Do Bell Experiments Show Local Overlap of Wave Functions Before Measurement?

[Fra]

It is a simple fact that a measurement* on A by Alice appears to place distant entangled partner B (measured by Bob) into a state 100% correlated to Alice's choice of measurement basis. There is no single theory/interpretation that explains the mechanism of this observed fact

I agree, and this is I think the interesting still open question! We have a external description but without intrinsic explanation, and I think we should be able to eventually do better. If one wish, this is an "incompleteness" of QM, but not necessarily "in specific the way" Bell or Einstein might have thought of it.

/Fredrik

 

[vanhees71]

We have a theory that explains this, QT! It's not A's measurement "that places the distant entangled partner into a state 100% correlated to Alice's choice of measurement basis" but the preparation of the entangled system before A and B do their measurements, i.e., the 100% correlation was prepared before the measurement although the measured observables are maximally uncertain and not in any way "predetermined", which is precisely what distinguishes QT from all kinds of "local realistic models".

 

[Lord Jestocost]

Reinhard F. Werner and Michael M. Wolf in “Bell inequalities and Entanglement” (https://arxiv.org/abs/quant-ph/0107093):

“There are many derivations of Bell inequalities in the literature. This may at first be a bit surprising for such a simple mathematical statement. However, the hard work in such a derivation is almost never mathematical but conceptual: if we want to draw far-reaching conclusions ruling out whole classes of theories, or ways of formulating natural laws, we have to analyze theories on a very general and abstract level in order to even state the assumptions of “Bell’s Theorem”. Naturally, there are many ways to say what the really essential assumptions are, depending on philosophical taste and scientific background. However, in all derivations two types of elements can be identified

Locality no-signalling non-contextuality

Classicality hidden variables classical logic joint distributions counterfactual definiteness ‘realism’

Since Bell’s inequalities are found to be violated in Nature ⁷, one of these two assumptions needs to be dropped. Quantum mechanics (in statistical interpretation) chooses locality, whereas hidden variable theories drop locality in order to retain a description by classical parameters. In either case, however, fundamental features of the pre-quantum way of describing the world are lost.”

 

[Fra]

We have a theory that explains this, QT! It's not A's measurement "that places the distant entangled partner into a state 100% correlated to Alice's choice of measurement basis" but the preparation of the entangled system before A and B do their measurements, i.e., the 100% correlation was prepared before the measurement although the measured observables are maximally uncertain and not in any way "predetermined", which is precisely what distinguishes QT from all kinds of "local realistic models".

I agree with what all you say except I would say that QT describes this (accuractely), which is not a bad achievement in itself of course! But it's explanatory value can certainly improve and such improvement need not (and will not IMO) Bell style "local realism".

The lack of deeper understanding of causal mechanisms, makes no practical difference for the mature QM applications, but I expect it to make a profound difference for the research on unification of all interactions in a coherent framework.

I just think there are so many interesting things in QM, that can not be a conicidence and hopefully can be understood in a deeper way. This is my firm conviction at least.

/Fredrik

 

[martinbn]

...
Further, in some Bell test scenarios, the components of the entangled pair have never existed in the same region of spacetime.
...

You like to say this, but you need to be more precise, otherwise readers have to guess what you mean and there is a chance that they will misunderstand you. For instance there is a region, say the whole spacetime (a lot less will do too), in which the pair have existed. So taken as written your statement is not correct.

..
It is a simple fact that a measurement* on A by Alice appears to place distant entangled partner B (measured by Bob) into a state 100% correlated to Alice's choice of measurement basis.

I disagree with this. It is not a fact at all, but an interpretation.

 

[vanhees71]

I agree with what all you say except I would say that QT describes this (accuractely), which is not a bad achievement in itself of course! But it's explanatory value can certainly improve and such improvement need not (and will not IMO) Bell style "local realism".

Natural sciences describe nature and don't explain her. Why Nature behaves as she does is in the realm of faith of all kinds (philosophical, religious) and has nothing to do with the natural sciences, because you cannot empirically test the one or the other "explanation".

The lack of deeper understanding of causal mechanisms, makes no practical difference for the mature QM applications, but I expect it to make a profound difference for the research on unification of all interactions in a coherent framework.

QT is perfectly causal, i.e., the state of a system is determined by its past. It's even "local in time", i.e., the knowledge of the state at one point in time together with the complete knowledge about the dynamics of the system (i.e., the Hamiltonian) determines the state at all later times. That's not different from classical physics. What's different is the probabilistic meaning of the state, but I don't see, what is unsatisfactory about this, because all observations show the corresponding randomness, particularly the Bell tests tell us that the assumption of predetermined values of all observables (in contradiction to QT), where the probabilistic description is only to be used because of some lack of knowledge about the system (as in classical statistical physics).

I just think there are so many interesting things in QM, that can not be a conicidence and hopefully can be understood in a deeper way. This is my firm conviction at least.

They are not a coincidence, because they are physical laws which have been discovered by the usual interplay between experiment and theory. It's not more a coincidence than that Newtonian mechanics and Maxwell electromagnetic theory are successful in describing a large part of how Nature behaves. That there are no hints for limits of validity of QT is indeed amazing. Of course the one thing we don't yet understand is the quantum description of the gravitational interaction ("quantum gravity").

 

[PeterDonis]

this is the very definition of statistical independence to me - not locality

The reason Bell calls this condition "locality" is simple: it is the natural way of expressing the idea that measurement settings at A cannot affect measurement results at B, and vice versa. Note that this is not the same as the measurement settings at A being statistically independent of measurement settings at B.

I find that bell also makes assumptions about the nature of causality in interactions, that is bundled together with his "realism".

What, specifically, in his papers leads you to this belief?

 

[PeterDonis]

Bell's papers are about any kind or local realistic models, contradicting any QT

Bell shows that the predictions of QT violate his inequalities, yes--of course that is easy to show. And therefore no "local realistic" model can reproduce the predictions of QT, since "local realistic" models will obey his inequalities. That was the whole point of his papers on this topic. And it does not contradict anything I said.

Then we have a different understanding of what Bell is saying.

Nothing in what you quote from Bell contradicts anything I said. I don't know what point you are trying to make.

 

[Fra]

Of course the one thing we don't yet understand is the quantum description of the gravitational interaction ("quantum gravity").

Just for perspective, I see you often leave it for a last as a minor note, "we do not yet understand quantum gravity". For me, understanding this unification of interactions is the main motivator. Without a solid spacetime and a classical background, you can not even describe quantum mechanics properly. So I would choose to put it first, not as a last or minor note. This probably explains some disagreements as our focuses are different. I am not interested in pure reinterpretations-only of QM. I agree that would not be quite rational science.

Natural sciences describe nature and don't explain her. Why Nature behaves as she does is in the realm of faith of all kinds (philosophical, religious) and has nothing to do with the natural sciences, because you cannot empirically test the one or the other "explanation".

Without going into the philosophy of science, I distinguish between the current mature state scientific knowledge, and it's method, and the method must be more than just random hypothesis generations and corroborations.

I think the idea is that the "right explanation" will make unification of interactions, including gravity easier, and then I think we will all by occams razor think that it's the better explanation. I personally have a hard time to see how we can find a conceptually sound theory that includes gravity, without in some way twisting the foundations of QFT as it stands today. One may wonder what such bell experiments has todo with quantum gravity, but I think connections is not unreasonble. (There are lots of papers ponderings on the EPR=ER, QM=GR ideas etc)

(i.e., the Hamiltonian) determines the state at all later times. That's not different from classical physics.

This is part of the problem for me. That its not worse than classical physics is not exactly much or an argument. QM is at least - in part - a theory of what an observer can infer from system from interaction, classical physics is not even close.

/Fredrik

 

[Fra]

What, specifically, in his papers leads you to this belief?

The same paper Vanhes referred to, on p404 the yellow ansatz contains a lot of stuff, and I guess you can bundle it up into "classical concepts/logic" etc, but I find that by doing that you reject some notions (such as subjective HV) that perhaps can be useful. After all, the reason for the HV is to explain a pre-set correlation. But then one tries to infer that such a preset correlation would imply this inequality (which I find doomed to start with). But in the ansatz many other assumptions of the nature of interactions seems to go in. (all consistent with classical physics of course, which is why the go in unnnoticed)

/Fredrik

 

[PeterDonis]

the yellow ansatz contains a lot of stuff

I'm not sure what you mean. Equation (2) in that paper is the locality assumption: the result $A$ does not depend on the settings $\vec{b}$ and vice versa. Other assumptions, including anything you might want to relate to "causality", are elsewhere in the paper.

 

[vanhees71]

Bell shows that the predictions of QT violate his inequalities, yes--of course that is easy to show. And therefore no "local realistic" model can reproduce the predictions of QT, since "local realistic" models will obey his inequalities. That was the whole point of his papers on this topic. And it does not contradict anything I said.Nothing in what you quote from Bell contradicts anything I said. I don't know what point you are trying to make.

Bell very clearly states that "local" means that there is no causal influence between far-distant measurements and "realistic" that the observables take determined values, and the statistics thus is due to our ignorance of information about their values, and this is described by the statistics over "hidden variables" in the following from the quoted paragraph of his famous paper. You need both assumptions to derive Bell's inequality, which is predicted (and nowadays empirically known with high significance to be) violated.

For me the case is pretty clear: Since local relativistic QFT is indeed "local" in Bell's sense, leading among other things to the validity of the cluster decomposition principle even for the S-matrix (which means the "locality assumption" even holds considering the asymptotic free initial and final states entering the definition of the corresponding S-matrix elements) one has to give up indeed "realism".

Of course, it could well be, that there are alternative relativistic QFTs that are "non-local" in some sense and "realistic" in Bell's sense, but hitherto no such viable alternative has been found nor are there any hints for the necessity of "hidden variables". Particularly the observation of the violation of Bell's inequalities in precisely the way predicted by Q(F)T is at least convincing evidence that the picture of a local but "non-realistic" description is indeed the right description of Nature.

 

[vanhees71]

Just for perspective, I see you often leave it for a last as a minor note, "we do not yet understand quantum gravity". For me, understanding this unification of interactions is the main motivator. Without a solid spacetime and a classical background, you can not even describe quantum mechanics properly. So I would choose to put it first, not as a last or minor note. This probably explains some disagreements as our focuses are different. I am not interested in pure reinterpretations-only of QM. I agree that would not be quite rational science.

I put it last to underline my opinion that the resolution of this problem is most probably indeed not in the foundations/interpretations of quantum theory but needs new empirical input to find a viable quantum theory of the gravitational interaction. Given the success of GR as the classical field theory describing the gravitational interaction with its implications for the spacetime model, most probably one will have to find a way to quantum-theoretically describe the classical spacetime model as an emergent phenomenon. Since for standard Q(F)T the classical spacetime "background" is the most important input to formulate a concrete model (by using the proper orthochronous Poincare group to derive the fundamental properties of the quantum fields and the corresponding "particles") it is very hard to find such an ansatz for a QT of gravitation.

Without going into the philosophy of science, I distinguish between the current mature state scientific knowledge, and it's method, and the method must be more than just random hypothesis generations and corroborations.

Indeed. The history of physics for me indicates that we need some empirical input to guide the direction in theory building.

I think the idea is that the "right explanation" will make unification of interactions, including gravity easier, and then I think we will all by occams razor think that it's the better explanation. I personally have a hard time to see how we can find a conceptually sound theory that includes gravity, without in some way twisting the foundations of QFT as it stands today. One may wonder what such bell experiments has todo with quantum gravity, but I think connections is not unreasonble. (There are lots of papers ponderings on the EPR=ER, QM=GR ideas etc)

That's for sure, but as I said, I don't think that pondering these philosophical issues brought up by EPR help much. For me, with the empirical Bell tests since Aspect et al. EPR is resolved in favor of Q(F)T.

This is part of the problem for me. That its not worse than classical physics is not exactly much or an argument. QM is at least - in part - a theory of what an observer can infer from system from interaction, classical physics is not even close.

/Fredrik

QT is indeed more comprehensive than classical physics, and it's also in part about what an observer "can infer from system from interaction".

 

[vanhees71]

I'm not sure what you mean. Equation (2) in that paper is the locality assumption: the result $A$ does not depend on the settings $\vec{b}$ and vice versa. Other assumptions, including anything you might want to relate to "causality", are elsewhere in the paper.

Indeed, that's the "cluster decomposition principles", fulfilled by local relativistic QFTs!

 

[PeterDonis]

Bell very clearly states that "local" means that there is no causal influence between far-distant measurements and "realistic" that the observables take determined values

Where does he state this?

You need both assumptions to derive Bell's inequality

Please say exactly which equations in Bell's paper correspond to "no causal influence between far-distant measurements" and "observables take determined values".

 

[kurt101]

You like to say this, but you need to be more precise, otherwise readers have to guess what you mean and there is a chance that they will misunderstand you. For instance there is a region, say the whole spacetime (a lot less will do too), in which the pair have existed. So taken as written your statement is not correct.

I disagree with this. It is not a fact at all, but an interpretation.

@DrChinese I second this. It is very misleading and I was confused until I read through the actual experiment.

 

[.Scott]

If the wave functions do overlap in space, then wouldn't we say the particles are actually "local" to one another (BEFORE measurement)? Or how do we define/decide when some particle is "local" to another, to mediate an influence?

I don't think I will be adding anything in the way of scientific principles to what has been said before in this thread, but I will attempt an answer that I think addresses the question in the terms that @msumm21 is working with.

Bell's Inequality provides a method of contradicting explanations of a particular entanglement experiment using any theory that is based on local realism. Explaining the Bell Inequality by expanding the particles to their full, shared wave function is not any kind of "loop hole". Quite the contrary, it demonstrates that the spatial extant of that wave function is part of the non-local "mechanism" that supports the accurate QM predictions.

Local realism addresses the communication of information. In a strict (and inaccurate) sense, if we attempt to postulate that a piece of information resides solely at a point within a particle, that information could only be "presently" local to another particle if that other particle also included that point. Allowing a single copy of that information to be spatially distributed (occupying more than a point) is an immediate violation of local realism. Allowing multiple copies of that information doesn't violate local realism, but it also can't be used to explain Bells Inequality.

 

[vanhees71]

Where does he state this?Please say exactly which equations in Bell's paper correspond to "no causal influence between far-distant measurements" and "observables take determined values".

I quoted the corresponding paragraph of Bell's famous paper above.

The paper is

J. S. Bell, Physics Vol. 1, No. 3, pp. 195—200, 1964

He states explicitly before Eq. (2) that he assumes that the choice of the observable being measured at A and that measured at B do not mutually influence the corresponding other measurement, and in Eq. (2) it's clear that this mimplies that the probabilities factorize, depending on the hidden variables:
$$P(\vec{a},\vec{b}) = \int \mathrm{d} \lambda \rho(\lambda) A(\vec{a},\lambda) B(\vec{b},\lambda).$$

 

[DrChinese]

We have a theory that explains this, QT! It's not A's measurement "that places the distant entangled partner into a state 100% correlated to Alice's choice of measurement basis" but the preparation of the entangled system before A and B do their measurements, i.e., the 100% correlation was prepared before the measurement although the measured observables are maximally uncertain and not in any way "predetermined", which is precisely what distinguishes QT from all kinds of "local realistic models".

This statement completely misses the point of the entire discussion. QT has properly predicted entanglement results for decades. And of course the "preparation of the entangled system" is responsible for the correlation in some sense. But the facts are:

a) The entangled system itself can be fully nonlocal, with A and B being distant at the initiation of entanglement and never having existed within a common light cone. The preparation need not be local (limited to a small volume of spacetime), as has been experimentally demonstrated many times.

b) The later choice of measurement by Alice on A casts distant Bob's B into an exact and precise state - and that is solely dependent on Alice's decision and nothing else. (Although it is worth noting that the ordering of Alice and Bob's measurements are not a factor, so you could claim that causality is time reversed and be just as correct.)My friend, that is quantum nonlocality - a generally accepted concept by physicists for over 50 years. Nothing in quantum theory explains what "force" acts on/causes distant Bob's B to change to a specific state based on a decision by distant Alice. QT does not "explain" this in a local manner, even though it predicts correctly. That is because QT is nonlocal in its prediction, and the interpretational debates are what attempt to "explain".

Denying "quantum nonlocality" in light of the above 2 facts is not a good look for anyone, unless you are pushing a valid interpretation (which discussion belongs in the subforum and not here, where it will confuse casual readers).

 

[vanhees71]

Your interpretation contradicts the mathematical foundation of relativistic qft. We've discussed this many times. There's no need to discuss it again.

 

[Fra]

I'm not sure what you mean. Equation (2) in that paper is the locality assumption: the result $A$ does not depend on the settings $\vec{b}$ and vice versa. Other assumptions, including anything you might want to relate to "causality", are elsewhere in the paper.

Equation (2) contains the assumption of statistical independence, but it also contains more - the partition assumption. Ie. the assumption that it makes senses to partition the probability into an average over the outcome given by the hidden variable.

partition assumption
$$P(A,B |O_ {A}) = \sum_{\lambda} P(A,B|\lambda|O_ {A}) P(\lambda|O_ {A})$$

statistical independence
$$P(A,B |O_ {A}) = \sum_{\lambda} P(A|\lambda|O_ {A}) P(B|\lambda|O_ {A}) P(\lambda|O_ {A})$$
$$\sim \int_{\lambda} P(A|\lambda) P(B|\lambda) d \lambda$$

The partition assumption makes sense there the causal role of the hidden variable is of the simple "experimenter ignorance type", and compliant also to the old pool-table realism. But other causal mechanisms that still make use of hidden variables are still possible, I am thinking of those that can be thought of as subjective, but still real.

So all Bell theorem disproves is the "naive" ignorance type of HV mechanism.

/Fredrik

 

[Fra]

most probably one will have to find a way to quantum-theoretically describe the classical spacetime model as an emergent phenomenon.

Yes, I also think spacetime needs to be emergent in some sense, but one must not fool oneself and think that such an emergence can be phrased in terms of the same QM. The way it's done is to just embedd the 4D space into a larger space, or avoid curvature by embedding it into a larger space which is asymptotically flat. But you can not cheat like that and get around the core issue that the formalism depends on the very thing that is supposed to be emergent.

I think the QM formalism itself, needs to be more flexible and emergent itself, from a more general logic from QM itself also emerges.

/Fredrik

 

[PeterDonis]

partition assumption

What is $O_A$? It would help if you would use the same notation that the paper you quoted from uses.

 

[Fra]

Nothing in quantum theory explains what "force" acts on/causes distant Bob's B to change to a specific state based on a decision by distant Alice. QT does not "explain" this in a local manner, even though it predicts correctly.

I agree, this again is the key point of the discussion!

Here it's hard to avoid addressing the link between entanglement and the makeup of space I would say. Because locality can be thought of both with respect to regular 3D space and "information space". And with these thoughts, I think there are MORE possibilities to find explanations than the original "naive" forms of causal mechanisms involving HV, that are what Bell inequality describes.

/Fredrik

 

[Fra]

What is $O_A$? It would help if you would use the same notation that the paper you quoted from uses.

Sorry, $O_A$ is Observer-A (ie. Alice), $O_B$ is obsever-B (ie. Bob). I consider all probabilities conditional to the observer. Soem of the orignal notation grosses over this, this is what i decomposed the conditional probabilities to illustrated what i mean.

/Fredrik

 

[*now*]

Bell shows that the predictions of QT violate his inequalities, yes--of course that is easy to show. And therefore no "local realistic" model can reproduce the predictions of QT, since "local realistic" models will obey his inequalities.

this paper discusses a view that has been said to be “local and realistic” https://arxiv.org/pdf/1806.08150.pdf

 

[PeterDonis]

$O_A$ is Observer-A (ie. Alice), $O_B$ is obsever-B (ie. Bob).

Ok, so how does your notation match up with what's in the Bell paper you quoted? Again, it would help if you'd just use the same notation Bell does. As you state it I have no idea how what you say relates to what Bell said.

I consider all probabilities conditional to the observer. Soem of the orignal notation grosses over this, this is what i decomposed the conditional probabilities to illustrated what i mean.

This still doesn't help me to match up what you say with what Bell said.

 

[msumm21]

Explaining the Bell Inequality by expanding the particles to their full, shared wave function is not any kind of "loop hole". Quite the contrary, it demonstrates that the spatial extant of that wave function is part of the non-local "mechanism" that supports the accurate QM predictions.

I think I understand. I realize that calling the entangled pair local to one another (because the wave function overlaps) is a bit satisfying at first, but of course there's still something "nonlocal" in a sense to "spread the information around the wavefunction's spatial extent."

Local realism addresses the communication of information. In a strict (and inaccurate) sense, if we attempt to postulate that a piece of information resides solely at a point within a particle, that information could only be "presently" local to another particle if that other particle also included that point. Allowing a single copy of that information to be spatially distributed (occupying more than a point) is an immediate violation of local realism. Allowing multiple copies of that information doesn't violate local realism, but it also can't be used to explain Bells Inequality.

Since the "copies of information" would need to "spread around the spatial extent of the wave function" faster than speed of light, that's why it would still need to violate local realism, right? If so, makes sense to me, just want to ensure I understand what you said. Thanks!

 

[.Scott]

Since the "copies of information" would need to "spread around the spatial extent of the wave function" faster than speed of light, that's why it would still need to violate local realism, right? If so, makes sense to me, just want to ensure I understand what you said. Thanks!

Right!

 

[vanhees71]

I think I understand. I realize that calling the entangled pair local to one another (because the wave function overlaps) is a bit satisfying at first, but of course there's still something "nonlocal" in a sense to "spread the information around the wavefunction's spatial extent."

It doesn't make sense to say "the entangled pair [is] local to one another". Locality in the standard sense of the HEP community is what relativistic QFT builds into the description of particles, i.e., the Hamilton density of the theory commutes with any local observable for arguments of the corresponding operators that are spacelike separated. This implies that there cannot be any causal influence between events (in this case measurement events like detector clicks registering the one and the other particles at far-distant places).

There is indeed "something nonlocal", and that's the strong correlations between the outcome of measurements on entangled states at far-distant places, and this correlations are due to the preparation of the particles before (!) the measurement. Entangled states describe an "utmost quantum situation", where the two particles cannot be described as individual, separated entities, but only as the pair in -well- an entangled state. It's much more precise to call it "inseparability" (Einstein) rather than "non-locality", because locality is already a clear mathematical statement of properties of relativistic QFTs. Since the Bell tests are all describable within relativistic QFTs there's no contradiction between this sharp definition of "locality" and the "inseparability" demonstrated by these very Bell tests.

Since the "copies of information" would need to "spread around the spatial extent of the wave function" faster than speed of light, that's why it would still need to violate local realism, right? If so, makes sense to me, just want to ensure I understand what you said. Thanks!

The problem is what "realism" means here. My understanding of Bell's writings is that he defines it as the property that all observables always take determined values, which are unknown to us due to hidden variables, which we can describe only probabilistically. This together with "locality" (and I understand Bell as precisely meaning by locality the usual HEP definition; one must not forget that Bell not only did his now more famous work on the foundations of QT but also before brillant work in relativistic QFT, discovering among others the (chiral) anomaly in gauge theories) leads to the Bell inequality, which is violated by QT for entangled states and made it a scientifically testable question, whether "local realism" (EPR) or "Q(F)T" is right, and the result, maybe to the bewilderment of Bell himself, is in favor of Q(F)T, and this with an amazing significance and accuracy!