I The notion of locality in (Quantum) Physics should be clearly defined

[martinbn]

You should know by now that I am too smart to be tricked by such a cheap play of words. "Discovered" in an experimental sense does not mean the same as "discovered" in theoretical physics or math. Yes, he made a theoretical discovery, he discovered a mechanism that can describe a "force" which can explain quantum correlations.

Of course, I had theoretically discovered in mind. So, you opinion is that there are more than four forces in nature?

https://arxiv.org/abs/1311.6852

I meant how specifically it applies. What are the events $A$ and $B$ in the Bell test scenario that are either causally related or have a common cause?

 

[Demystifier]

Of course, I had theoretically discovered in mind. So, you opinion is that there are more than four forces in nature?

Yes.

I meant how specifically it applies. What are the events $A$ and $B$ in the Bell test scenario that are either causally related or have a common cause?

A and B are clicks of two spatially separated detectors, I thought it was obvious.

 

[martinbn]

Indeed QFT is largely a red herring. Bell specifies a concern here when he says:QFT

He says that they immediately influence each other. That means an infinite speed of influence. But if you change the set up so that one of them measures later, then that would mean that the speed is very big and is just right to reach the second even. And that is the case no matter how much later the second event is. So the speed of this influence somehow depends on the set up. To me this is just like superdeterminism, except that the conspiracy is not in the initial conditions but in the evolution laws.

 

[Lord Jestocost]

There are no "magic dice". There's just relativistic QFT. As in any QT Born's rule, i.e., the probabilistic meaning of the quantum states, is one of the basic postulates and part of the minimal statistical interpretation, which just accepts one of the great objective findings about Nature, i.e., that it is inherently random. There's no magic involved, it's just a fact about Nature, which contradicts the outdated worldview of deterministic classical physics, and that's why many philosophers even today cannot accept it and build up all kinds of presumed paradoxes against this inevitable conclusion.

The heart of all problems people have with quantum theory is their "unwillingness" to simply accept the irreducible randomness of individual events.

For example, Bohm and Bub in their paper “A Proposed Solution of the Measurement Problem in Quantum Mechanics by a Hidden Variable Theory“ (Rev. Mod. Phys. 38, 453, 1966):

“It is not easy to avoid the feeling that such a sudden break in the theory (i.e., the replacement, unaccounted for in the theory, of one wave function by another when an individual system undergoes a measurement) is rather arbitrary. Of course, this means the renunciation of a deterministic treatment of physical processes, so that the statistics of quantum mechanics becomes irreducible (whereas in classical statistical mechanics it is a simplification – in principle more detailed predictions are possible with more information).”

 

[WernerQH]

The heart of all problems people have with quantum theory is their "unwillingness" to simply accept the irreducible randomness of individual events.

I have no problem at all with quantum theory, or the "irreducible randomness of individual events", and I think neither has @vanhees71 . My question was about his explanation of the correlations, according to QFT. It's more subtle than saying that the correlations arise from a common cause (the initial state preparation), because of quantum theory's inherent indeterminism. The future is not fully determined by the initial state.

 

[martinbn]

Yes.

I think this is the reason for the debates not that there is more than one definition of locality. You, and others, are convinced that there is non-local causality, and @vanhees71 and others make the point that given that there is at least one locally causal model (relativistic QFT) you cannot claim that Bell and all that proves that QM and nature are non-local in the sense that there is non-local causality.

A and B are clicks of two spatially separated detectors, I thought it was obvious.

Not to me, and it is still unclear. Assuming we are in the ideal situation there are always clicks at the detectors! So $A$ and $B$ occur with 100% probability.

 

[martinbn]

I have no problem at all with quantum theory, or the "irreducible randomness of individual events", and I think neither has @vanhees71 . My question was about his explanation of the correlations, according to QFT. It's more subtle than saying that the correlations arise from a common cause (the initial state preparation), because of quantum theory's inherent indeterminism. The future is not fully determined by the initial state.

What kind of explanation do you expect? Personally I am not convinced that the common cause principle is applicable when you have a fundamentally probabilistic theory and conservation laws. So, I don't think an explanation is needed. To me it seems that to ask for an explanation requires to assume that there is causality between the space-like events or a common cause.

 

[WernerQH]

Personally I am not convinced that the common cause principle is applicable when you have a fundamentally probabilistic theory and conservation laws.

Agreed.

What kind of explanation do you expect?

I was (and still am) curious about his view how the probabilities/correlations arise in the formalism of QED. My view is that it is essential that the propagators also reach into the backward light cone, i.e. that you have waves travelling backwards in time. But this smacks of retrocausality (at least for some people) and may conflict with another cherished principle of @vanhees71 , causality.

 

[hutchphd]

It was you who started talk about Bell's "realism", which is a philosophical concept.

I approached this thread with some excitement. Yet your second entry was an ad hominem attack. Ideas would be better.

 

[Demystifier]

I think this is the reason for the debates not that there is more than one definition of locality. You, and others, are convinced that there is non-local causality, and @vanhees71 and others make the point that given that there is at least one locally causal model (relativistic QFT) you cannot claim that Bell and all that proves that QM and nature are non-local in the sense that there is non-local causality.

That's a good point. Bell proves what it proves under one additional assumption, which is a notion of mathematical macroscopic realism. This means that macroscopic measurement outcome exists even if nobody observes it, and that it can be analyzed mathematically. Relativistic QFT in its minimal form usually accepts that outcome exists even if nobody observes it, but refuses to analyze it mathematically, which is why it cannot see the Bell theorem. It refuses to analyze it simply because the theory in its minimal form does contain the corresponding mathematical objects, and since the theory makes the right predictions even without them, refuses to consider additional mathematical objects which are not needed for predictions. Minimal QFT is somewhat like naive set theory, which refuses to consider some additional structures which are not needed in practical math, but is then unable to see deeper theorems about set theory, such as those related to the continuity hypothesis.

Not to me, and it is still unclear. Assuming we are in the ideal situation there are always clicks at the detectors! So $A$ and $B$ occur with 100% probability.

I was sloppy because I was still thinking that I am saying the obvious. By "click", I mean showing a definite state, typically either "up" or "down". The probability that it will be "up" is not 100%.

 

[Simple question]

There are no "magic dice". There's just relativistic QFT. As in any QT Born's rule..

Indeed, because dice of QFT are non-local, no magic is involved.
The Born's rule only project philosophical vector made of imaginary number into real philosophical numbers

the probabilistic meaning of the quantum states, is one of the basic postulates and part of the minimal statistical interpretation,

That's the only correct part of you sentence. Sadly your vague philosophy does not allow you to interpret it correctly.

which just accepts one of the great objective findings about Nature, i.e., that it is inherently random. There's no magic involved, it's just a fact about Nature,

Incorrect.
The only fact is that the theory in stochastic. If you understood how "natural science" works, without prejudice, you would be able to produce an experiment that show that events are "inherently random".
Good luck with that.
You would also produce a theory that mathematically predict where/when exactly/locally an event will occurs.
Good luck with that too.

which contradicts the outdated worldview of deterministic classical physics, and that's why many philosophers even today cannot accept it and build up all kinds of presumed paradoxes against this inevitable conclusion.

A conclusion should follow from premises using logic, not hand-waving. In my book equations of QM are linear, not "inherently random", not even "chaotic". Like "good old" classic theories.

Using your own maximal statistical interpretation, non-locality is clearly defined:
You can prepare an ensemble (a fiction) of identically prepared photons (a simple double slit experiment will do). But instead of running it 10 thousand time, you prepare 10 thousands labs, and you arrange them to run the ensemble all at once, and only once.

The result will still be described by QM. That's non-locality for you.

 

[PeterDonis]

the theory in stochastic

In my book equations of QM are linear, not "inherently random"

You are contradicting yourself. QM can't be both linear and stochastic.

In fact, which you consider it to be depends on which interpretation you adopt. According to the MWI, QM is in fact always linear and never stochastic. According to an interpretation in which collapse of the wave function is an actual, physical process, QM is stochastic and is not linear during wave function collapses.

 

[WernerQH]

The only fact is that the theory in stochastic.

I think I understand what you mean. Whether something in Nature is "inherently" random or not is undecidable -- until we happen to detect regular patterns (perhaps involving sequences like the digits of $\pi$?) we use probability theory as a workaround. Quantum theory (or its more powerful successor) might be based on deterministic laws, but Superdeterminism, even it were to be formulated some day, is unlikely to turn out to be useful. There is a reason why we use statistical mechanics. In my opinion, @vanhees71 has only very very slightly exaggerated the case for "inherent" randomness.

If [...], you would be able to produce an experiment that show that events are "inherently random".

I can't conceive of such an experiment, ever.

In my book equations of QM are linear, not "inherently random", not even "chaotic". Like "good old" classic theories.

There's more to quantum mechanics than Schrödinger's equation. The Born rule was added as an afterthought (in a footnote), but it is an integral part of the theory. Naively, I once thought it should be derivable somehow from Schrödinger's equation. It looked alien to the theory, and I found unitary evolution much more appealing than "measurements". Now I know better. The apparent determinism and continuity expressed by the time-dependent Schrödinger equation has misled many people to forget that quantum theory actually describes the graininess (discontinuities) and randomness we observe in the real world.

 

[Simple question]

You are contradicting yourself. QM can't be both linear and stochastic.

OK, let's not call it that. Will qualifying it "a probabilistic" theory do ?

In fact, which you consider it to be depends on which interpretation you adopt.

That's true as far as interpretation goes, but not as far as math goes. There is no mapping, no mathematical recipe, to map the theory to individual events.
And using probabilities requires an ensemble of events, a big one. I am concerned that @vanhees71 is not required to back up his extraordinary claims about "nature" 's locality, in all the sense of that word.

I found also strange that he does not recognize that QFT's micro-causality, which explicitly requires a non-local constraint to select the correct solutions using it's own equations, is thus either:

1. Unrealistic - that is: Nature cannot "behaves according to a local but non-realistic theory, namely relativistic local QFT", because Nature is real (by definition)... and nonlocal (in Bell's sense) and a-causal (in relativistic sense)
2. Realistic - that is: Nature does in fact solves QFT equations on the regular, using non-local "hardware" to probe the entire universe to check that everything commute.
   Still Nature can not use only QFT which is incomplete and cannot be used to produce events.
   So Nature is apparently also using a big non-local ledger, and big non-local dices to help keep ensemble in checks, which does not seems less "minimal" than WMI.

All this to safeguard the the outdated worldview of classical local physics.

 

[PeterDonis]

Will qualifying it "a probabilistic" theory do ?

No, the same issue I described is still there.

There is no mapping, no mathematical recipe, to map the theory to individual events.

That, again, depends on which interpretation you adopt. Some interpretations (such as the MWI and "objective collapse" interpretations) have this. Others (such as ensemble interpretations) don't.

using probabilities requires an ensemble of events

Yes, which means we cannot verify the basic math of QM (for example, the PF "7 Basic Rules" that I linked to) without running an ensemble of experiments using the same preparation and measurement procedures. But that does not mean QM interpretations cannot make claims about individual events or link them to the math. As noted above, many interpretations do that.

 

[PeterDonis]

QFT's micro-causality, which explicitly requires a non-local constraint to select the correct solutions

What non-local constraint are you referring to?

 

[Fra]

That's a good point. Bell proves what it proves under one additional assumption, which is a notion of mathematical macroscopic realism. This means that macroscopic measurement outcome exists even if nobody observes it, and that it can be analyzed mathematically.

The problem I have with this macroscopic realism of Bell, is that it does not just assume existence, it goes further and assume that this hidden variable determines the way the rest of the system interacts with it, in despited that the rest of the system is only "informed" about it's preparation. This is as if it's just the physicist that doesn't know the variable, therefore one assumes it's valid to simply make a classical "average" of the outcomes. This is the key assumption in Bells ansatz that was never plausible in my eyes, regardless of what you think about QM.

The pair needs to be ISOLATED not only from the physicists, but from ALL interactions(otherwise the entanglement is broken in QM terminology)

As far as I understand, the solipsist HV, has the exact same property, that are hidden not only to one particular observer - they are hidden to ALL obserers and ALL the environment, except the one that encodes it.

This is why it seems perfectly logically possible, that there are theories competing with QM, that also violates Bell inequality, becuase the set of theories it applies to is very narrow. So Bell inequality hardly proves that no other theory than QM, can do the same job ( or rather that there is more explanatory value to be found in such future theory, which is at the core of the discussion, though some seem to have no "need" for a better explanation)

/Fredrik

 

[DrChinese]

Let’s be clear about @vanhees71 assertions about QFT: there is nothing predicted by QFT regarding entanglement that wasn’t something equally predicted by QM. Things like entanglement swapping are not dependent on some nuance in QFT. So there is no sense in defining locality in terms of QFT.

In one form of locality: there is signal locality but there is no quantum nonlocality. In quantum nonlocality: signal locality is respected. But… expectation values are dependent on the measurement choices of distant observers. In another form of nonlocality: even signal locality is not respected.

No one is currently asserting this last version. The general consensus is that of quantum nonlocality, with full respect for signal locality. Again, how many quotes need to be provided here to back up a position? The existence of quantum nonlocality is posited as part of most experimental papers on the subject.

 

[vanhees71]

Let’s be clear about @vanhees71 assertions about QFT: there is nothing predicted by QFT regarding entanglement that wasn’t something equally predicted by QM. Things like entanglement swapping are not dependent on some nuance in QFT. So there is no sense in defining locality in terms of QFT.

True, entanglement is a generic property of QT, no matter whether it's relativistic or non-relativistic.

However, if you want to discuss whether a phenomenon obeys the assumption of locaility in the sense of relativistic causality, according to which space-like separated events cannot be in causal relation, you have to use a relativistic theory. There is no notion of locality in this sense in non-relativistic physics (neither in classical nor quantum theory). So it's no surprise that there's no constraint on causal connections between events, i.e., it's no contradiction that there are instantaneous interactions possible (to the contrary, it's the usual paradigm in non-relativistic physics as in Newtonian theory of gravitation). Of course it's very clear that Newtonian physics is only an approximation to relativistic physics and Nature behaves relativistically, i.e., the locality principle (in the above defined sense of relativistic causality) must be fulfilled, and that's why it's implemented into local relativisic QFT via the microcausality constraint, i.e., space-like separated local observable-operators must commute at space-like separated arguments.

Of course, experiments with photons must be described by QED, and all Bell tests, demonstrating the inseparability of entangled states, which is unfortunately and misleadingly called a "non-local" effect, although there's no violation of relativistic causality constraints whatsoever within QED.

In one form of locality: there is signal locality but there is no quantum nonlocality. In quantum nonlocality: signal locality is respected. But… expectation values are dependent on the measurement choices of distant observers. In another form of nonlocality: even signal locality is not respected.

Of course are the outcomes of measurements dependent on the choice what's measured. It's also demonstrated that in such measurements the causal order of local measurements on parts of the systems doesn't play any role. The measurement events (i.e., the moment where at the place of the detector a measurement results gets manifest) can even be space-like separated. Together with the microcausality constraint of relativistic QFT this implies that there cannot be any causal connection between these measurement events, and indeed the correlations described by entanglement are due to the preparation of the system in this entangled state. Thus there is no need for any causality-breaking "spooky interactions at a distance", contradicting relativistic causality and its implementation in relativistic QFT. Signal locality is strictly obeyed by construction. The great majority of physicists working in this field does not deny this, including Zeilinger et al.

No one is currently asserting this last version. The general consensus is that of quantum nonlocality, with full respect for signal locality. Again, how many quotes need to be provided here to back up a position? The existence of quantum nonlocality is posited as part of most experimental papers on the subject.

Yes, and that's why you should call relativistic QFT local, since in fact it is local. There are strong correlations of measurement results at far distant places when accordingly entangled systems are measured. This has nothing to do with any violation of locality. It's just the inseparability of entangled states, and it's all about correlations and not causal connections, which would violate relativistic causality. The existence of nonseparability is posited as part of most experimental papers on the subject. I don't know any paper, where locality and relativistic causality is denied. To the contrary, there was a lot of experimental effort in performung loop-hole free Bell tests in achieving space-like separated choices of the measured observable and measurements with the argument to exclude (!!!) any possible causal influences between the far-distant local measurements!

 

[vanhees71]

Agreed.I was (and still am) curious about his view how the probabilities/correlations arise in the formalism of QED. My view is that it is essential that the propagators also reach into the backward light cone, i.e. that you have waves travelling backwards in time. But this smacks of retrocausality (at least for some people) and may conflict with another cherished principle of @vanhees71 , causality.

There is no propagation backward in light cone either. That's dealt with by the famous Stueckelberg trick, i.e., writing a creation operator in front of the negative-frequency modes in the mode decomposition of the (free) field operators. Together with microcausality this leads to the correct causality properties in the sense of Minkowski spacetime and to a stable ground state, the vacuum (i.e., positive definiteness of energy).

 

[vanhees71]

Let’s be clear about @vanhees71 assertions about QFT: there is nothing predicted by QFT regarding entanglement that wasn’t something equally predicted by QM. Things like entanglement swapping are not dependent on some nuance in QFT. So there is no sense in defining locality in terms of QFT.

A relativistic physical theory must be consistent with relativistic causality. Otherwise it's not a relativistic theory. That's why inevitably physicists found local relativistic QFT as a very well working relativistic QT, in fact it's the only realization of a relativistic QFT fulfilling all the necessary consistency constraints of a relativistic QFT, including causality. Causality it implemented in the even stronger form of microcausality and assuming strictly local interactions. AFAIK there's no example for a working non-local QFT that obeys the causality constraints.

Also in classical relativistic physics the obstacle of having both, the impossibility of instantaneous interactions, and validity of the conservation laws (energy, momentum, angular momentum, center-of-energy motion) implied by the symmetry of Minkowski space (proper orthochronous Poincare transformations) has been solved even before this problem was known to the physicists by introducing the field concept and with it the paradigm of locality of interactions: The fields themselves become dynamical entities carrying all these conserved quantities. The price that had been paid is that the point-particle picture becomes highly problematic, if not impossible to realize (at least there's no fully consistent relativistic theory of interacting point particles; the best effective approximative model in electromagnetically interacting particles is the Landau-Lifshitz approximation of the Lorentz-Abraham-Dirac equation). That's why also a field-theoretical description of matter is necessary. In the classical realm this works well in terms of relativistic continuum mechanics (mostly relativistic fluid dynamics) and relativistic transport equations.

The most consistent picture about interacting matter, however, is indeed relativistic local QFT.

In one form of locality: there is signal locality but there is no quantum nonlocality. In quantum nonlocality: signal locality is respected. But… expectation values are dependent on the measurement choices of distant observers. In another form of nonlocality: even signal locality is not respected.

No one is currently asserting this last version. The general consensus is that of quantum nonlocality, with full respect for signal locality. Again, how many quotes need to be provided here to back up a position? The existence of quantum nonlocality is posited as part of most experimental papers on the subject.

I commented on this already.

 

[Demystifier]

I approached this thread with some excitement. Yet your second entry was an ad hominem attack. Ideas would be better.

Saying that he's using philosophy is not ad hominem. It would be ad hominem if I implied that using philosophy is something wrong, but I didn't imply that. Indeed, I use philosophy all the time, including this reply that you just read. However, the idea behind my claim that he's using philosophy is implicit, and you are right that it would be better if the idea was explicit. The explicit idea is that one cannot expect non-philosophical discussion if one starts with an argument full of philosophical claims.

 

[Quantum Waver]

There's more to quantum mechanics than Schrödinger's equation. The Born rule was added as an afterthought (in a footnote), but it is an integral part of the theory. Naively, I once thought it should be derivable somehow from Schrödinger's equation. It looked alien to the theory, and I found unitary evolution much more appealing than "measurements". Now I know better. The apparent determinism and continuity expressed by the time-dependent Schrödinger equation has misled many people to forget that quantum theory actually describes the graininess (discontinuities) and randomness we observe in the real world.

There's still a question of how the unitary evolution becomes non-unitary upon measurement, making the Born rule necessary. Saying it's inherently random is to make the stochastic part of QM a brute fact of nature. But perhaps that is giving up too soon. There are still supporters of MWI working on deriving the Born rule.

It also makes measurement a fundamental part of the theory, which is unlike other scientific theories. Invoking decoherence (as some do) just pushes the problem out farther beyond the measurement to the wider world, which is what MWI says happens. So although the measurement looks discontinuous, technically it's part of a much larger superposition. Unless the measurement doesn't involve Schrödinger's equation at all until it's completed. Which would seem to be at odds with decoherence.

Or it means the macroscopic world is not fundamentally quantum, even though it's made up of the microphysical. Perhaps because measurements are constantly being made on the scale of the macro? So there's constant stochastic collapse. Or perhaps I should say it's not fundamentally described by the wave equation if that's the case. But again, that seems to be in conflict with decoherence (which is unitary).

 

[WernerQH]

There is no propagation backward in light cone either.

That's just semantics. Of course you can redefine something that travels backwards in time as something else that travels forward.

I think you cannot have both, locality and strictly forward evolution in time. A single photon emitted by an atom can be detected by only one detector. If you surround the atom by several detectors, how could these detectors "negotiate" in a local way who is doing the detecting? The only way to do this in a local way is by sending signals back and forth, i.e. also backwards in time. (Leading eventually to some infamous collapse!) Nature's book-keeping seems to be perfect: energy, momentum, and angular momentum are deposited in only one detector. Since you are harping on locality, I think you have to give up the idea that quantum systems can evolve only forward in time.

 

[vanhees71]

The detectors don't negotiate anything. It's just the interaction of the photon with the material around it. Where it will be detected is random, and the probability distribution is given by accordingly normalized expectation value of the energy density taken with the state the photon is prepared in.

 

[WernerQH]

It's just the interaction of the photon with the material around it. Where it will be detected is random [...]

Local interactions? Obviously you don't understand.

 

[vanhees71]

Of course, QED is local QFT, and that's why interactions are local. Obviously you don't understand.

 

[WernerQH]

There's still a question of how the unitary evolution becomes non-unitary upon measurement, making the Born rule necessary. Saying it's inherently random is to make the stochastic part of QM a brute fact of nature.

Yes, I think it's necessary to accept it as "brute fact of nature". Although we cannot really talk about facts of nature, but only about the most reasonable attempts to describe her. But the hard split between unitary evolution and "measurements" isn't necessary. There is a formalism that joins them in a natural way: the Schwinger-Keldysh closed time-path formalism. I've already tried several times to explain it here on PF, for example in
https://www.physicsforums.com/threa...-be-proved-or-disproved.1004469/#post-6507873
but most people seem to think that it's in the wrong box and has nothing to do with quantum theory and measurements. Yet I was delighted to discover in a recent article
https://arxiv.org/abs/2305.16828
the Schwinger-Keldysh functional being mentioned as a "decoherence functional". So some members of the Consistent Histories faction have noticed the usefulness of forward and backward moving "times" for ensuring consistency in (our emulation of) nature's book-keeping.

 

[Lord Jestocost]

A relativistic physical theory must be consistent with relativistic causality. Otherwise it's not a relativistic theory. That's why inevitably physicists found local relativistic QFT as a very well working relativistic QT, in fact it's the only realization of a relativistic QFT fulfilling all the necessary consistency constraints of a relativistic QFT, including causality. Causality it implemented in the even stronger form of microcausality and assuming strictly local interactions. AFAIK there's no example for a working non-local QFT that obeys the causality constraints.

Also in classical relativistic physics the obstacle of having both, the impossibility of instantaneous interactions, and validity of the conservation laws (energy, momentum, angular momentum, center-of-energy motion) implied by the symmetry of Minkowski space (proper orthochronous Poincare transformations) has been solved even before this problem was known to the physicists by introducing the field concept and with it the paradigm of locality of interactions: The fields themselves become dynamical entities carrying all these conserved quantities. The price that had been paid is that the point-particle picture becomes highly problematic, if not impossible to realize (at least there's no fully consistent relativistic theory of interacting point particles; the best effective approximative model in electromagnetically interacting particles is the Landau-Lifshitz approximation of the Lorentz-Abraham-Dirac equation). That's why also a field-theoretical description of matter is necessary. In the classical realm this works well in terms of relativistic continuum mechanics (mostly relativistic fluid dynamics) and relativistic transport equations.

The most consistent picture about interacting matter, however, is indeed relativistic local QFT.

I commented on this already.

In a footnote of their paper “Bell nonlocality”/1/, Nicolas Brunner et al. point to a maybe reason of misunderstandings regarding the term locality:

"In 1964, Bell proved that the predictions of quantum theory are incompatible with those of any physical theory satisfying a natural notion of locality¹ (Bell, 1964). ...........

¹To avoid any misunderstanding from the start, by “locality” we do not mean the notion used within quantum mechanics and quantum field theory that operators defined in spacelike separated regions commute. Bell’s notion of locality is different and is clarified below."

/1/ “Bell nonlocality” by Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner, Rev. Mod. Phys. 86, 419 – Published 18 April 2014

 

[vanhees71]

Just look at section A. The key points are clearly stated:

Even though the two systems
may be separated by a large distance, and may even be
spacelike separated, the existence of such correlations is
nothing mysterious. In particular, it does not necessarily
imply some kind of direct influence of one system on the
other, for these correlations may simply reveal some depend-
ence relation between the two systems which was established
when they interacted in the past. This is at least what one
would expect in a local theory.

The point, however, is that in (3) they tacitly assumed not only "locality" but also realism, and that's leads to the Bell inequalities, which distinguishes all "local, realistic theories" from "non-realistic theories".

Unfortunately they do not discuss microcausality at all, except in this footnote, where they explicitly say that they do not take it into account, which is strange, because that's the very way, "locality" is mathematically implemented into the only viable relativistic QT we have today, i.e., relativistic, local QFT.

On the other hand in discussing Eq. (3) they state:

This decomposition now represents a
precise condition for locality in the context of Bell experi-
ments.2 Note that no assumptions of determinism or of a
“classical behavior” are being involved in Eq. (3): we assumed
that a (and similarly b) is only probabilistically determined by
the measurement x and the variable λ, with no restrictions on
the physical laws governing this causal relation. Locality is the
crucial assumption behind Eq. (3). In relativistic terms, it is the
requirement that events in one region of space-time should not
influence events in spacelike separated regions.

For me that's a clear contradiction of the very footnote they make "for clarity" in the very beginning. So for me the paper does not discuss adequately the precise meaning of "locality/non-locality" in the relativistic context.