply be this:
Fields in empty space have physical reality; the medium that supports them does not.

Having thus removed the mystery from electrodynamics, let me immediately do the same for quantum mechanics:
Correlations have physical reality; that which they correlate does not."

Assuming well defined and prepared values for correlations does not imply that the correlated quantities themselves have well-defined values, so I do not see any need to assume realism/non-contextuality for QFT.

I also somewhat disagree with the following point:

My point is the other way: experimental fact, plus virtually any assumption about quantum theory (QM or QFT or whatever that includes the HUP) shows us that Alice's choice of measurement basis casts Bob's particle into a pure state determined solely by Alice (from an infinite number of such).
I see no reason for this claim. There is a joint choice of measurement bases for Alice and Bob and QFT (and every correct theory) yields the correct results for this combination of measurements. Within this framework it does not matter which measurement comes first and one does not have to assume any causal influence. It of cause does not rule out such an influence either, but there is no need to assume one.
 

DrChinese

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This can't be right since in some frames Bob's measurement occurs before Alice's if their measurements are spacelike separated.
Then you didn't read my example completely. The B particle is measured well after Alice steers. The B particle, distant at that time, is later re-routed back to Alice and is measured in Alice's reference frame (it could be measured by Bob, present there as well, who tells Alice the result). The point is that both measurements occur at the same place in the same frame, but one after the other, so there is no ambiguity about which comes first.

Surely it's not that difficult to see that relativity plays absolutely no role in this situation. There is no adjustment needed to the quantum expections regardless of reference frames anyway. You can have any measurement order, any reference frames, and the results are the same. Assuming no retrocausality (an easy assumption when we are debating quantum nonlocality), then either Alice steers Bob - or Bob steers Alice. Presto, we have spooky action at a distance, better known as quantum nonlocality.
 

DarMM

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What's excluded in fact IS Bell's local realistic HV theories. What's confirmed by the experiments is QT and particularly also relativistic local (microcausal) QFT! I think this is the point, where we cannot agree upon, but the experimental facts speak for themselves
I don't think @DrChinese is disagreeing with any of that, he clearly says he's not saying local hidden variables are true. As a third party this all reads as a discussion spun from confusing terminology.

You are using "local" to mean microlocality, @DrChinese is using it to mean classical correlations. Thus to him your denial of nonlocality appears as denying CHSH violation and to you saying QFT is nonlocal (by which he only means "contains nonclassical correlation") appears to be a rejection of microlocality and cluster decomposition.
 

vanhees71

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I agree that it seems like there must be some underlying mechanism that produces the correlations that violate the Bell inequalities, and "nonlocal connection" is as good a name for this unknown mechanism as any. But the fact remains that the mechanism is unknown (and even our belief that there must be some such mechanism might possibly be wrong).
I couldn't agree more with what you said in the part I deleted. Thanks for telling @DrChinese what I'm telling him for ages in other words. Maybe it helps!

The only point is that you don't need any "unknown mechanism". It's all described by standard QT (and of course relativistic QFT, which is just a special case of QT with the special feature that it's in accordance with the SRT space-time structure and all causality constraints implied by this space-time structure) entanglement.

Entanglement occurs naturally when you have two separable parts of a system, e.g., two particles. Here separable means that you can prepare product states ##|\psi_1 \rangle \otimes |\psi_2 \rangle##, e.g., when you have to dinstinguishable (sic!) particles. Then the common Hilbert space is ##\mathcal{H}_1 \otimes \mathcal{H}_2##, which consists of course not only of product states but all linear combinations thereof. Of course, the product states are part of the Hilbert space, and thus it is possible to prepare the two-particle system in such product states. These are by definition the states, for which the particles are NOT entangled. Einstein called this very nicely "separability", i.e., there are states.

But as is easy to see, the separable states (i.e., the product states) are quite special, and indeed interactions between the two particles lead to linear combinations which cannot be written as product states, and then you call the parts of the system "entangled". That's the origin of the violation of the Bell inequalities and thus the stronger-than-classical correlations of far-distant parts on an entangled quantum system.

To start with you always use particles created in some local process and usually the entanglement is due to some conservation law:

E.g., in the original EPR argument you can think of two (asymptotic) free particles originating from a particle decay. The original particle has a pretty well defined momentum. Now suppose it decays at some time ##t=0## in some region (e.g., take an ##\alpha##-decaying nucleus in a cloud chamber, decaying to the ##\alpha## particle and the daughter nucleus). The resulting asymptotic free state is a free ##\alpha## particle and the doughter nucleus with pretty well defined total momentum and a pretty well defined relative position. Note that these to observables are compatible, and you can prepare the two-particle system in a product state of these two observables,
$$\Psi(r,P)=\psi_{\text{rel}}(r) \tilde{\psi}_{\text{CM}}(P).$$
This you can Fourier transform to the product state
$$\Psi(r,R)=\psi_{\text{rel}}(r) \psi_{\text{CM}}(R),$$
where ##\psi_{\text{CM}}(R)## is a pretty broad distribution.

Now it's easy to transform this to the single-particle positions. You simply need to set
$$r=x_1-x_2, \quad R=\frac{m_1 x_1+m_2 x_2}{m_1+m_2}.$$
Wrt. to these observables you end up in the entangled state
$$\Phi(x_1,x_2)=\Psi(x_1-x_2,(m_1 x_1+m_2 x_2)/(m_1+m_2))=\psi_{\text{rel}}(x_1-x_2) \psi_{\text{cm}}[(m_1 x_1+m_2 x_2)/(m_1+m_2)].$$
Through the usual manipulations it's easy to see that the probability distributions for both ##x_1## and ##x_2## alone are broad, i.e., both positions are pretty much indetermined. The same holds true for the momenta (which you get by Fourier transforming ##\Phi## wrt. ##x_1## and ##x_2## of course).

If you determine by a measurement, which can be as accurate as you wish, the position of particle 1, then you get also a narrow distribution for the position of particle 2 (since ##\psi_{\text{rel}}(x_1-x_2)## is narrowly peaked). The same is true in momentum space: Determining ##p_1## well also determines ##p_2##. Of course you can never determine both ##x_1## and ##p_1## well at the same time, because the precise position measurement prevents the momentum to be determined well too and vice versa.

As you see, there's no need for any further "mechanism" to describe the correlations due to entanglement (i.e., "inseparability") than the known quantum-dynamical rules, and entanglement is the rule rather than the exception.

If it comes to indistinguishable particles, it's even difficult to define separable states. For bosons the two-boson state with the two particles in the same state is an example. All other two-particle states are entangled in the one or the other observable due to the necessity of Bose symmetrization (most conveniently taken account of by using creation and annhilation field operators).
 

DarMM

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Sure it does. The authors talking about quantum nonlocality all talk about the Schrodinger Equation. The Schrodinger Equation is not QFT. It's non-relativistic QM
Technically it is in QFT, though not often used.

Usually the nonlocality in quantum foundations is defined in the ontological models framework which is a general framework that applies equally to discussing QM and QFT.

There is no confirmed experimental fact that "Alice steers Bob"
I think @DrChinese may be referring to Quantum Steering which is a term in Quantum Information.
 

DrChinese

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1. I do not see how the assumption that QFT as outlined by @vanhees71 is classically local causal is warranted.

2. I also somewhat disagree with the following point:

DrChinese said:
My point is the other way: experimental fact, plus virtually any assumption about quantum theory (QM or QFT or whatever that includes the HUP) shows us that Alice's choice of measurement basis casts Bob's particle into a pure state determined solely by Alice (from an infinite number of such).

I see no reason for this claim. There is a joint choice of measurement bases for Alice and Bob and QFT (and every correct theory) yields the correct results for this combination of measurements. Within this framework it does not matter which measurement comes first and one does not have to assume any causal influence. It of cause does not rule out such an influence either, but there is no need to assume one.
1. Naturally I agree. :biggrin:


2. I mostly agree with your statement, except you skip the situation in which one measurement unambiguously occurs first. So here's how I would summarize:

a. In a Bell test in which the order of Alice and Bob's measurements is NOT well defined: there is no clear underlying statement about causality that can be made. We agree on this.

b. In a Bell test in which the order of Alice and Bob's measurements IS well defined with Alice acting first: Alice can be said to steer Bob. (Of course the outcomes are themselves random and are not determined by any known factor.) This is what Weinberg means when he states: "according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem.. " Of course he is referring to the original EPR paradox as the basis for this statement, where ordering was assumed. But he also means that nothing currently prevents us from executing the experiment so that ordering is in fact clear.

c. Even in the b. case, there are quantum interpretations which there is no causality; i.e. the decisions of both Alice and Bob are part of the overall context. In these, the action at a distance cannot be said to be caused by anything and there is no direction of action. Relational Blockworld is such a theory, for example. So even though we say there is steering (which implies causal direction), this is more of a linguistic aid than anything else.


NOTE: Just in case you would like a specific reference, here is an incredible experiment that demonstrates not only steering; it demonstrates ONE-WAY steering! That is: Alice can steer Bob but Bob cannot steer Alice!! Of course, I am simplifying somewhat as this is a very complex setup.


The distinctive non-classical features of quantum physics were first discussed in the seminal paper by A. Einstein, B. Podolsky and N. Rosen (EPR) in 1935. In his immediate response E. Schrödinger introduced the notion of entanglement, now seen as the essential resource in quantum information as well as in quantum metrology. Furthermore he showed that at the core of the EPR argument is a phenomenon which he called steering. In contrast to entanglement and violations of Bell's inequalities, steering implies a direction between the parties involved. Recent theoretical works have precisely defined this property. Here we present an experimental realization of two entangled Gaussian modes of light by which in fact one party can steer the other but not conversely. The generated one-way steering gives a new insight into quantum physics and may open a new field of applications in quantum information.
 

DarMM

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Figure 1 in this paper has a nice diagram of the correlation hierarchy:
 

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