# Locality vs Non-Locality

## Main Question or Discussion Point

In trying to grasp the Bell Theorem that "reality must be non-local" I have a question---what exactly does it mean to say that two physical objects are "local" vs "non-local" in their interactions ?

In reading Nick Herberts book, (1985), Quantum Reality, he states that local interaction = direct contact with mediation; non-local interaction = non-direct unmediated contact.

For example, in classical macroscopic view, the proton [P] and neutron [N], when they combine to form the deuteron [NP]--the interaction between the two is always "local" because the strong force is mediated by p-mesons (pions). In microscopic quark-gluon view the [P] is itself a local physical object of three quarks (uud) that are in local contact, and mediated by gluon color force.

Now, this view of "local" makes sense to me, I can grasp that things like pions and gluons mediate physical objects like nucleons and quarks to make the cybernetic system "local", e.g., holistic.

But, Bell Theorem tells me that the deuteron [NP] is a physical object where the [N] and [P] are held together by a "non-local" interaction (and by definition this cannot be pions otherwise it would be local), and same logic for [P] at quark level.

So, could someone please explain to me in mathematical formalism the physical nature of this "non-local" force or field or whatever it is that Bell Theorem claims to be holding together reality at both the macroscopic nucleon [NP] and microscopic quark (uud) spatial scales ? Thank you for any help on this confusing (for me) subject.

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There are differing opinions about Bell's Theorem. For me, quantum entanglement better explains what is supposed to be explained by Bell's. Bell seems to have thought that a distant particle could have cause on a near particle, or vice versa. Spooky action at a distance, as Einstein called it.

Entanglement says two particles, prepared together, will have spin which is interdependant on the particles, that is, if one particle is examined it's spin state will *predict* with 100% probablity, the spin state of the other particle regardless of the distance between the particles.

Well, that means in preparation (creation), the two particles are created in pairs of opposing spin. There is no cause/effect from one particle to the other; the states are deternined at creation. You can't predict which particle will have a certain spin in advance. Observation/measurement is the only way to tell, but when one is observed you will then know the state of the other.

I think Bell got a little carried away with 'realism' sinilar to his predecessors affliction of positivism in the late 1800's and early 1900's, wherein it was beleived that something was not 'real' until it was observed.

Sum; I find it better to ignore Bell completely and go with quantum theory.

kublai said:
Sum; I find it better to ignore Bell completely and go with quantum theory.
Thank you for these comments--but now I am more confused--you seem to imply that Bell Theorem is somehow disconnected from "quantum theory"--but I thought Bell Theorem, and further Bell Tests, are used as strong evidence in favor of "quantum theory".

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So, could someone please explain to me in mathematical formalism the physical nature of this "non-local" force or field or whatever it is that Bell Theorem claims to be holding together reality at both the macroscopic nucleon [NP] and microscopic quark (uud) spatial scales ? Thank you for any help on this confusing (for me) subject.
I think you may be confusing 'non-local' with 'delocalized'. In a molecule an electron can be spread over several different atoms and this forms a bond holding the molecule together (delocalization). I assume the same happens for nucleons in a nucleus but I'm not an expert on that. I would say that such effects were 'local' in the other sense. 'Non-local' typically means having correlations which appear to need information travelling faster than light, or correlations which don't seem to be caused by an intervening force.

It is often said if one accepts Bell's theorem. either quantum mechanics is wrong, or local realism is wrong. Most people have come to disfavor local realism.

Numerous tests have shown Bell's Inequality is violated in numerous instances,.

If you are not familiar with Quantum Entanglement better bone up on it.

chronon said:
'Non-local' typically means having correlations which appear to need information travelling faster than light, or correlations which don't seem to be caused by an intervening force.
Thank you, just so I am clear, are you then saying that for Bell Theorem to hold true for the deuteron [NP] bound state as defined by Herbert (e.g., "reality must be non-local"), then the [P] and [N] in the deuteron are held together by (1) "information" travelling faster than speed of light ? -- or -- (2) by "no intervening force", or perhaps some combination of (1) + (2) ? Now, I can grasp (1) because there is evidence of faster than speed of light phenomenon, but I cannot grasp dynamics of (2).

ZapperZ
Staff Emeritus
There is a severe misunderstanding of the term "local" and "non-local" as applied in this case. It has NOTHING to do with "local realism" that is being tested using Bell tests. Let's not confuse the two.

An electron in an insulator is "localized". It stays in one location within the insulator and its motion is highly limited to that region. An electron in a metal or superconductor is NOT localized. The wavefunction that describes it are plane waves, and it has no particular location over the bulk of the material. It has no prefered site to sit for a very long time. Thus, it is "non-local".

I'd like to know what is this faster-than-light evidence here. If it's the NEC experiment with anomolous dispersion, I strongly suggest you REREAD the paper.

Zz.

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ZapperZ said:
There is a severe misunderstanding of the term "local" and "non-local" as applied in this case. It has NOTHING to do with "local realism" that is being tested using Bell tests. Let's not confuse the two.
OK, but I am confused, --what do you mean by the local "it" above -- that differs from "local realism" ? As I stated in the first post, Nick Herbert in his book (p. 212, second paragraph, last sentence )made this statement ..."Bell's theorem says that reality must be non-local"...(his words). So, since the deuteron is a real and stable physical entity [NP], what then does it mean to say that the deuteron [NP] is "non-local" vis-a-vis Bell Theorem ? This is my confusion. Is it that Bell Theorem does not apply to real and stable macroscopic entities such as the deuteron ? -- is that my confusion ?

ZapperZ said:
I'd like to know what is this faster-than-light evidence here.
From this site:http://actualites.epfl.ch/index.php?module=epflfiles&func=getFile&fid=5521&inline=1, to be published in August 2005 issue of Applied Physics Letters.

Hurkyl
Staff Emeritus
Gold Member
The nonlocality guaranteed by the Bell Theorem can simply be taken to be the lack of classical "observation independence" -- causally separated experiments need not be statistically independent.

Or, to put it differently, if you know everything about A and everything about B, that does not mean you know everything about A and B when considered jointly.

Rade, that paper you refered to is talking about the speed of light in a fiber cable. They have found a way to speed it up a bit. However this has nothing to do with C, the speed of light in a vacuum.

Light, when traveling through a *medium* such as a fiber-optic cable does not travel at C. It's speed then depends on the refractory index of the medium.

Hurkyl said:
The nonlocality guaranteed by the Bell Theorem can simply be taken to be the lack of classical "observation independence" ...Or, to put it differently, if you know everything about A and everything about B, that does not mean you know everything about A and B when considered jointly.
OK, so if I apply this logic to the deuteron [NP] as a real entity, then what you are saying (please correct me if I error) is that if I know everything about the proton [P], and everything about the neutron [N], this does not mean (from those independent facts alone) that I know everything about [NP] when the two nucleons are considered jointly. But, did it take Bell to figure this out ? -- seems like common sense to me. For example, I can know everything about carbon, hydrogen, oxygen, but when I put them together to form a sugar, a new property called "taste" emerges that was not part of the complete knowledge of the three parts. Surely there is more to Bell Theorem than this

kublai said:
Rade, that paper you refered to is talking about the speed of light in a fiber cable. They have found a way to speed it up a bit. However this has nothing to do with C, the speed of light in a vacuum. Light, when traveling through a *medium* such as a fiber-optic cable does not travel at C. It's speed then depends on the refractory index of the medium.
Thank you, my error.

 I have a question. Are Bell tests done within a vacuum or a medium ? If within a medium, then would it be correct to assume from the above experiment that the entities tested in Bell test could then be forced to travel faster than c if the correct medium was used ? Has anyone tried this experiment ?

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Hurkyl
Staff Emeritus
Gold Member
Classically, in principle, we could have figured out that combining carbon, hydrogen, and oxygen to make a sugar would lead to the taste of sweetness (note that you're involving new things here -- e.g. to talk about sweetness, you'd have to also include knowledge of, for example, taste buds, the nervous system, and the brain), whether or not we have enough computational power, or even had the idea for looking for such a thing.

But this isn't really what I was talking about, so let me try again.

Observation independence says that if:

(1) I have the ability to make the best possible prediction of the outcome of any experiment that can possibly be done at point A.
(2) I have the ability to make the best possible prediction of the outcome of any experiment that can possibly be done at point B.

Then,

(3) I have the ability to make the best possible prediction of the joint outcome of any experiments that can possibly be done at points A and B.

Quantum mechanics denies that (1) and (2) are sufficient for (3).

(I guess I should add that I take the viewpoint (which I believe is quite atypical) that the outcome of an observation is a random variable)

what causes it to be insufficient for (3) ?

Hurkyl
Staff Emeritus
Gold Member
Here's a ridiculously abstract viewpoint that makes it clear to me:

Suppose what happens at point A is made up of two "equal parts", we'll call them u and v. So, the state near A is simply u + v.

Similarly, the state near B happens to be x + y.

Classically, to get the joint state, we just "multiply". The state near A and B must be given by:

(u + v) * (x + y) = u*x + u*y + v*x + v*y

Notice that we can now go backwards -- to get the what is happening near A, we simply ignore the second factor in each term, and see that the state near A is given by:

u + u + v + v = 2(u + v).

(Constant factors out front don't matter to states -- this is still equal parts of u and v)

Quantum mechanics says other things are possible. For example, the joint state could also be:

u*x + v*y

or

u*y + v*x

Note that if we take either of these states and look at what's happening near A, we get that the state near A is (u + v), and similarly the state near B is (x + y).

So, if we happen to know everything about A (that it's equal parts u and v), and of B (it's equal parts x and y), that isn't enough to figure out what the joint state of A and B are. It could be equal parts ux and vy, or equal parts uy and vx, the classical state, or any number of yucky things.

samalkhaiat
"NON-LOCAL INTERACTION"? This is an absolute garbage. All four interactions we know are local (locally mediated by bosons).
As for NON-LOCALITY in QM: It is about "correlations" (not interactions) between parts of one system, So it does not apply to BOUND STATES which are held by local interactions. if you are to separate the neutron from the proton in your deuteron, you will have to destroy the N-P bound state (you wont have deutron any more), rather you will end up with totally different system. I wonder wether experimental physicists would be able to setup a correlation between N AND P in this case?
You should know that NON-LOCALITY requires superposition principle(linear theory)This is why it shows up in QM.
As for field theories:there exists no satisfactory field theory which avoids locality.

samalkhaiat said:
As for NON-LOCALITY in QM: It is about "correlations" (not interactions) between parts of one system, So it does not apply to BOUND STATES which are held by local interactions. if you are to separate the neutron from the proton in your deuteron, you will have to destroy the N-P bound state (you wont have deutron any more), rather you will end up with totally different system. I wonder wether experimental physicists would be able to setup a correlation between N AND P in this case?You should know that NON-LOCALITY requires superposition principle(linear theory)This is why it shows up in QM.As for field theories:there exists no satisfactory field theory which avoids locality.
OK, so you seem to conclude that Bell's tests would not apply to bound states such as the deuteron [NP], since by definition, the [NP] is a real system that is a local reality (e.g., bound by pions), but the [P] and [N] are not entangled--would that be correct ?

ttn
kublai said:
There are differing opinions about Bell's Theorem. For me, quantum entanglement better explains what is supposed to be explained by Bell's. Bell seems to have thought that a distant particle could have cause on a near particle, or vice versa. Spooky action at a distance, as Einstein called it.
Entanglement says two particles, prepared together, will have spin which is interdependant on the particles, that is, if one particle is examined it's spin state will *predict* with 100% probablity, the spin state of the other particle regardless of the distance between the particles.
Well, that means in preparation (creation), the two particles are created in pairs of opposing spin. There is no cause/effect from one particle to the other; the states are deternined at creation. You can't predict which particle will have a certain spin in advance. Observation/measurement is the only way to tell, but when one is observed you will then know the state of the other.
I think Bell got a little carried away with 'realism' sinilar to his predecessors affliction of positivism in the late 1800's and early 1900's, wherein it was beleived that something was not 'real' until it was observed.
Sum; I find it better to ignore Bell completely and go with quantum theory.
This is all based on an extremely bad confusion. What kublai is saying above is that, according to regular quantum mechanics, the individual particles in an entangled spin state have some definite spin values (along various directions) but we simply aren't aware of those values. But we know that, whatever value one of the particles has, the other particle has the opposite value. So if we measure (say) the x-component of the spin of one particle, we learn immediately the value of the x-component spin of the distant particle. But (it is claimed) this doesn't mean there's any causal interaction between the two particles. Nothing in the distant particle changes as a result of our measurement on the nearby particle.

But all of this is wrong. First off, to talk about each particle carrying specific values for the spin components along different directions, is to talk about (what is normally called) "hidden variables". The quantum state -- the wave function -- does *not* attribute these values to the particles. So to say that the particle possesses these values is to deny that the wave function description is complete. Furthermore, to deny that there is any causal interaction between the two particles after they fly apart, is to insist that one's hidden variable theory be local.

In other words, the theory kublai is advocating above is a local hidden variable theory -- it is *precisely* the kind of theory that Bell's Theorem proves cannot agree with the QM predictions (and we now know, with reasonable certainty, that the QM predictions are empirically correct).

So it's really quite preposterous to accuse Bell of getting "carried away". What Bell did was analyze precisely the kind of theory kublai is advocating here, and prove that this theory is not empirically viable!

Bottom line: orthodox QM (that is, QM with the completeness doctrine) is a non-local theory. You can see this explicitly from the collapse of the wave function, which happens "instantaneously" (which is faster than light!). Einstein believed that if you dropped the completeness doctrine and added "hidden variables", you could get rid of this non-locality, interpreting the collapse as merely an updating of knowledge with no real causal influence. That's why he never believed that QM was the real deal -- he was looking for some kind of local hidden variable theory that would make the same predictions as QM but wouldn't suffer from non-locality. But after Einstein's death, Bell proved that there cannot be a local hidden variable theory that agrees with the QM predictions. (So no wonder Einstein never found one!) And that means we're stuck with non-locality whether we believe QM is complete or not. Non-locality is a necessary feature of any theory that agrees with experiment. That is, non-locality is a fact of nature.

*That* is what Bell proved.

ttn, there is nothing *hidden* and once the particles are prepared there are no *variables*; all properties are set before the particles are separated.

ttn
kublai said:
ttn, there is nothing *hidden* and once the particles are prepared there are no *variables*; all properties are set before the particles are separated.
Not according to (orthodox) quantum mechanics!

Think about what you're saying. Suppose two spin 1/2 particles are in a spin singlet state:

|psi> = ( |1up> |2down> - |1down> |2up> ) / sqrt(2)

where the kets mean up and down along (say) the z axis.

You're saying that the outcome for a spin-along-z measurement on particle 2 is already determined by the state |psi>. That just isn't true. The state is not an eigenstate of the z-spin operator for particle 2 -- it's in an (entangled) superposition of being spin up and spin down along z. It's only when a measurement is made that (according to orthodox QM) the state collapses and becomes an eigenstate of the operator you just measured -- i.e., the state collapses to having a definite value for the observable measured.

Now maybe you think that the "obvious" way to interpret this is to say that the wf is just an incomplete description, so we should interpret the measurements as simply revealing pre-existing values that were somehow encoded in the real state of the real particle. That's fine (and I think quite reasonable). But then you're rejecting the orthodox completeness doctrine and positing hidden variables.

(And as I said before, Bell tells us that we can't escape from the apparent non-locality associated with wf collapse by taking this route -- a hidden variable theory that is local will necessarily disagree with the QM predictions.)

ttn, relax and take a look at this:

http://arxiv.org/PS_cache/quant-ph/pdf/0502/0502016.pdf [Broken]

VI. CONCLUSIONS
There were two basic elements to all proofs of non-locality: the fact that the de Broglie-Bohm interpretation of a
2-particle singlet wavefunction generated non-local forces on each particle, and the “local realistic” Bell inequality,
S < 2. We have seen that the analysis of both elements was flawed; the former by arbitrarily restricting the full
wavefunction, the latter by assuming a violation of Heisenberg’s Uncertainty Principle.
The implicit assumption of the temporal order-independence of measurements at different orientations coupled with
the explicit assumption of locality meant that Bell’s claim of a locality bound was actually a classicality constraint (i.e.
that one measurement has no effect on another). Classical local hidden variable theories are precluded by experiment,
but non-classical (non-commutative or quantum) local hidden variable theories are not subject to Bell’s original limit
of 2, but Cirel’son’s limit [26] of 2√2. The additional terms of our inequality, equation 10, or the quantum analog,
equation 17, only contribute if non-classical effects occur locally; none of these inequalities requires a distant point to
affect a nearby point’s behavior in any way. What is precluded by violations of Bell’s inequality is not local realism
per se, but the Newtonian “idealism” of Heisenberg-violating hidden variable theories.
The de Broglie-Bohm interpretation of Quantum Mechanics [27] is a Heisenberg-compliant theory, and as long as
the full product-form wavefunction is used, and not some arbitrarily restricted form that incorporates all or part of
the measurement operator, Bohmian mechanics will provide a local description of the EP-B data.

There are dozens of papers like this one in the *recent* literature.

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kublai said:
ttn, relax and take a look at this:
http://arxiv.org/PS_cache/quant-ph/pdf/0502/0502016.pdf [Broken]
VI. CONCLUSIONS
There were two basic elements to all proofs of non-locality: the fact that the de Broglie-Bohm interpretation of a
2-particle singlet wavefunction generated non-local forces on each particle, and the “local realistic” Bell inequality,
S < 2. We have seen that the analysis of both elements was flawed; the former by arbitrarily restricting the full
wavefunction, the latter by assuming a violation of Heisenberg’s Uncertainty Principle.
The implicit assumption of the temporal order-independence of measurements at different orientations coupled with
the explicit assumption of locality meant that Bell’s claim of a locality bound was actually a classicality constraint (i.e.
that one measurement has no effect on another). Classical local hidden variable theories are precluded by experiment,
but non-classical (non-commutative or quantum) local hidden variable theories are not subject to Bell’s original limit
of 2, but Cirel’son’s limit [26] of 2√2. The additional terms of our inequality, equation 10, or the quantum analog,
equation 17, only contribute if non-classical effects occur locally; none of these inequalities requires a distant point to
affect a nearby point’s behavior in any way. What is precluded by violations of Bell’s inequality is not local realism
per se, but the Newtonian “idealism” of Heisenberg-violating hidden variable theories.
The de Broglie-Bohm interpretation of Quantum Mechanics [27] is a Heisenberg-compliant theory, and as long as
the full product-form wavefunction is used, and not some arbitrarily restricted form that incorporates all or part of
the measurement operator, Bohmian mechanics will provide a local description of the EP-B data.
There are dozens of papers like this one in the *recent* literature.
Please note that a paper that appears on arxiv.org is not neccesarily peer reviewed. The paper you cited has not even been submitted to a peer reviewed journal. That doesn't mean it is wrong, it just means you should be more skeptical than normal of the correctness and assertations made in that paper.

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ttn
kublai said:
ttn, relax and take a look at this:...
As Norman pointed out, one can't believe everything one reads in a physics paper (especially if it's just on arxiv.org).

I stand by everything I said earlier.

Read the paper and THEN judge the author.

Like I said in the previous post, there are dozens of recent papers on the subject, not just arXiv, browse the journals, take your pick.

ttn
kublai said:
Read the paper and THEN judge the author.
Actually, I have read the paper. In fact I've had extensive private discussions with the author about it. I think he's quite confused about Bell, although I like him personally.

Like I said in the previous post, there are dozens of recent papers on the subject, not just arXiv, browse the journals, take your pick.
I'm aware of lots of the papers. In fact some of them are written by me.

If you don't want to accept or even discuss what I've said, so be it. But I believe your original comments (the ones I posted a response to) were pretty confused, and I'd be happy to try to clarify things if you're interested. Or not. Your choice.