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

#### DrChinese

Gold Member
Yes, this is a fair point.
PeterDonis: 25,872
DrChinese: 1

No disagreement, but I hope we don't have to say that every time...
But what else could you say? You could say they can't be explained by Bell-local theories, but that's a tautology. Bell's theorem has quite a few assumptions, as does the ontological models framework.

#### DrChinese

Gold Member
But what else could you say?
Well, I guess my vote would be... Quantum Nonlocality.

#### Cthugha

Just a short response as it is getting late here.

He is also saying QFT is local microcausal. I admittedly do not follow the distinction between "local causal" and "local microcausal". However, if I don't follow that distinction, I doubt many others do either unless they are knee deep in QFT. The term "microcausal" does not show up in papers on entanglement, ergo I assume it is not relevant. In fact, I would say as a rule that elements of QFT (as opposed to older QM) are not usually referenced in papers on entanglement.
Well, we have Witten, who wrote quite a detailed review paper on entanglement in QFT (Rev.Mod.Phys. 90, 045003 (2018), https://arxiv.org/abs/1803.04993). Reinhard Werner and others also frequently emphasize that the story is more complicated than one usually assumes. Indeed semi-popular papers rarely make use of anything more complicated. They would be pretty dumb to do so. Let me give more details in the next response.

2. I agree with everything you say here. So apparently the point missed is: whether it is non-locality or non-realism/contextuality that rules, the effect is called Quantum Nonlocality in the literature and it is a generally accepted feature in the quantum world. Attempting to mask this by calling it "nonlocal correlations that result from local microcausality" goes against the grain of almost any publication, either lay or scientific. Just this year, an entire book was written on this so I guess we should call them up and tell them to retitle it "Local Microcausality". So I would say it is very misleading to label it "local microcausality" when the Bell options are to reject locality or to reject realism/contextuality.
Well, let me put it this way: Physics is the art of making models that make predictions that match reality (as quantified by experiments). So of course any effect should be considered within its model or framework. If one uses standard QM, which is not relativistically invariant anyway, it is quite natural to consider nonlocality and consider entanglement as a property of the states. It is the natural way of looking at entanglement in QM. In QFT, entanglement is already a property of the algebra of observables (see e.g. Witten's review above) and not just of the states. It is quite natural to consider different mechanisms and terminology.

I find it perfectly reasonable to talk about non-locality in the sense used within this thread, if both author and reader are aware that they are having a discussion on the QM level. This is the framework most publications use. I just think it is good practice to keep in mind that there are more complete theoretical frameworks out there.

#### zonde

Gold Member
Although I think what's sometimes missing in these accounts is that dropping determinism is not enough to get nonclassical correlations, you also have to drop the existence of countertfactuals.
The standard meaning in Quantum Foundations, that variables unmeasured have values.

Chapter 6 of Peres's monograph "Quantum Theory: Concepts and Methods" discusses it and it is used very explicitly in his proof of Bell's theorem. It's not an assumption called out in the original Bell proof, but it is the assumption Copenhagen rejects so it is important to recognize. He says famously "Unperformed experiments have no results"

I do not mean (and I want to empasize this as it is what people seemed to think it means in previous discussions) the trivial fact that unperformed experiments did not happen.
Rejecting assumptions about unmeasured variables goes not give way out of Bell type inequalities.
There is Eberhard's proof that is not assuming any mechanism behind detection events. Well it considers only models that take choice of measurement settings as an external variables (no superdeterminism) and detection events as experimental facts (single world), but then any scientific model has to do that.
I reproduced Eberhard's proof here as paper containing the proof is behind paywall.

#### DarMM

Gold Member
Rejecting a common sample space clearly permits violations of Bell's inequality, it's what QM actually does where there is no Gelfand homomorphism mapping all four CHSH variables into one sample space.

#### zonde

Gold Member
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."
I don't see how this statement can be taken seriously.
In Bell experiments correlations correlate detection events given measurement settings. Would you say following Mermin that either or both detection events and measurement settings do not have physical reality?

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.
What do you mean by "joint choice of measurement bases for Alice and Bob"? Choices of measurement bases are made by Alice and Bob at two spacelike separated events. You need nonlocality influencing choice of measurment settings (!) or superdeterminism to have someting like that.
Well, if you know the choice of measurement basis for either Alice or Bob at the moment when entangled particles are produced you can replicate correlations with LHV, no doubt about that.

#### zonde

Gold Member
Rejecting a common sample space clearly permits violations of Bell's inequality, it's what QM actually does where there is no Gelfand homomorphism mapping all four CHSH variables into one sample space.
Basically you are saying that Many local Worlds permits violations of Bell's inequality? Or I didn't understood you correctly?

#### Demystifier

2018 Award
Neither formulation has states for spatially extended systems
The Schrodinger picture does have a state $|\psi(t)\rangle$ for spatially extended system. It is not manifestly Lorentz invariant, but there is a Lorentz-invariant version based on many-time formalism.

#### Demystifier

2018 Award
Note the path integral is only well-defined in a Riemannian space, not in Lorentzian spacetimes. Since some spacetimes have no analytic continuation to a Riemannian space there is no path integral in general.
But at least Minkowski spacetime has an analytic continuation to an Euclidean space, right? This means that path integral QFT in the absence of gravity is well defined. QFT in curved spacetime has other problems too, but the full theory of quantum gravity is expected to solve those one day.

2018 Award

#### Cthugha

I don't see how this statement can be taken seriously.
In Bell experiments correlations correlate detection events given measurement settings. Would you say following Mermin that either or both detection events and measurement settings do not have physical reality?
Huh? experimental correlations on detectors do not fall from the sky. You can measure spin correlations, momentum correlations, OAM correlations time-bin correlations or whatever. The message is quite clear. Having a state with well-defined correlations does not imply that the individual correlated quantites are well defined. Well-defined values of spin correlations do not imply that the individual spin values are well-defined. In fact, quite the opposite is true as these are usually complementary quantities. See, e.g. Phys. Rev. A 62, 043816 (2000) or Phys. Rev. A 63, 063803 (2001).

What do you mean by "joint choice of measurement bases for Alice and Bob"? Choices of measurement bases are made by Alice and Bob at two spacelike separated events. You need nonlocality influencing choice of measurment settings (!) or superdeterminism to have someting like that.
Well, if you know the choice of measurement basis for either Alice or Bob at the moment when entangled particles are produced you can replicate correlations with LHV, no doubt about that.
I do not get your post. Why do you bring LHV models into play? This thread is not about LHV models. By joint choice I mean just that: a set of detector settings. Ordinary standard QM already gives the correct predictions for every possible detector setting Alice and Bob might use. It does so irrespective of which interpretation of QM you might use as long as it is consistent with QM, which means that it cannot be local realistic. QFT as the more demanding theory contains ordinary QM in the non-relativistic limit and of course also already gives the correct predictions for every possible detector setting Alice and Bob may use. I do not see how this could be even controversial. The math of QFT also does so irrespective of how you want to interpret QFT as long as your interpretation is consistent with QFT. This again means no local realism. However, as QFT is relativistically invariant already, it would be somewhat awkward to sacriface this feature by going for a non-local interpretation. At least unless you assume that there is some need for potentials with an infinite number of derivatives in some even deeper theory or something like that.

#### DarMM

Gold Member
But at least Minkowski spacetime has an analytic continuation to an Euclidean space, right? This means that path integral QFT in the absence of gravity is well defined. QFT in curved spacetime has other problems too, but the full theory of quantum gravity is expected to solve those one day.
Definitely it's well defined in Minkowski spacetime. It's just an interesting fact as such.

#### DarMM

Gold Member
Basically you are saying that Many local Worlds permits violations of Bell's inequality? Or I didn't understood you correctly?
No, I'm saying the lack of a common sample space/context permits violation of Bell's inequalities. This isn't really anything to do with Many Worlds.

#### atyy

He is also saying QFT is local microcausal.
It is standard and correct to say that relativistic QFT is "local microcausal". "Microcausality" means no superluminal communication.

No superluminal communication is a distinct concept from the classical relativistic causality addressed by Bell's theorem. Thus the violation of Bell's inequalities disallows classical relativistic causality, but it allows no superluminal communication or microcausality.

The funny thing about microcausality, is that a technical trick to impose it in QFT is to pretend the observables are real, and to follow steps that are pretty much the same as imposing classical relativistic causality. Thus some people mistake microcausality for classical relativistic causality, and mistakenly say that QFT has microcausality (true) and therefore it has classical relativistic causality (false). I believe this is the mistake that @vanhees71 is making when he says that the nonlocality of collapse is at odds with microcausality.

BTW, I should note that even Weinberg occasionally uses sloppy language that makes this mistake. See the comments of @Demystifier and @humanino in this thread: https://www.physicsforums.com/threads/cluster-decomposition-and-epr-correlations.409861/.

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#### DrChinese

Gold Member
It is standard and correct to say that relativistic QFT is "local microcausal". "Microcausality" means no superluminal communication.
Thanks for clarifying that.

I don't fully understand why that label "microcausal" would be a useful distinction in this thread. After all: the issue here is "spooky action at a distance" via entanglement, which does not offer FTL signalling. On the other hand, I guess it makes sense to point out that a relativistic formulation of QM explicitly requires signal locality. Which also answers the OP.

#### Cthugha

After all: the issue here is "spooky action at a distance" via entanglement, which does not offer FTL signalling. On the other hand, I guess it makes sense to point out that a relativistic formulation of QM explicitly requires signal locality. Which also answers the OP.
Just to add to that, it should be said that we already know that "no signalling" is an assumption that is too weak to represent reality. It is well known that in theory one can consider states that are non-signaling as defined by relativistic causality and still not realizable in quantum mechanics. We know that e.g. from the seminal paper by Popescu and Rohrlich.
We also know that it is locality applied to uncertainty relations (or rather: a general formulation of uncertainty and a certain version of locality termed relativistic independence that in a nutshell boils down to being unable to tinker with local uncertainty relations from a distance) that exactly give the bounds: https://advances.sciencemag.org/content/5/4/eaav8370 (should be open access).

#### zonde

Gold Member
Huh? experimental correlations on detectors do not fall from the sky. You can measure spin correlations, momentum correlations, OAM correlations time-bin correlations or whatever. The message is quite clear. Having a state with well-defined correlations does not imply that the individual correlated quantites are well defined. Well-defined values of spin correlations do not imply that the individual spin values are well-defined. In fact, quite the opposite is true as these are usually complementary quantities. See, e.g. Phys. Rev. A 62, 043816 (2000) or Phys. Rev. A 63, 063803 (2001).
Well, you was the one who quoted Mermin who said correlations fall from the sky. If the quote is viewed in context it might become clear Mermin meant that correlated quantities are not well defined, that way it makes more sense actually.
But still this approach does not resolve Bell inequality question as Bell type inequality is provable without any reference to hypothetical quantities relying only on measurement settings and detections: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.47.R747 (see part II Bell inequalities for n<100%)

However, as QFT is relativistically invariant already, it would be somewhat awkward to sacriface this feature by going for a non-local interpretation.
And the alternative in your viewpoint is ... ?

#### bobob

Weinberg phrases the answer as: "Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem..."
But that cannot be correct. The measurements are spacelike separated, so they are made simultaneously. Neither measurement can occur "before" the other and create a cause and effect relationship because they cannot be time ordered. You would have to reject relativity. Apparently, what people must be arguing about is whether relativity is correct.

#### zonde

Gold Member
No, I'm saying the lack of a common sample space/context permits violation of Bell's inequalities. This isn't really anything to do with Many Worlds.
Can you explain what do you mean by "sample space/context" because it seems that you attach different meaning to "sample space" than the one used in probability theory.
Wikipedia: In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

#### zonde

Gold Member
But that cannot be correct. The measurements are spacelike separated, so they are made simultaneously. Neither measurement can occur "before" the other and create a cause and effect relationship because they cannot be time ordered. You would have to reject relativity. Apparently, what people must be arguing about is whether relativity is correct.
No, relativity does not become incorrect if you add preferred reference frame to it. Only consensus interpretation of relativity becomes invalid.

#### Cthugha

Well, you was the one who quoted Mermin who said correlations fall from the sky. If the quote is viewed in context it might become clear Mermin meant that correlated quantities are not well defined, that way it makes more sense actually.
He does quite the opposite. I linked the full article. It is of course using basic language, but I do not see how your statement relates to Mermin's.

But still this approach does not resolve Bell inequality question as Bell type inequality is provable without any reference to hypothetical quantities relying only on measurement settings and detections: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.47.R747 (see part II Bell inequalities for n<100%)
So? Who claimed that it does? My post was in response to the assumption that the QFT version outlined above is local realistic. It is obviously not as assuming that something has well-defined correlations does not mean that the correlated quantities on their own have well-defined values or are local realistic hidden variables. That is all.

And the alternative in your viewpoint is ... ?
If I had to bet money, I would always go for non-realism/contextuality or whatever you would like to call it. From my point of view, during the last few years, studies of uncertainty relations (which is what "non-realism" usually boils down to) with respect to entanglement have been the most relevant studies to advance the field, such as the paper linked in my last post or Science 330, 1072 (2010) (https://arxiv.org/abs/1004.2507). Of course, other people will have a different opinion about what is significant. That is perfectly fine.

#### DarMM

Gold Member
Can you explain what do you mean by "sample space/context" because it seems that you attach different meaning to "sample space" than the one used in probability theory.
Wikipedia: In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.
I'm using it in the same sense as in probability theory. See Chapter 6 of Streater's "Lost Causes in Theoretical Physics". He has a good explanation of it.

#### DarMM

Gold Member
Just to add to that, it should be said that we already know that "no signalling" is an assumption that is too weak to represent reality. It is well known that in theory one can consider states that are non-signaling as defined by relativistic causality and still not realizable in quantum mechanics. We know that e.g. from the seminal paper by Popescu and Rohrlich.
We also know that it is locality applied to uncertainty relations (or rather: a general formulation of uncertainty and a certain version of locality termed relativistic independence that in a nutshell boils down to being unable to tinker with local uncertainty relations from a distance) that exactly give the bounds: https://advances.sciencemag.org/content/5/4/eaav8370 (should be open access).
There's quite a few of these results now, obtaining the Tsirelson bound from some principle. Others are information causality or Cabello's exclusion principle. @RUTA has a pretty good derivation in terms of conservation of angular momentum and discrete outcomes.

I wonder are they all facets of some core principle or aspect of the theory or is more fundamental than the others.

#### DrChinese

Gold Member
But that cannot be correct. The measurements are spacelike separated, so they are made simultaneously. Neither measurement can occur "before" the other and create a cause and effect relationship because they cannot be time ordered. You would have to reject relativity. Apparently, what people must be arguing about is whether relativity is correct.
No one is questioning relativity per se. Experiments support it. (And as a point worth mentioning, the equations of relativity are time symmetric anyway. So that could potentially explain the appearance of quantum nonlocality, although that is speculation at this time.) But there seems to be a gray area when it comes to entangled systems: they have spatial extent but act as if that extent doesn't constrain the system as might be otherwise expected.

And on the quantum side: ordering of the following makes no discernible difference to the outcome in any reference frame:

a. Pair A and B entangled.
b. A measured.
c. B measured.

And you can even entangle A and B after they are measured (although that is a subject for another thread). In no scenario can any signal be transmitted FTL, as the A and B outcomes appear completely random by themselves.

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

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