Undergrad EPR and Non-Locality - For and Against

[vanhees71]

I accept that in a Bell test, the entangled system cannot be considered as two separate photons (or other particles). However, a system with such spatial extent as is used in Bell test (say 2 photons) cannot be considered as being "localized" either. In fact, I am not sure it even makes sense to say a single photon system is "localized" as in many cases, a single photon can be considered to have a very large* spatial extent.

I think that's the point! If you have two photons in an entangled state they are not localized (despite the fact that even a single photon cannot be strictly localized, because it hasn't even a position) but nevertheless correlated in the sense that you don't have a product of two single-photon states. Nevertheless that's not "non-locality" in a causal sense but what Einstein much more elegantly dubbed "inseparable", and Einstein emphasized that it is inseparability that bothered him most. It's also clear that this is only in tension with causality if you take the collapse of the state when measurements are done on the inseparated parts of the system as a physical process rather than an adaption of our description of the system after the measurement. His suggestion famously were hidden variables, but only with Bell's work this got a physical statement, i.e., a conjecture that could be tested by experiment, and immediately the experimental challenge was taken up by Aspect et al, and QT and inseparability turned out to be correct and not local hidden variable models (apparently to somewhat of a surprise for Bell). The conclusion thus indeed is that nature seams to allow for "inseparable" states in the sense of QT.

And in either case, we are witnessing quantum nonlocality. I can't imagine any definition of such systems that imply otherwise. We can have systems that are many kilometers in size, and still have perfect correlations in Bell tests with observers Alice and Bob.

As I said, the common naming this as nonlocality is confusing in the context with relativistic QFT, where one emphasizes from the very beginning the locality of interactions and microcausality. You can have perfect correlations between inseparable parts of a system at any distance though it is more and more difficult to maintain the entanglement by sufficiently isolating the entire system from the interaction with "the environment" to avoid decoherence.

So I would certainly say that if you retreat to the position that there is no quantum nonlocality as Alice and Bob perform their respective measurements, and that it is the system instead that has spatial (and/or temporal) extent: you haven't eliminated the quantum nonlocality, you have simply moved it.

The "nonlocality" (or rather in my preferred Einsteinian lingo "inseparability") is due to the state preparation rather than the measurement. That's an important point to understand that there's in fact no violation of Einstein locality in Bell tests. As discussed some time ago in these forums, this also holds for realizations of entanglement swapping, which is due to filtering according to local measurements preparing entanglement between parts of a quantum system which never have been interacting themselves.

And further: Alice can take the portion of an entangled system she receives... and teleport that entanglement FTL to another system as far distant as she likes. And again we can perform Bell tests on the newly enlarged entangled system, and get perfect correlations. That's a pretty good trick if there is no quantum nonlocality.*Perhaps even as large as the observable universe?

It's not FTL, because at the instant A does her local measurement it's only her who knows that she has teleported a state. B who does the measurement doesn't know it at this instant but only when A and B share their measurement protocols they can establish the corresponding correlations (on the then enlarged system). That's why it is so important to take the collapse not as a physical process as some Copenhagen-flavored interpretations seem to suggest but simply as an update of the state description, depending on (local) observations.

 

[vanhees71]

Consider how many human-years have been spent working to “figure out how those facts happen” without resolution. By “how” we mean by “constructive efforts” (per Einstein). It’s interesting that the same is true of time dilation and length contraction in SR, where the physics community long ago decided to accept Einstein’s “principle account” and gave up looking for a “constructive” counterpart. It’s also interesting that Bell state entanglement follows from the same principle account, i.e., the relativity principle (no preferred reference frame). Perhaps the physics community will again eventually accept this principle account and give up looking for a constructive counterpart there, too.

It's figured out, how those facts are to be perfectly described, namely by quantum (field) theory, discovered in 1925/26 by Heisenberg, Born, and Jordan.

 

[Morbert]

But thousands of experiments show there is not local realism at the base. And that means there IS quantum nonlocality (since that's the usual definition).

For the purposes of this thread I'd agree. I'll sometimes go to bat for Griffiths's local realist consistent histories but it's not too relevant here. Quantum nonlocality, as described above, is consistent with most mainstream interpretations.

It's NOT some coincidence as is claimed by some here (mere "correlations"). Selection of a measurement basis by Alice leads to an exact predicted result by far distant Bob on that basis. [...] A system which stretches many kilometers in extent manages to take on a specific value of an observable instantaneously.

I think all the subtleties lie in the sentences above.

According to a typical antirealist position, if Alice performs a measurement on this extended system, she will create a record of a measurement outcome in her apparatus, and this record will inform her expectations of measurements Bob might perform on this same extended system.

What she did not create, however, is a quantum property of the extended system corresponding to a specific value of an observable. If we adopt an antirealist position, then we must fully commit: QM does not describe properties of quantum systems, extended or otherwise. Instead it describes frequencies and correlations in experimental records that are produced in response to interactions with quantum systems.

 

[vanhees71]

Exactly. The "collapse" due to Alice's measurement is only that she adapts her description due to its outcome. Then she knows what Bob must find when measuring the corresponding 100% correlated property. E.g., taking the standard example of two photons in the singlet-polarization state then she knows, when she has measured H-polarization on her photon, Bob must measure helicity V-polarization if he measures in the same polarization direction. That's the 100% correlation described by the entanglement.

Of course Bob can also measure the polarization in any other direction. Then Alice can still predict the corresponding conditional probabilities for the outcome of Bob's measurement given here measurement result. What Bob measures for the full ensemble are just unpolarized photons (which is also what Alice measures). Only if Alice and Bob share their measurement protocols they can figure out that their photons were entangled, no matter whether both measure the polarization in the same or in a different direction.

Nothin changes instantaneously in a causal sense on Bob's photon due to Alice's measurement. The collapse is just the adaption of the description of the system after the measurement by Alice. Bob cannot instantaneously update his description, because it needs the information about Alice's outcome, and that Bob can not get instantly or by any faster than light signal. Of course I assume that standard relativistic QFT is correct, which by construction doesn't allow for FTL communication.

 

[martinbn]

If you deny non-locality, then what does Bell theorem really prove, in your opinion?

I might be wrong, but my impression is that no one denies the result of Bell. People only say that non-locality is a poor choice of terminology. Why use it if it is already in use! Because I am cynical, I think the reason is the BM adherents. BM is non-local, so they don't miss any opertunite to say that Bell + experiment have proven that nature is non-local.

 

[martinbn]

Haha, yes, we have covered this before. In this forum, and you participated in at least some of it (see your post #33).

https://www.physicsforums.com/threa...rpretation-of-quantum-mechanics.989890/page-2

You ask "in what sense"? Per Steven Weinberg, Lectures on Quantum Mechanics, 12.1 Paradoxes of Entanglement (talking about EPR-B):

"There is a troubling weirdness about quantum mechanics. Perhaps its weirdest feature is entanglement, the need to describe even systems that extend over macroscopic distances in ways that are inconsistent with classical ideas. ... Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem - it just doesn't change the density matrix."

Of course, you interpreted another statement by Weinberg as implying QM is local (or something that I couldn't agree as saying QM is local). I'd love to an actual quote by Weinberg where he denies quantum non-locality, or otherwise denies the obvious implications of Bell. Since the quote above explicitly says:

According to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem...

Of course, to be fair: there is no apparent direction of the change referred to. It could be in either direction.

To me this is a very sloppy language. The claim is that the measurement here changes the state of the subsystem over there. But what is the state of the system before the measurement? It doesn't make sense to talk about the state of the subsystem (in fact about subsystems) at all. So what state changes!

 

[vanhees71]

Indeed, this apparent problem only occurs if you interpret the collapse of the state as something dynamical really happening in nature, but that's not necessary to assume to use QT. It's also contradicting the very foundations of relativistic LOCAL QFT! There's simply no FTL change on one far distant part of an entangled quantum system due to a local measurement (and all measurements I know of are local) on the other part of it.

 

[RUTA]

It's figured out, how those facts are to be perfectly described, namely by quantum (field) theory, discovered in 1925/26 by Heisenberg, Born, and Jordan.

As I explained many times here, QFT does not resolve the mystery of QM entanglement because QM is QFT for the Bell state phenomena. This is equivalent to saying Newtonian mechanics is special relativity at low velocities. So saying you want to bring QFT to bear on the mystery of QM entanglement is redundant, just like saying you want to bring SR to bear on a mystery of Newtonian mechanics where Newtonian mechanics matches experiment beautifully. If there was a QM prediction that deviated from experiment, then it would perhaps be reasonable to bring the subsuming theory (QFT) to bear on that experiment. But, that's not the case for violations of the Bell inequality to 8 sigma as predicted by QM.

 

[Minnesota Joe]

The experimenters are irrelevant. The particles are entangled - you can't say for sure they exist as separate particles for the idea of locality to even make sense.

Here is the math. Let's say we have two systems that can be in state |a> and |b>. If system 1 is in state |a> and system 2 in state |b> we write this as |a>|b>. Conversely if system 1 is in state |b> and system 2 in state |a> we write it as |b>|a>. By the principle of superposition a possible state of both systems is 1/√2 (|a>|b> + |b>|a>). In such a state what state each system is in, or even if there is still two systems, is unclear - you can only speak with certainty of the combined system 1 and 2. If they have no individuality the idea of signals passing between the two systems does not even make sense.

Thank you for the response Bill. This last sentence is my first point of confusion. Your combined state is an extended object with boundaries, "ends" if you will. We know this because Alice and Bob have something to measure. When those ends reach Alice and Bob, there is distance between the ends since there is separation between Alice and Bob. The idea of a signal passing between two different points in space does make sense.

But as Peter correctly points it is just semantics on what you mean by non-locality.

I don't think the disagreements are merely semantic and I didn't read Peter's comment that way, but dogmatically insisting on our own definitions while ignoring other people's definition can cause us to talk past one another. I hope we are all adults and can provisionally adopt each other's senses of a word for the sake of polite discussion and understanding.

 

[RUTA]

I don't think the disagreements are merely semantic and I didn't read Peter's comment that way, but dogmatically insisting on our own definitions while ignoring other people's definition can cause us to talk past one another. I hope we are all adults and can provisionally adopt each other's senses of a word for the sake of polite discussion and understanding.

Exactly. The meaning of a term within a community obtains via de facto consensus. Attempting to idiosyncratically assign a different meaning to the term defeats the point of language as a means of communication. The same holds for any means of communication, you must adhere to convention within the community where you use it: https://www.businessinsider.com/hand-gestures-offensive-different-countries-2018-6

 

[vanhees71]

As I explained many times here, QFT does not resolve the mystery of QM entanglement because QM is QFT for the Bell state phenomena. This is equivalent to saying Newtonian mechanics is special relativity at low velocities. So saying you want to bring QFT to bear on the mystery of QM entanglement is redundant, just like saying you want to bring SR to bear on a mystery of Newtonian mechanics where Newtonian mechanics matches experiment beautifully. If there was a QM prediction that deviated from experiment, then it would perhaps be reasonable to bring the subsuming theory (QFT) to bear on that experiment. But, that's not the case for violations of the Bell inequality to 8 sigma as predicted by QM.

There is no mystery to begin with, and I've no clue, what you mean by "QM is QFT for the Bell state phenomena". QM is a non-relativistic approximation of relativistic QFT. That's all. There is no contradiction between QM and experiment, where it is applicable. There's neither a contradiction between experiment and relativistic QFT.

 

[RUTA]

There is no mystery to begin with, and I've no clue, what you mean by "QM is QFT for the Bell state phenomena". QM is a non-relativistic approximation of relativistic QFT. That's all. There is no contradiction between QM and experiment, where it is applicable. There's neither a contradiction between experiment and relativistic QFT.

QM works beautifully to predict and analyze Bell state phenomena and QM is just the low energy approximation to QFT. So appeals to QFT as resolving any "mystery" associated with Bell state entanglement is vacuous. Whether or not you see anything "mysterious" is irrelevant. If you are going to engage those who do see mystery, then you cannot simply say there is no mystery because QFT is this or that. They already know full well what QFT says about the phenomenon because they know what QM says and, as you agree, QM is QFT when dealing with that experiment.

 

[RUTA]

Here is a relevant quote from Mermin published in Physics Today:

To this moderate point of view I would only add the observation that contemporary physicists come in two varieties.
Type 1 physicists are bothered by EPR and Bell’s theorem.
Type 2 (the majority) are not, but one has to distinguish two subvarieties.
Type 2a physicists explain why they are not bothered. Their explanations tend either to miss the point entirely (like Born’s to Einstein) or to contain physical assertions that can be shown to be false.
Type 2b are not bothered and refuse to explain why. Their position is unassailable. (There is a variant of type 2b who say that Bohr straightened out the whole business, but refuse to explain how.)

 

[Minnesota Joe]

Exactly. The meaning of a term within a community obtains via de facto consensus. Attempting to idiosyncratically assign a different meaning to the term defeats the point of language as a means of communication.

That's half of it, but it cuts both ways. If someone is using 'non-locality' in a way you think is non-standard, it is pointless and disingenuous to pretend they are using it in a way that "obtains via de facto consensus" in order to refute them. You've likely done no such thing.

Besides, different communities in physics might use the same word to mean different things. In that case the dictionary of physics has multiple entries under 'non-locality', one for each sense of the word as it is actually used by physicists.

 

[vanhees71]

I only appeal to relativistic QFT to disprove claims that there's something nonlocal or that there's something "instantaneously caused" by a local measurement on a part of an entangled system as often claimed referring to naive collapse interpretations. You cannot counter such arguments using non-relativistic QM, because in non-relativistic (Galean-Newtonian spacetime) physics nothing prevents the theory predict instantaneous influcences. To the contrary, it's in fact the way how interactions are described (e.g., Newton's theory of the gravitational interaction).

I'm not bothered by EPR at all. Why should I be? Bell's theorem is a breakthrough in making the claims of the EPR paper a scientific statement, i.e., something that can be checked by experiment. It rules out all local deterministic HV theories, and all experiments verify QT. For me the case is closed concerning all the confusion with the EPR paper and Bohr's answer to it. Anyway, Einstein didn't like the EPR paper himself and he clarified the point very well himself in a later paper introducing the notion of "inseparability", which is the real issue here.

If it is really the case that "non-locality" means different things in different communities, then one shouldn't use the expression when cross-communicating within differen communities without giving a clear definition of it.

 

[RUTA]

That's half of it, but it cuts both ways. If someone is using 'non-locality' in a way you think is non-standard, it is pointless and disingenuous to pretend they are using it in a way that "obtains via de facto consensus" in order to refute them. You've likely done no such thing.

Besides, different communities in physics might use the same word to mean different things. In that case the dictionary of physics has multiple entries under 'non-locality', one for each sense of the word as it is actually used by physicists.

It would certainly violate the goal of language to pretend they intended to use the term per convention defined by the context (here in talking about Bell state entanglement) when they were in fact violating convention. Communication would be thwarted. The parties involved in a conversation must simply agree on the meaning of the terms being used, lest they violate the first principle of logic, A = A. When the principles of logic are violated, confusion ensues.

 

[RUTA]

I only appeal to relativistic QFT to disprove claims that there's something nonlocal or that there's something "instantaneously caused" by a local measurement on a part of an entangled system as often claimed referring to naive collapse interpretations. You cannot counter such arguments using non-relativistic QM, because in non-relativistic (Galean-Newtonian spacetime) physics nothing prevents the theory predict instantaneous influcences. To the contrary, it's in fact the way how interactions are described (e.g., Newton's theory of the gravitational interaction).

Again, QM is QFT for this experiment so, yes, I can use whatever I like from QM to "explain" the experiment. Indeed, that's exactly what I am doing from the start when I predict violations of the CHSH inequality to the Tsirelson bound using low-energy QFT (aka QM). In order for your analogy with Newtonian gravity to be applicable, you would have to use QFT to predict some violation of the QM prediction. In the case of Newtonian gravity, one would appeal to the appropriate GR solution and show that GR predicts a time delay between changes in the matter configuration and distant "gravitational effects" contra the Newtonian prediction. One does the experiment to verify the GR prediction thus dispelling the "mysterious" but erroneous prediction by Newtonian gravity of instantaneous causation. There is no such QFT intervention for Bell state correlations because we do realize the Tsirelson bound per QM and that alone is what people find "mysterious." So, again, your claim that QFT in any way dispels the mystery of Bell state correlations is vacuous. And, again, whether or not you understand why so many people in foundations find such correlations mysterious is absolutely irrelevant.

 

[PeterDonis]

QM is QFT for this experiment so, yes, I can use whatever I like from QM to "explain" the experiment.

This is not correct as you state it. You can use the math of QM to predict the results of the experiment. But you cannot use an interpretation of QM that is inconsistent with QFT to "explain" the experiment, even if that interpretation is consistent with the math of QM in the non-relativistic approximation. So you can't use "whatever you like" from QM; you can only use the things from QM that remain valid in QFT.

Consider a similar claim for gravity: Newtonian gravity is GR for this experiment (say predicting the orbit of the ISS), so I can use whatever I like from Newtonian gravity to "explain" the experiment. That is not correct. You can predict the orbit of the ISS to very high precision using the math of Newtonian gravity that models it as an instantaneous inverse square law force. But you can't "explain" the orbit of the ISS by saying that gravity "really is" an instantaneous inverse square law force, because in GR, it isn't.

 

[RUTA]

This is not correct as you state it. You can use the math of QM to predict the results of the experiment. But you cannot use an interpretation of QM that is inconsistent with QFT to "explain" the experiment, even if that interpretation is consistent with the math of QM in the non-relativistic approximation. So you can't use "whatever you like" from QM; you can only use the things from QM that remain valid in QFT.

Consider a similar claim for gravity: Newtonian gravity is GR for this experiment (say predicting the orbit of the ISS), so I can use whatever I like from Newtonian gravity to "explain" the experiment. That is not correct. You can predict the orbit of the ISS to very high precision using the math of Newtonian gravity that models it as an instantaneous inverse square law force. But you can't "explain" the orbit of the ISS by saying that gravity "really is" an instantaneous inverse square law force, because in GR, it isn't.

Let's follow your analogy and see how it relates to Bell state correlations. What is "mysterious" about Newtonian gravity is its prediction of instantaneous causation. So, you conduct an experiment to see if there is any time delay between gravitational influences and the (distant) ISS. GR says there will be a time delay and Newtonian gravity says there will not be a time delay. What does the experiment find (in analogy with Bell state correlations)? The experiment shows a time delay to 8 sigma, refuting the "mysterious" prediction of Newtonian gravity. What is the analogous situation with Bell state correlations? Local hidden variable theories predict adherence to the CHSH inequality while QFT predicts a violation of the CHSH inequality. The experiment is conducted and we find the CHSH inequality is violated to 8 sigma per the QFT prediction. Unlike the Newtonian gravity/GR "mystery" it is the "mystery" that is actually vindicated in this case. Totally the opposite of your analogy.

 

[DrChinese]

To me this is a very sloppy language. The claim is that the measurement here changes the state of the subsystem over there. But what is the state of the system before the measurement? It doesn't make sense to talk about the state of the subsystem (in fact about subsystems) at all. So what state changes!

Sloppy? Easy to say. It's as descriptive as can be. And I think it summarizes the situation pretty well, which is why I quoted it (the reputation of the author might have also been a factor).

So what state changes? Before there is a measurement, we have an system of 2 photons in an entangled (non-separable) state. After Alice performs a Bell measurement on that system, she has a photon in a known spin state. The remainder of the system, now quite distant and near to Bob, instantaneously changes its state too - also to a known spin state. How is this confusing?

The only question remaining is whether it is Alice's measurement that leads to the state change (causal), or Bob's later measurement that leads to the state change (retrocausal), or both/neither (acausal). RUTA would choose the last of those (acausal). And in fact if you look at the formula* for predicting coincidences, there are only 2 significant variables: the relative angle settings of Alice and Bob. So the coincidence function does not distinguish order, which you could see as a nod to the acausal explanation as much as anything else.*Typically: cos^2(A-B) or sin^2(A-B), depending on entanglement type.

 

[PeterDonis]

GR says there will be a time delay

No, it doesn't, not for this experiment, or for any experiment where the Newtonian approximation is valid. See this classic paper by Carlip:

https://arxiv.org/abs/gr-qc/9909087

 

[RUTA]

No, it doesn't, not for this experiment, or for any experiment where the Newtonian approximation is valid. See this classic paper by Carlip:

https://arxiv.org/abs/gr-qc/9909087

By definition, so that is also not an apt analogy because in our case there are competing predictions.

 

[PeterDonis]

that is also not an apt analogy because in our case there are competing predictions

No, there aren't. The "competing predictions" you refer to are those of local hidden variable theories. But we aren't talking about local hidden variable theories vs. QM. We are talking about QM vs. QFT. We have all agreed that, for the cases in question (Bell-type experiments), QM and QFT make the same predictions. The difference is only in "interpretation"--"interpretations" of QM that aren't consistent with QFT can't be used to "explain" the results of Bell-type experiments, even though non-relativistic QM predicts the same results as QFT does. Just as Newtonian gravity can't be used to "explain" the results of gravity experiments, even in cases where Newtonian gravity and GR make the same predictions.

 

[RUTA]

No, there aren't. The "competing predictions" you refer to are those of local hidden variable theories. But we aren't talking about local hidden variable theories vs. QM. We are talking about QM vs. QFT. We have all agreed that, for the cases in question (Bell-type experiments), QM and QFT make the same predictions. The difference is only in "interpretation"--"interpretations" of QM that aren't consistent with QFT can't be used to "explain" the results of Bell-type experiments, even though non-relativistic QM predicts the same results as QFT does. Just as Newtonian gravity can't be used to "explain" the results of gravity experiments, even in cases where Newtonian gravity and GR make the same predictions.

There is no QM vs QFT for this experiment because QM is QFT for this experiment. The only competing prediction is due to local hidden variable theories. So, when comparing theories for the CHSH experiment, we are comparing QFT and hidden variable theories. Appealing to a "QM interpretation" of this experiment is appealing to a "QFT interpretation" of this experiment. There is no distinction, so there is no sense in which "QFT resolves the mystery of the violation of the CHSH inequality created by QM." You have just written, "QFT resolves the mystery of the violation of the CHSH inequality created by QFT."

 

[RUTA]

There is at least one thing meaningful concerning the compatibility of QM and SR that can be said regarding Bell state entanglement and I say it in my Insight:

Of course, we know QM is not Lorentz invariant and so it deviates trivially from SR in that fashion. In order to get QM from Lorentz invariant quantum field theory one needs to make low energy approximations [21, p. 173]. But, the charge of incompatibility based on QM entanglement actually carries serious consequences, because we have experimental evidence confirming the violation of the CHSH inequality per QM entanglement. So, if the violation of the CHSH inequality is in any way inconsistent with SR, then SR is being challenged empirically. By analogy, we know Newtonian mechanics deviates from SR because it is not Lorentz invariant. As a consequence, Newtonian mechanics predicts a very different velocity addition rule, so suppose we found experimentally that velocities do add as predicted by Newtonian mechanics. That would not merely mean that Newtonian mechanics and SR are incompatible, that would mean Newtonian mechanics has been empirically verified while SR has been empirically refuted. So, if one believes the violation of the CHSH inequality is in any way inconsistent with SR, and one believes the experimental evidence is accurate, then one believes SR has been empirically refuted. Clearly that is not the case, so their reconciliation as regards the violation of the CHSH inequality must certainly obtain in some fashion and here we see how the principle of NPRF does the job.

I'm sure NPRF isn't unique in this respect

 

[PeterDonis]

Appealing to a "QM interpretation" of this experiment is appealing to a "QFT interpretation" of this experiment.

You apparently aren't even reading my posts. We can't have a conversation if you don't read what I'm saying.

 

[RUTA]

You apparently aren't even reading my posts. We can't have a conversation if you don't read what I'm saying.

Haha, you and I almost always talk past one another. I'm not sure why that is because we are both very conventional physicists.

 

[martinbn]

Sloppy? Easy to say. It's as descriptive as can be. And I think it summarizes the situation pretty well, which is why I quoted it (the reputation of the author might have also been a factor).

So what state changes? Before there is a measurement, we have an system of 2 photons in an entangled (non-separable) state. After Alice performs a Bell measurement on that system, she has a photon in a known spin state. The remainder of the system, now quite distant and near to Bob, instantaneously changes its state too - also to a known spin state. How is this confusing?

The only question remaining is whether it is Alice's measurement that leads to the state change (causal), or Bob's later measurement that leads to the state change (retrocausal), or both/neither (acausal). RUTA would choose the last of those (acausal). And in fact if you look at the formula* for predicting coincidences, there are only 2 significant variables: the relative angle settings of Alice and Bob. So the coincidence function does not distinguish order, which you could see as a nod to the acausal explanation as much as anything else.*Typically: cos^2(A-B) or sin^2(A-B), depending on entanglement type.

The confusing part is where you say that the remainder of the system, at Bob, insantaneuosly changes its state. What was its state before that?

 

[vanhees71]

Again, QM is QFT for this experiment so, yes, I can use whatever I like from QM to "explain" the experiment. Indeed, that's exactly what I am doing from the start when I predict violations of the CHSH inequality to the Tsirelson bound using low-energy QFT (aka QM). In order for your analogy with Newtonian gravity to be applicable, you would have to use QFT to predict some violation of the QM prediction. In the case of Newtonian gravity, one would appeal to the appropriate GR solution and show that GR predicts a time delay between changes in the matter configuration and distant "gravitational effects" contra the Newtonian prediction. One does the experiment to verify the GR prediction thus dispelling the "mysterious" but erroneous prediction by Newtonian gravity of instantaneous causation. There is no such QFT intervention for Bell state correlations because we do realize the Tsirelson bound per QM and that alone is what people find "mysterious." So, again, your claim that QFT in any way dispels the mystery of Bell state correlations is vacuous. And, again, whether or not you understand why so many people in foundations find such correlations mysterious is absolutely irrelevant.

For which experiment? The Bell experiment with polarization-entangled photons is for sure not describable by QM but only by QED, i.e., relativistic QFT. QM is based on actions at a distance and thus by construction violates Einstein causality. It's no argument against the fact that there is a QT obeying Einstein causality, which is local relativistic QFT.

 

[vanhees71]

No, there aren't. The "competing predictions" you refer to are those of local hidden variable theories. But we aren't talking about local hidden variable theories vs. QM. We are talking about QM vs. QFT.

But you can't use QM, where it's not applicable, and you can't use it particularly for answering the question whether there are non-local interactions or not. By definition in QM the interactions are instantaneous as in classical Newtonian mechanics, and that's why QM is only applicable, where non-relativistic approximations are valid. As in classical electrodynamics of course quasistationary approximations violate locality because you neglect retardation effects and you cannot conclude from that approximation that there's non-locality in classical electrodynamics, you cannot claim there are actions at a distance by the argument that you use an approximation assuming such interactions. The point is that local relativistic QFT shows that QT is compatible with Einstein causality. You simply cannot disprove this by using a non-relativistic approximation.