# Locality in Bell Experiments

• I
• msumm21

#### msumm21

TL;DR Summary
Could the particles in Bell experiments be considered local in some sense?
Consider experiments that demonstrate violations of Bell inequalities. I'm wondering about the spatial extent of the wave function of the particles BEFORE measurement. I assume the spatial extent is "very large," and my main question is whether they overlap.

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?

kurt101
Summary: Could the particles in Bell experiments be considered local in some sense?

Consider experiments that demonstrate violations of Bell inequalities. I'm wondering about the spatial extent of the wave function of the particles BEFORE measurement. I assume the spatial extent is "very large," and my main question is whether they overlap.

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?
Each particle does not have its own wave function. Instead, there is a wavefunction describing the entangled two-particle system.

mattt
I understand they're entangled. For example as a gross simplification let's say the state was ##R_1 \otimes R_2 + R_3 \otimes R_4## where this represents uniform distribution over "regions" ##R_i## in space. If e.g. ##R_1 \cap R_2 \supset \emptyset## then they overlap in some sense.

I understand they're entangled. For example as a gross simplification let's say the state was ##R_1 \otimes R_2 + R_3 \otimes R_4## where this represents uniform distribution over "regions" ##R_i## in space. If e.g. ##R_1 \cap R_2 \supset \emptyset## then they overlap in some sense.
I don't know what this means in terms of entangled particles. The maximally entangled Bell states are given here:

https://en.wikipedia.org/wiki/Quantum_entanglement#Entangled_states

I don't know what this means in terms of entangled particles. The maximally entangled Bell states are given here:

https://en.wikipedia.org/wiki/Quantum_entanglement#Entangled_states

That's referring to the spin portion of the state, I'm referring here to the position. So the full state may be ##P_1 \otimes S_1 \otimes P_2 \otimes S_2## (or more generally a sum of such terms) where the ##P_i## are the position wavefunctions and the ##S_i## are the spin.

That's referring to the spin portion of the state, I'm referring here to the position. So the full state may be ##P_1 \otimes S_1 \otimes P_2 \otimes S_2## (or more generally a sum of such terms) where the ##P_i## are the position wavefunctions and the ##S_i## are the spin.
That doesn't look like an entangled state. You may be missing the whole idea of entanglement: that the particles do not have independent states.

That's referring to the spin portion of the state
No, it's not. The ##0## and ##1## labels on the kets refer to spin states, but the ##A## and ##B## subscripts refer to positions (or more precisely to different detectors and the paths leading to them).

Lynch101
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?
One should distinguish the notion of local from the notion of localized. The classical electromagnetic field, for instance, is local but not localized. Point-particles in Newtonian gravity are localized, but the gravitational force between them is not local. Likewise, the wave functions you discuss above are not localized, but that has nothing to do with non-locality due to entanglement.

mattt, kurt101, Lynch101 and 4 others
"Non-locality due to entanglement" is a misnomer. One should rephrase this somehow. My favorite is by Einstein, who called it "inseparability". Locality means, at least in my scientific community (relativistic QFT), that particles are described by quantum fields that transform in a local way under proper orthochronous Poincare transformations and obey the microcausality condition, i.e., the fields commute (bosons) or anticommute (fermions) at space-like separated spacetime arguments. The Hamilton density is always commuting with any local quantity at spacelike separated spacetime arguments by construction. That rules out causal effects that propagate faster than light. The non-separability of entangled states and the long-ranged correlations between observables of parts of such entangled systems observed at far distances is in full accordance with relativistic causality and locality in this sense.

mattt, kurt101, Lynch101 and 4 others
"Non-locality due to entanglement" is a misnomer.
That's correct within minimal interpretation(s) of QM. But if one wants to interpret QM non-minimally, in terms of ontic (either deterministic or stochastic) variables, then Bell theorem implies that such variables are necessarily non-local, in the sense that some kind of influence between variables propagates instantaneously. An ontic variable is a variable that obeys the following two properties:
(i) It is defined (in either deterministic or stochastic sense) as a property of an individual member of the statistical ensemble, not as a property of the whole ensemble.
(ii) It is defined (in either deterministic or stochastic sense) even in the absence of measurement.

How does the minimal interpretation of QM avoid non-locality implied by the Bell theorem? By rejecting the notion of ontic variables. In particular, the wave function satisfies (ii), but it's not ontic because it does not satisfy (i). The individual measurement outcome satisfies (i), but it's not ontic because it does not satisfy (ii). There are also operator valued observables, but (in the Schrodinger picture) they are not variables.

Lynch101, PeroK and DrChinese
This doesn't belong here, but in the interpretations subforum. Independently from the interpretation you follow, one should name different things with different names, and inseparability is clearly different from non-locality in the sense of my previous posting.

Lynch101
The non-separability of entangled states and the long-ranged correlations between observables of parts of such entangled systems observed at far distances is in full accordance with relativistic causality and locality in this sense.
Are you saying that, in the relativistic QFT community, Bell violation experiments are considered consistent with locality? Because the wave functions are not separable? (I'm not familiar with the "proper orthochronous Poincare transformations ...".)

kurt101
Are you saying that, in the relativistic QFT community, Bell violation experiments are considered consistent with locality?
The term "locality" has different possible definitions. The definition of "locality" that @vanhees71 is using is basically "measurements at spacelike separated events commute" (meaning their results do not depend on the order in which they are done). That is true for quantum experiments. But the definition of "locality" that the QM community usually uses is "does not violate the Bell inequalities", which is obviously false for quantum experiments.

A common issue in discussions in this field is for people to be using different definitions of the same terms and talking past each other.

kurt101, DrChinese, vanhees71 and 4 others
But if one wants to interpret QM non-minimally, in terms of ontic (either deterministic or stochastic) variables, then Bell theorem implies that such variables are necessarily non-local, in the sense that some kind of influence between variables propagates instantaneously.
I think this only follows if you make certain assumptions(as is done in bell proof) about how uncertainty about HV influence causal mechanisms. These assumptions are an implicit legacy from old mechanistic causation that i consider invalid for inference interactions.

If one entertain alternatives, such as associating tje ontic variables to invidivual agent states(not just their equivalence classes or population average), i think it is conceptually possible to seek causal mechanisms that does not violate causality.

Something that involves non-causal mechanisms does not even qualify as an explanation to me. I don't see why such oddness should be required to move beyond the minimal interpretation.

/Fredrik

Lynch101
Are you saying that, in the relativistic QFT community, Bell violation experiments are considered consistent with locality? Because the wave functions are not separable? (I'm not familiar with the "proper orthochronous Poincare transformations ...".)
Of course. The usual experiments are done with photons, and those are described by QED, which is the paradigm of a local relativistic QFT (and the most successful theory ever concerning accordance between theory and experiment).

Proper orthochronous Poincare transformations form the symmetry group of special relativistic spacetime. It consists of temporal and spatial translations as well as all those Lorentz transformations which are continuously connected to unity, i.e., boosts and rotations, that do not change the direction of time.

The term "locality" has different possible definitions. The definition of "locality" that @vanhees71 is using is basically "measurements at spacelike separated events commute" (meaning their results do not depend on the order in which they are done). That is true for quantum experiments. But the definition of "locality" that the QM community usually uses is "does not violate the Bell inequalities", which is obviously false for quantum experiments.

A common issue in discussions in this field is for people to be using different definitions of the same terms and talking past each other.
That's not accurate either. My point is that all the Bell experiments are not in any way ruling out local QFT. To the contrary the usual Bell experiments with photons are all described by QED, the paradigmatic example for a local relativistic QFT. The confirmation of the violation of Bell's inequality in such experiments thus rather shows the violation of what Bell calls "realistic", which for me is a synonym for "deterministic", i.e., the assumption that the values of observables of a system are always determined but unknown and thus described statistically in QT. Behind this is the old idea by Einstein that there must be "hidden variables" that are unknown but determine the values of all observables of a system. Together with locality (in the sense of relativistic QFT) the violation of Bell's inequality rules out this type of "realism". The big confusion is in the imprecise use of everyday language to describe these experiments; particularly "locality" and "realism" is used with zillions of meanings. The only way to really describe it properly is the mathematical frame work of quantum (field) theory.

Behind this is the old idea by Einstein that there must be "hidden variables" that are unknown but determine the values of all observables of a system.
It's the bold part that i call the legacy. The first part can in principle still be fine and explain the correlation in combination with an alternative causal mechanism with ontic elements (yet to be understood though!)

The key is that the bell pair is isolated not just from the physicist, but from the the whole measurement setup up until the final point of interaction. This is why averaging over the physicists ignorance misses the depth if the problem. We should ask how the propagation of the correlated systems are influences along the way from not beeing in tune with(ie not having communucated with) the environment. This is what the quantum mechanical model "describes" statistically but not explains to the level some of us wish (including me).

/Fredrik

But a Bell measurement is not simply a single "measurement event" (say, for a measurement of a photon a click of a detector at a certain spacetime point) but (at least) two, i.e., you make a measurement on each of two parts of an entangled system (e.g., the polarization of the idler and signal photons from a parametric-down conversion entangled photon pair at two far-distant places). If then the two "measurement events" are space-like separated the measurement of the idler cannot causally influence the result of the measurement of the signal photon and vice versa. This holds true for both the local deterministic hidden-variable theory and local relativistic QFTs (here particularly QED). Now Bell's inequality is violated, and the predictions of QED found to be valid. Since both models are local (in the standard sense of QFT and the hidden variable theory in a classical sense) the determinism ("realism" in Bell's lingo) must be given up.

Lord Jestocost
If then the two "measurement events" are space-like separated the measurement of the idler cannot causally influence the result of the measurement of the signal
Agreed
the determinism ("realism" in Bell's lingo) must be given up.
Agreed

The "HV option" entertain is another option and it has nothing todo with determinism and such a model would not obey bells inequality. Causal relation need not be deductive? it can inductive or guiding.

I agree the bell style realism does not work. But i tried to separate what is often lumped together in bells proof. One easily dismisses all of it, when the problem is not necessarily all of it.

The "HV" i refer to is just the single observers knowledge. This is fundamentally hidden as two observers with the same info shuld be indistinguishable.

/Fredrik

That's not accurate either
What's not accurate? I get that you have your own preferred definition of "locality" and you refuse to acknowledge any other definition, but that doesn't mean other definitions don't exist.

My point is that all the Bell experiments are not in any way ruling out local QFT.
Nobody has ever claimed that Bell inequality violations rule out "local QFT" by your preferred definition of "local". You are attacking a straw man (and it's not the first time you have attacked this particular straw man in PF threads). Other people simply don't share your belief that your preferred definition is the only possible definition of "local" that could ever make sense. For many workers in the field, as I said, "local" means "does not violate the Bell inequalities", so any violation of Bell inequalities is not "local" by their preferred definition, even though it is by yours.

zonde, gentzen, DrChinese and 1 other person
The confirmation of the violation of Bell's inequality in such experiments thus rather shows the violation of what Bell calls "realistic"
This has the same issue that I've already brought up with "local": not everyone agrees on what "realistic" means. At least here you do give a more detailed explanation of what you mean by "realistic".

Doc Al and DrChinese
I agree that the different definitions is part of the confusion here. On "locality", I personally side with vanhess, i think of "the principle locality" as there is not instant influence or communication between distant systems. Entanglement is merely "correlation" for me, I find it akward to speka of locality here. But this just terminology I agree.

But the other distinction I tried to make had nothing to do with neither locality nor statistical correlations, it was that Bells definition of "real" contains IMO two parts:
1) The notion of hidden variables
2) Assumption of HOW these hidden variables determine the total action of the system

My point was that, I have not problems with (1) but (2) is the real problem and the implicit legacy of old mechanistic thinking of the nature of causal mechanism.

In the old days of Newton and probably Einsteins, the idea was that causal mechanism (action and reaction) are described in terms of (local, it you add locality) ontic elements of the universe. In contrast my takeaway from insights of QM and modern physics is that the ontic elements are not those of the universe, but the observers or agents best informed STATE of knowledge of the universe that determines its action. The reaction from the environement may not necessarily be in perfect tune in the general case. This difference concernts to the second point in bells ansatz. The other takeaway is not that we do not have any "reality", the problem is that even reality needs to pass the rules of inference, and the process of establishing the "ultimate reality" is necessarily physical process, whose causal mechanism we apparently still to not understand properly. This also concerns the second point in bells ansatz. Current laws are as i see it necessarily a "simplification" we arrived at from the timeless perspective that comes from the assymmmetry between a massive observer and subatomic systems. So it's not strange that we have such trouble to merge this conceptually with gravity and cosmology. All these things IMO relates to the second point of bells ansatz.

/Fredrik

What's not accurate? I get that you have your own preferred definition of "locality" and you refuse to acknowledge any other definition, but that doesn't mean other definitions don't exist.

Nobody has ever claimed that Bell inequality violations rule out "local QFT" by your preferred definition of "local". You are attacking a straw man (and it's not the first time you have attacked this particular straw man in PF threads). Other people simply don't share your belief that your preferred definition is the only possible definition of "local" that could ever make sense. For many workers in the field, as I said, "local" means "does not violate the Bell inequalities", so any violation of Bell inequalities is not "local" by their preferred definition, even though it is by yours.
Your statement that locality alone is ruling out the violation of Bell inequalities. That's not true. In addition you need what Bell calls "realism". It may well be that one day somebody finds a non-local "realistic" theory compatible with relativistic causality constraints.

It's not my "preferred definition of local" but the usual definition of locality in relativistic QFT. It's not a straw man, I'm attacking, but it's often claimed, and it has been claimed in this thread too, and obviously even you do it right here, that locality is not consistent with the violation of Bell's inequality. All successful relativistic QFTs are by construction local (and that's how locality is defined in the physical literature; I don't care about metaphysical and other philosophical flavors when discussing physics) but predict precisely the violation of Bell's inequality that is observed in all Bell tests so far.

Again: It's you who claims that locality alone leads to Bell's inequalities, which is wrong, because you also need "realism" to derive them. It doesn't make sense to use another definition of locality than is used in the standard physics literature! That only leads to confusion!

Fra
This has the same issue that I've already brought up with "local": not everyone agrees on what "realistic" means. At least here you do give a more detailed explanation of what you mean by "realistic".
In Bell's papers and in the physics literature locality and realism has a specific meaning.

Locality is built into the construction of local relativistic QFTs in the form of the microcausality constraints, which leads to the physical properties of the observable quantities like the S-matrix (unitarity, Poincare invariance, cluster decomposition principle (!)...). It means that the Hamilton density is built by quantum fields that transform locally under Poincare transformations, and such that it commutes with local observables at space-like separated arguments (microcausality constraint). This is a sufficient condition to lead to the above listed properties of the S-matrix. In addition it predicts the relation between spin and statistics (half-integer spin -> fermions; integer spin -> bosons) and CPT symmetry, both of which are empirically very well confirmed. It's also conistent with all Bell tests.

"Realism" means that, in contradiction to the (minimally interpreted) QT, all observables take always determined values. You need both, locality and "realism", to derive Bell's inequalities. Relativistic QFT is by construction local but not "realistic" and in accordance with the observed violations of Bell's inequalities, i.e., the statistical properties of observations predicted by QFT is confirmed. The only conclusion thus can be that it is realism that is incompatible with the observations.

But a Bell measurement is not simply a single "measurement event" (say, for a measurement of a photon a click of a detector at a certain spacetime point) but (at least) two, i.e., you make a measurement on each of two parts of an entangled system (e.g., the polarization of the idler and signal photons from a parametric-down conversion entangled photon pair at two far-distant places). If then the two "measurement events" are space-like separated the measurement of the idler cannot causally influence the result of the measurement of the signal photon and vice versa. This holds true for both the local deterministic hidden-variable theory and local relativistic QFTs (here particularly QED). Now Bell's inequality is violated, and the predictions of QED found to be valid. Since both models are local (in the standard sense of QFT and the hidden variable theory in a classical sense) the determinism ("realism" in Bell's lingo) must be given up.

Besides everything that is wrong with these comments, this comes back to an interpretational issue and therefore belongs in the subforum.

In this thread, @msumm21 is asking whether or not the entangled particles have wave functions that overlap, and therefore whether there can be local interactions. As has been already said, the entangled particles form a single quantum system and cannot be said to be separable. Further, in some Bell test scenarios, the components of the entangled pair have never existed in the same region of spacetime.

As to vanhees71's comments: obviously this is a loop of conversions we have had previously, and serves no purpose rehashing in this thread itself. 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 to everyone's satisfaction, and certainly QFT has not resolved that any better than old fashioned QM. Otherwise interpretations would cease to exist.

*It doesn't matter how many measurements are made, and in fact the measurements do NOT need to be spacelike separated.

gentzen and Doc Al
Your statement that locality alone is ruling out the violation of Bell inequalities. That's not true.
Please stop mistaking choices of terminology that are different from yours for claims about physics. We do not disagree on any of the actual physics. We just disagree on choice of terminology. I have already explained that to some people, "locality" means "does not violate the Bell inequalities". I realize that is not your definition of "locality". But when I say that it is some people's definition of "locality", I am not saying your claim about the physics is wrong. I am only saying some people make different choices of terminology than you do. It is extremely frustrating that you are unable to comprehend this despite repeated attempts in multiple threads over a considerable period of time (and I do not think I am the only PF member who has had this experience with you).

I will respond to some actual substantive statements you make in a separate post.

zonde, gentzen, Motore and 2 others
In Bell's papers and in the physics literature locality and realism has a specific meaning.

Locality is built into the construction of local relativistic QFTs
Bell's papers say nothing whatever about "local relativistic QFTs".

"Realism" means that, in contradiction to the (minimally interpreted) QT, all observables take always determined values. You need both, locality and "realism", to derive Bell's inequalities.
As Bell defines the terms in his papers, "locality" means that the joint probability distribution factorizes into separate distributions for the two measurements, and "realism" means that we can make meaningful statements about the results of particular measurements that are not made (which is not the same as having to make meaningful statements about the results of all possible measurements). Neither of these is the same as what you are claiming that those terms mean: Bell's "locality" is not the same as the QFT definition (that measurements at spacelike separated events commute) and Bell's "realism" is not the same as "all observables take always determined values"; the latter is a much stronger statement that Bell never claims or uses in his reasoning.

As Bell defines the terms in his papers, "locality" means that the joint probability distribution factorizes into separate distributions for the two measurements,
This looks like the "misnomer" of Bell, Vanhees talks about as this is the very definition of statistical independence to me - not locality. How does Bell then label the other meaning of locality?

Especially for someone like Bell, i presume the distinction is important.

and "realism" means that we can make meaningful statements about the results of particular measurements that are not made
What always annoyed me is that I find that bell also makes assumptions about the nature of causality in interactions, that is bundled together with his "realism". I prefer to separate these things.

Difference between:

1) Is the moon there when nobody looks?

2) What causal influence does the moons existence or non-existence have on those parts of the system(say those agents) that are isolated from this information?

This distinction is imo about the nature of interactions, not about realism. I always found bell discussions blur these up.

/Fredrik

Bell's papers say nothing whatever about "local relativistic QFTs".
True, but Bell's papers are about any kind or local realistic models, contradicting any QT (i.e., also non-relativistic QT).
As Bell defines the terms in his papers, "locality" means that the joint probability distribution factorizes into separate distributions for the two measurements, and "realism" means that we can make meaningful statements about the results of particular measurements that are not made (which is not the same as having to make meaningful statements about the results of all possible measurements). Neither of these is the same as what you are claiming that those terms mean: Bell's "locality" is not the same as the QFT definition (that measurements at spacelike separated events commute) and Bell's "realism" is not the same as "all observables take always determined values"; the latter is a much stronger statement that Bell never claims or uses in his reasoning.
Then we have a different understanding of what Bell is saying. This goes again in the direction of interpretation rather than physics.

[EDIT:] I refer to

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

The first paragraph of II reads:

Last edited:
Lord Jestocost
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

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".

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.

Delta2, gentzen and 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".
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

kurt101
...
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.

kurt101