Why is it assumed communication through entanglement would be FTL?

[DarMM]

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]

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 something 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]

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]

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]

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.

 

[Demystifier]

**Our own @Demystifier published an article

Nice to see that there is a popular journalist exposition of my work. Thanks!

 

[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 something 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]

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]

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/.

 

[DrChinese]

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]

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]

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]

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]

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]

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]

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.

 

[bobob]

No, relativity does not become incorrect if you add preferred reference frame to it. Only consensus interpretation of relativity becomes invalid.

I disagree. There is no sensible definition of "preferred" that would be self-consistent.

 

[zonde]

He does quite the opposite.

Really? "Correlations have physical reality; that which they correlate does not." does not mean correlations fall from the sky but quite the opposite?
We have communication problem.

So? Who claimed that it does?

...

If I had to bet money, I would always go for non-realism/contextuality or whatever you would like to call it.

You claim the very thing in the same post. You say non-realism/contextuality allows violation of Bell inequality without non-locality. Unless you attribute non-realism/contextuality to detections themselves you are proved wrong by Eberhard.

 

[zonde]

I disagree. There is no sensible definition of "preferred" that would be self-consistent.

I'm not sure I understand. You are a bit too short for me to get what you mean.

 

[bobob]

No one is questioning relativity per se. Experiments support it.

Yes, experiments support it, but I disagree that relativity is not being questioned, at least unconsciously.

(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 qft is a strictly local theory. I have an entire textbook devoted to that very thing, "Local Quantum Physics: Fields, particles, Algebras," Rudoplf Haag.

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 in the typical Bell type experiment, the detectors are separated from the source by null intervals, since obviously, photons live on the light cone. So between the source and each detector, the distance is zero, regardless of the spatial separation between the detectors. That seems to be a missed point.

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.

I really have no idea what you are trying to say here.

 

[bobob]

I'm not sure I understand. You are a bit too short for me to get what you mean.

Define a "preferred frame" that is consistent with relativity. The only definition of "preferred" that makes sense is one in which the measured values are some "true values" to which other frames can be referenced and not lead to contradictions.

 

[zonde]

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.

I gave definition of "sample space": In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.
Is that the definition you are using?

It seems that the book you gave was freely available online some time ago but it is no more. But "sample space" is such a basic concept in probability theory that it should not require specific book to give it's definition. Googling gave plenty explanations of this concept and they were all consistent with definition I gave.

 

[zonde]

Define a "preferred frame" that is consistent with relativity. The only definition of "preferred" that makes sense is one in which the measured values are some "true values" to which other frames can be referenced and not lead to contradictions.

You can take any inertial reference frame in SR and label it as preferred. Then label any measured values in that reference frame as "true values" and measured values in other inertial reference frames as "apparent values". No inconsistency with SR arises because nothing in the math of SR was changed by that labeling.
Lorentz transformation ensures any "apparent values" in other reference frames can be transformed into "true values" of preferred reference frame.
That labeling just introduces asymmetry on top of SR that SR by itself does not have.

 

[Michael Price]

As far as I can tell nobody actually knows how quantum entanglement really works,[...]

Sorry, this thread is predicated on a falsehood. Entanglement is a known and understood consequence of many particle quantum mechanics. And it does not enable communication of any kind, faster or slower than the speed of light.

 

[Demystifier]

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.

You would have to reject fundamental relativity, but you would not have to reject effective relativity valid only under restricted set of circumstance. This restricted set of circumstances must involve all experiments performed so far, but one cannot exclude the possibility that some future experiments, perhaps experiments with the next generation of particle colliders, will show violations of relativity.

 

[Cthugha]

Really? "Correlations have physical reality; that which they correlate does not." does not mean correlations fall from the sky but quite the opposite?
We have communication problem.

I am really and honestly puzzled as I really think this is trivial. If you have two quantities that are connected via some kind of uncertainty relation, you can prepare states, in which one of these properties is well defined, while the other is not (or both are defined to some extent). If I prepare a state of known position, momentum is ill-defined and vice versa. For entangled states, entanglement and coherence in the entangled property are another pair of properties connected via an uncertainty relation. Entanglement boils down to the presence of non-classical correlations of some chosen property. Coherence boils down to sharply defined values of this property. So if I prepare a state such, that the individual properties (e.g. the spin of two photons) are well defined, well-defined non-classical correlations cannot exist. If I prepare a state with well-defined non-classical correlations, well-defined values of the individual properties cannot exist. Correlations are an element of reality in the latter case, while the correlated quantities are not. In order to achieve this, you simply have to prepare an entangled state (or equivalently prepare well-defined non-classical correlations - and to emphasize it again: ONLY the correlations, not the individual spin/energy/OAM/polarization/whatever values). You need to explicitly prepare the state as such. I do not see why explicit preparation of such a state would correspond to falling from the sky.

You claim the very thing in the same post. You say non-realism/contextuality allows violation of Bell inequality without non-locality. Unless you attribute non-realism/contextuality to detections themselves you are proved wrong by Eberhard.

I disagree. Eberhard explicitly develops several concepts of locality in his paper(s) (Bell's Theorem and the Different Concepts of Locality, Il Nuovo Cimento 46, 392 (1978)). Concepts 1-3 more or less lead to deterministic or probabilistic LHV theories and are at odds with quantum theory. Notion 4 is the simple relativistic notion of locality, which means no FTL-signaling and is not at odds with quantum theory as explicitly pointed out by Eberhard. This is the relevant notion of locality in this case.

 

[DarMM]

I gave definition of "sample space": In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.
Is that the definition you are using?

It seems that the book you gave was freely available online some time ago but it is no more. But "sample space" is such a basic concept in probability theory that it should not require specific book to give it's definition. Googling gave plenty explanations of this concept and they were all consistent with definition I gave.

I'm not using Streater to give a definition of sample spaces, as I said I am using the normal definition in Probability theory as Wikipedia gives. He just gives a good example of how QM uses multiple sample spaces.

 

[PeterDonis]

relativity does not become incorrect if you add preferred reference frame to it. Only consensus interpretation of relativity becomes invalid.

Discussion of such alternate interpretations of relativity is out of bounds here at PF. Please do not refer to it.

 

[vanhees71]

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):

Just to make it very clear: I do not state that QFT is classically local. That contradicts the plethora of Bell tests that prove QFT to be not compatible with local deterministic HV models. Mermin's article, of course, is a gem!

 

[Cthugha]

Just to make it very clear: I do not state that QFT is classically local.

Also just to make it clear: I intended to say that it is not warranted to assume that you think that QFT is classically local. I did not intend to say that your position is unwarranted because you think that QFT is classically local. My post might have been easy to misinterpret. ;)

 

[bhobba]

To the contrary it's ruled out by the very construction of this QFT as made explicit in Weinberg's books much more explicitly than in most other QFT textbooks.

It's not quite true its ruled out - things just come out more rationally and elegantly if you rule it out. It like the aether in LET. I can't rule LET out - all I can do is give a very elegant explanation of SR based on symmetry rather than an inherently undetectable aether. Things get more and more difficult the deeper you go into areas like GR and QFT. Its scientific tact really that's actually at the base of what's in many of our theories. I know its not entirely satisfactory things in science are like that. I believe the cluster decomposition property as explained by Weinberg makes things harder if you allow the concept of locality to apply to correlations. Of course you can do it - but one must ask why?

Thanks
Bill