Binney's interpretation of Violation of Bell Inequalities

[DrChinese]

You make it sound like in that experiment it's arbitrary two photons that are entangled. But it's not. These two photons have to be similar enough to produce Hong-Ou Mandel interference. And in that particular experiment that you linked both photon pairs are produced from the same pulse of the same pump laser. And then of course there are four types of entanglemet that you can get. So there is quite a number of loopholes in your argument.

I am sure you are familiar with experiments such as the following but I point it out for those that are not:

http://arxiv.org/abs/1209.4191
Entanglement Between Photons that have Never Coexisted

http://arxiv.org/abs/0809.3991
High-fidelity entanglement swapping with fully independent sources

The pairs do not need to be produced from the same laser (regardless of the particular experiment I referenced earlier). They need only be phase locked together. It doesn't matter how many types of entanglement are produced, you know which one to expect. In fact you can can choose to cause it if you like.

My point is that a lot of folks picture a situation where the photons start from a common source so "naturally" they exhibit correlations - there is a common cause. But these pairs of photons have NO common point of overlap since they are never in a common light cone. And they do not exhibit the perfect correlations unless they are entangled, something which can be done anywhere and at anytime before or after detection.

 

[stevendaryl]

Axes x, y and z are spacelike so measurement referred to them are independent of spacelike separation.
The Bell's inequalities imply that + and - outcomes are related by commutative relations.

Huh? I was talking about settings being chosen at a spacelike separation.

Let's get concrete. Alice is at one location. 1/4 of a mile away, Bob is at another location. Alice chooses her setting \alpha. She makes a measurement (which presumably means she looks at the book and sees whether the front side or back side is visible to her).

Bob chooses a setting \beta. He makes an observation.

What are the settings \alpha and \beta? If they are angles of rotation of a normal-sized book, then it's not possible for Alice and Bob to both make their settings if they are far apart. The book is only in one place.

So that's exactly what Bell's inequalities have to do with locality. You can't get a violation of Bell's inequality using a toy classical model, provided that the settings for the two observers are chosen at a spacelike separation. If they aren't chosen at a spacelike separation, then you can get a model that violates Bell's inequalities. For example, in your book example, if Bob chooses an angle to rotate the book about some axis, and Alice chooses an angle, and they both broadcast their angles to the person holding the book, who carries out their commands, then the resulting correlations may very well violate Bell's inequalities.

 

[TrickyDicky]

Huh? I was talking about settings being chosen at a spacelike separation.

Let's get concrete. Alice is at one location. 1/4 of a mile away, Bob is at another location. Alice chooses her setting \alpha. She makes a measurement (which presumably means she looks at the book and sees whether the front side or back side is visible to her).

Bob chooses a setting \beta. He makes an observation.

What are the settings \alpha and \beta? If they are angles of rotation of a normal-sized book, then it's not possible for Alice and Bob to both make their settings if they are far apart. The book is only in one place.

So that's exactly what Bell's inequalities have to do with locality. You can't get a violation of Bell's inequality using a toy classical model, provided that the settings for the two observers are chosen at a spacelike separation. If they aren't chosen at a spacelike separation, then you can get a model that violates Bell's inequalities. For example, in your book example, if Bob chooses an angle to rotate the book about some axis, and Alice chooses an angle, and they both broadcast their angles to the person holding the book, who carries out their commands, then the resulting correlations may very well violate Bell's inequalities.

But can't you get the same effect as spacelike separation(since the spacelike separation reflects the demand of impossibility of info transmission between Bob and Alice) by taking sequential 90º rotations of the book and two machines(one for each side of the book and for each sequential rotated angle) that register the information about cover position from their side encrypted so that no information can be shared between the machines?

My claim would be that after collecting all the info registered by the two machines once it is put together and decoded, the results obtained would not respect the inequality in #90.

With the following correspondences: in the z axis the cover in position up is +>, and in position down is ->, for the y-axis the cover at the right position is +> and at the left position is ->, and for the x-axis the cover at the fron is +> and at the back is ->.

 

[Derek Potter]

But can't you get the same effect as spacelike separation(since the spacelike separation reflects the demand of impossibility of info transmission between Bob and Alice) by taking sequential 90º rotations of the book and two machines(one for each side of the book and for each sequential rotated angle) that registers the information about cover position from their side encrypted so that no information can be shared between the machines?

No. Alice's information about turning her side passes through the book and turns Bob's side too. To simulate blocking that information flow, you need to break the Born rigidity of the book by allowing the sides to rotate separately. Good luck patching your toy model to allow that.

 

[TrickyDicky]

Alice's information about turning her side passes through the book and turns Bob's side too.

True, but is that information about angle relevant? In the standard setting with particles the angles in which Bob and Alice measure spin of each particle can be planned beforehand, no?

 

[Derek Potter]

In the standard setting with particles the angles in which Bob and Alice measure spin of each particle can be planned beforehand, no?

Yes they can be planned ahead and the Bell Inequality will still be violated. But that is not in the least bit significant because the required conditions for Bell's Theorem are not met.

True, but is that information about angle relevant?

Yes, the angle information is crucial - though I should have said rotation, not angle. My bad. It is crucial because without it, Alice can turn the book from z+ to z-. But the back still faces z-, meaning that the book now has two back covers and no front one.

 

[Derek Potter]

I feel that maybe I am not understanding your proposed toy model. If so, may I ask you to spell it out in detail? Otherwise the thread will drag on for ever, picking over details, modifying the toy model and generally losing track of the point.

In particular it would help if you say exactly what it is you are trying to illustrate. Originally you were saying that EPR correlations can be explained by the non-commutivity of Alice and Bob's observations. The trade-off between entanglement and non-commutivity is dealt with in the paper by Michael Seevinck and Jos Uffink but for your statement to be relevant you would have to say why the non-commutivity of separated observations is a local explanation i.e. you need to explain how the non-commutivity of remote observations arises under assumptions of local causality. Otherwise you are just saying that it happens, which we know, and can be formulated in different ways, which is interesting but does not explain anything. The onus is on you to justify the claim that it does explain rather than simply describe.

Hopefully you can answer that quicker than it took to ask it

Anyway, if we can get that cleared up, I really would like to know exactly what the model is: Who rotates the book, i.e. from what place is it rotated? What rotations are allowed? What exactly are the observations, and in particular what happens to rotations that end up with the book edgewise-on? How is spacelike separation simulated without introducing unintended Born rigidity that would violate relativity if the separation was truly spacelike? Pre-arrangement might circumvent the rigidity but then the model is not local in the sense required by Bell's Theorem.

If there are no fatal flaws in the model, can you then demonstrate the violation of the Bell Inequality numerically - as I asked you before - please?

I'm not trying to put you to a lot of work, I just want to get it clear what you're talking about.

Thanks.

 

[TrickyDicky]

In particular it would help if you say exactly what it is you are trying to illustrate. Originally you were saying that EPR correlations can be explained by the non-commutivity of Alice and Bob's observations. The trade-off between entanglement and non-commutivity is dealt with in the paper by Michael Seevinck and Jos Uffink but for your statement to be relevant you would have to say why the non-commutivity of separated observations is a local explanation i.e. you need to explain how the non-commutivity of remote observations arises under assumptions of local causality. Otherwise you are just saying that it happens, which we know, and can be formulated in different ways, which is interesting but does not explain anything. The onus is on you to justify the claim that it does explain rather than simply describe.

Maybe I can only claim that it describes but the "book toy model" was intended to explain that if the property of non-commutativity can be made geometrical like it happens with euclidean rotations, it could help understand how one can dodge the locality-nonlocality dichotomy, since it is obvious that geometrical properties are somewhat local and non-local at the same time.

But I wanted the setting of the book experiment to be such that the cover and the back of the book are separated for all practical purposes, thus the machines, registering encrypted info, rotating sequentially in a predetermined set of angles in such a manner that machine A can register its + and - independently form machine B, it is obvious they can't do it simultaneously like in the real experiment with particles for the reasons you pointed out, but I think it can be done sequentially and register the statistics in the different angles independently. In this sense the toy model wouldn't be showing anything different than the experiment with photons or electrons, because if the experiment is done correctly the info gathered from machine A can be taken independently from the info gathered from machine B, the whole point being that it can be done in a book(or a coin for that matter) because the information is geometrical.

Anyway, if we can get that cleared up, I really would like to know exactly what the model is: Who rotates the book, i.e. from what place is it rotated? What rotations are allowed? What exactly are the observations, and in particular what happens to rotations that end up with the book edgewise-on? How is spacelike separation simulated without introducing unintended Born rigidity that would violate relativity if the separation was truly spacelike? Pre-arrangement might circumvent the rigidity but then the model is not local in the sense required by Bell's Theorem.

The machines rotate the book sequentially on any angles programmed on them, each machine follows one side of the book so there is no edge-on, and for each angle it registers either up vs down, left vs right, or front vs rear depending on the axis spatial orientation of the machine.
One could argue the model is neither local nor nonlocal, but the key point here is that it be able to allow independent gathering of the info for machine A and B (thus the pre-arrangement, sequentiality, and encryption of what the machines record to be put together, decoded and analyzed at a late time, thsi should make it equivalent to the spatial separation of the experiment with particles.

If there are no fatal flaws in the model, can you then demonstrate the violation of the Bell Inequality numerically - as I asked you before - please?

I should say that I'm not sure if there are fatal flaws in the setup because I thought it up on the fly as an example of something that seemed obvious to me and I have been "often wrong, never in doubt" (hopefully not always wrong, as Landau claimed of cosmologist's assertions) around here before.
A numerical demonstration would I think give similar results as the polarization experiment with photons, I'll look into it if I have the time.

 

[Derek Potter]

Maybe I can only claim that it describes but the "book toy model" was intended to explain that if the property of non-commutativity can be made geometrical like it happens with euclidean rotations, it could help help understand how one can dodge the locality-nonlocality dichotomy, since it is obvious that geometrical properties are somewhat local and non-local at the same time.

But I wanted the setting of the book experiment to be such that the cover and the back of the book are separated for all practical purposes, thus the machines, registering encrypted info, rotating sequentially in a predetermined set of angles in such a manner that machine A can register its + and - independently form machine B, it is obvious they can't do it simultaneously like in the real experiment with particles for the reasons you pointed out, but I think it can be done sequentially and register the statistics in the different angles independently. In this sense the toy model would be showing anything different than the experiment with photons or electrons, because if the experiment is done correctly the info gathered from machine A can be taken independently from the info gathered from machine B, the whole point being that it can be done in a book(or a coin for that matter) because the information is geometrical.

The machines rotate the book sequentially on any angles programmed on them, each machine follows one side of the book so there is no edge-on, and for each angle it registers either up vs down, left vs right, or front vs rear depending on the axis spatial orientation of the machine.
One could argue the model is neither local nor nonlocal, but the key point here is that it be able to allow independent gathering of the info for machine A and B (thus the pre-arrangement, sequentiality, and encryption of what the machines record to be put together, decoded and analyzed at a late time, thsi should make it equivalent to the spatial separation of the experiment with particles.

I should say that I'm not sure if there are fatal flaws in the setup because I thought it up on the fly as an example of something that seemed obvious to me and I have been "often wrong, never in doubt" (hopefully not always wrong, as Landau claimed of cosmologist's assertions) around here before.
A numerical demonstration would I think give similar results as the polarization experiment with photons, I'll look into it if I have the time.

Okay well I have no idea what any of that means. If someone else can make sense of it, I'll leave it to them.

 

[TrickyDicky]

Okay well I have no idea what any of that means.

Would you say that a geometrical feature like say equality of right angles implying isotropy of the space and that figures may be moved to any location and still be congruent is a local or a nonlocal property? Does the fact that figures with arbitrary spacelike separation can be measured to be congruent if they are put together again mean that measuring one figure is affecting the measure of the other figure making it congruent with itself?
Now this particular geometrical property is commutative so it would not violate the inequalities, but a non-commutative geometrical property like euclidean rotations is not commutative and does violate the inequalities, the spatial separation(local-vs nonlocal) is not the important feature for such properties because they are pervasive(ubiquitous) and independent of spatial separation of the objects on which it is observed.
Is this more understandable?

 

[stevendaryl]

Would you say that a geometrical feature like say equality of right angles implying isotropy of the space and that figures may be moved to any location and still be congruent is a local or a nonlocal property? Does the fact that figures with arbitrary spacelike separation can be measured to be congruent if they are put together again mean that measuring one figure is affecting the measure of the other figure making it congruent with itself?
Now this particular geometrical property is commutative so it would not violate the inequalities, but a non-commutative geometrical property like euclidean rotations is not commutative and does violate the inequalities, the spatial separation(local-vs nonlocal) is not the important feature for such properties because they are pervasive(ubiquitous) and independent of spatial separation of the objects on which it is observed.
Is this more understandable?

It isn't to me. As I said, Bell's inequalities are about a very specific situation: Alice has a device that is capable of producing a measurement result of \pm 1. The device has (at least) two possible settings, a or a'. Bob similarly has a device with two possible settings, b or b'. For many rounds, you perform the following procedure and collect statistics:

On round number n,

1. Alice chooses a setting a_n.
2. She performs a measurement, and gets a result A_n
3. Bob chooses a setting b_n.
4. Bob gets result B_n

Then we compute: E(a,b) = the average, over all rounds n such that a_n = a and b_n = b, of A_n \cdot B_n

That's the context for which Bell derived his inequality. If you allow for Alice's choice a_n to affect Bob's result, B_n, and vice-verse, then there is no reason to expect the inequality to hold. That's where locality comes in: without assuming locality, there is no reason to assume that the inequality holds. Locality in the context of Bell's theorem means a very specific thing: that Alice's choice cannot affect Bob's result, and vice-verse. So your musings about whether congruence of geometric figures is local or nonlocal don't seem to be related to Bell's notion of locality.

Bell defined a hidden variables theory to be an explanation of the correlations along the following lines:

1. Each round, there is a hidden variable \lambda_n influencing the results. The variable may take on different values on different rounds (hence the subscript).
   
2. There are deterministic functions F_A(a, b, \lambda) and F_B(a, b, \lambda) such that A_n = F_A(a_n, b_n, \lambda_n) and B_n = F_B(a_n, b_n, \lambda_n)
3. Each round, \lambda_n is chosen randomly according to some probability distribution P(\lambda)

Those three define what Bell means by a "hidden variables theory". The special case of a "local" hidden variables theory makes the additional assumption that F_A does not depend on b and F_B does not depend on a. That is,

A_n = F_A(a_n, \lambda_n) and B_n = F_B(b_n, \lambda_n)

That's the critical assumption that allows him to derive his inequality. Right off the bat, I don't see how his derivation has anything to do with whether a and b are described by a commutative or noncommutative algebra.

Now, what someone has shown is that QM only predicts a violation of Bell's inequality in the case where the two measurements corresponding to Alice's settings a and a' are described by noncommuting operators, and the two measurements corresponding to Bob's settings b and b' are described by noncommuting operators. But that's a fact about quantum mechanics. Bell's derivation doesn't (as far as I can see) assume anything at all about whether things commute or not. The noncommutativity is about the two choices that Alice (or Bob) might make, not about Alice's measurements versus Bob's. Alice's measurements do commute with Bob's measurements.

 

[stevendaryl]

Bell defined a hidden variables theory to be an explanation of the correlations along the following lines:

1. Each round, there is a hidden variable \lambda_n influencing the results. The variable may take on different values on different rounds (hence the subscript).
   
2. There are deterministic functions F_A(a, b, \lambda) and F_B(a, b, \lambda) such that A_n = F_A(a_n, b_n, \lambda_n) and B_n = F_B(a_n, b_n, \lambda_n)
3. Each round, \lambda_n is chosen randomly according to some probability distribution P(\lambda)

Those three define what Bell means by a "hidden variables theory". The special case of a "local" hidden variables theory makes the additional assumption that F_A does not depend on b and F_B does not depend on a. That is,

A_n = F_A(a_n, \lambda_n) and B_n = F_B(b_n, \lambda_n)

I should say that the above form for F_A and F_B are not the most general form compatible with local realism. More generally, the outcome A might also depend on an additional hidden variable \alpha_n that is local to Alice, and Bob's outcome B might depend on a hidden variable \beta_n that is local to Bob. But the fact that in an EPR-type experiment, there are perfect correlations at some settings implies that there can't be any dependency on additional local variables.

 

[TrickyDicky]

It isn't to me. As I said, Bell's inequalities are about a very specific situation: Alice has a device that is capable of producing a measurement result of \pm 1. The device has (at least) two possible settings, a or a'. Bob similarly has a device with two possible settings, b or b'. For many rounds, you perform the following procedure and collect statistics:

On round number n,

1. Alice chooses a setting a_n.
2. She performs a measurement, and gets a result A_n
3. Bob chooses a setting b_n.
4. Bob gets result B_n

Then we compute: E(a,b) = the average, over all rounds n such that a_n = a and b_n = b, of A_n \cdot B_n

That's the context for which Bell derived his inequality. If you allow for Alice's choice a_n to affect Bob's result, B_n, and vice-verse, then there is no reason to expect the inequality to hold. That's where locality comes in: without assuming locality, there is no reason to assume that the inequality holds. Locality in the context of Bell's theorem means a very specific thing: that Alice's choice cannot affect Bob's result, and vice-verse. So your musings about whether congruence of geometric figures is local or nonlocal don't seem to be related to Bell's notion of locality.

Bell defined a hidden variables theory to be an explanation of the correlations along the following lines:

1. Each round, there is a hidden variable \lambda_n influencing the results. The variable may take on different values on different rounds (hence the subscript).
   
2. There are deterministic functions F_A(a, b, \lambda) and F_B(a, b, \lambda) such that A_n = F_A(a_n, b_n, \lambda_n) and B_n = F_B(a_n, b_n, \lambda_n)
3. Each round, \lambda_n is chosen randomly according to some probability distribution P(\lambda)

Those three define what Bell means by a "hidden variables theory". The special case of a "local" hidden variables theory makes the additional assumption that F_A does not depend on b and F_B does not depend on a. That is,

A_n = F_A(a_n, \lambda_n) and B_n = F_B(b_n, \lambda_n)

That's the critical assumption that allows him to derive his inequality. Right off the bat, I don't see how his derivation has anything to do with whether a and b are described by a commutative or noncommutative algebra.

Now, what someone has shown is that QM only predicts a violation of Bell's inequality in the case where the two measurements corresponding to Alice's settings a and a' are described by noncommuting operators, and the two measurements corresponding to Bob's settings b and b' are described by noncommuting operators. But that's a fact about quantum mechanics. Bell's derivation doesn't (as far as I can see) assume anything at all about whether things commute or not. The noncommutativity is about the two choices that Alice (or Bob) might make, not about Alice's measurements versus Bob's. Alice's measurements do commute with Bob's measurements.

Is F_A× F_B the same as F_B× F_A for the inequalities ?

 

[stevendaryl]

Is F_A× F_B the same as F_B× F_A for the inequalities ?

Yes, because they are real numbers, not operators.

 

[TrickyDicky]

Yes, because they are real numbers, not operators.

Got it, thanks!

 

[Pat71]

No, it counters Popper's original claim that QM's indeterminacy(HUP) was falsified by a certain outcome of his thought experiment. Both Shih's 1999 and more recent 2015(see http://phys.org/news/2015-01-popper-againbut.html) papers agreed on this too.

Interesting...observations suggesting nonlocal interference between randomly paired - i.e. not pre-entangled - photons??

 

[Derek Potter]

Do you understand the experiment, Pat? I can't make sense of the article.

 

[morrobay]

It isn't to me. As I said, Bell's inequalities are about a very specific situation: Alice has a device that is capable of producing a measurement result of \pm 1. The device has (at least) two possible settings, a or a'. Bob similarly has a device with two possible settings, b or b'. For many rounds, you perform the following procedure and collect statistics:

On round number n,

1. Alice chooses a setting a_n.
2. She performs a measurement, and gets a result A_n
3. Bob chooses a setting b_n.
4. Bob gets result B_n

Then we compute: E(a,b) = the average, over all rounds n such that a_n = a and b_n = b, of A_n \cdot B_n

That's the context for which Bell derived his inequality.

Those three define what Bell means by a "hidden variables theory". The special case of a "local" hidden variables theory makes the additional assumption that F_A does not depend on b and F_B does not depend on a. That is,

A_n = F_A(a_n, \lambda_n) and B_n = F_B(b_n, \lambda_n)

That's the critical assumption that allows him to derive his inequality.

In summery then the above applies to this inequality : (AB) + (AB') + (A'B) - (A'B') ≤ 2
where A,A',B,B' = ± 1
With assumptions that p (a,b) depend only on past variable λ and local measurements at x and y
p(ab|xy,λ) = p(a|x,λ) p(b|y,λ)

 

[Pat71]

Do you understand the experiment, Pat? I can't make sense of the article.

If you can't, Derek, I don't think there's much chance I can!

It does say:

"The randomly paired photons do not have any pre-prepared entanglement, which means they are considered to be a classical system. This raises the question, how could a classical system produce the same result as a quantum system?"

"...The observations suggest that the photon pair is interfering with itself instantaneously in a phenomenon called nonlocal interference. In the new experiment, the randomly paired photons have two different yet indistinguishable properties to be simultaneously annihilated at two distant photodetectors. The observations are the result of the superposition of these two probability amplitudes."


Quote from the abstract of the paper itself (I can't access the full text without buying it):

"Although the observation cannot be considered as a violation of the uncertainty relation as Popper believed, this experiment reveals a concern about nonlocal interference of a random photon pair, which involves the superposition of multi-photon amplitudes, and multi-photon detection events at a distance."

 

[TrickyDicky]

That's where locality comes in: without assuming locality, there is no reason to assume that the inequality holds. Locality in the context of Bell's theorem means a very specific thing: that Alice's choice cannot affect Bob's result, and vice-verse. So your musings about whether congruence of geometric figures is local or nonlocal don't seem to be related to Bell's notion of locality.Those three define what Bell means by a "hidden variables theory". The special case of a "local" hidden variables theory makes the additional assumption that F_A does not depend on b and F_B does not depend on a. That is,

A_n = F_A(a_n, \lambda_n) and B_n = F_B(b_n, \lambda_n)

That's the critical assumption that allows him to derive his inequality. Right off the bat, I don't see how his derivation has anything to do with whether a and b are described by a commutative or noncommutative algebra.

I still see something confusing about what it implies to assume locality, if we agree on defining locality for two spacelike separated subsystems as the absence of influence of measurement of one subsystem on the other, I'm not sure how the expression above exhausts this definition.
It is obvious that assuming that F_A does not depend on b and F_B does not depend on a assures us locality, but that is not the same as saying that assumptions that violate it are automatically not obeying the locality principle, because there might be ways to assure locality independent of that assumption that we are not aware of.

In other words to say that a theory is local only if and only if it assumes the inequalities is a very strong assertion and assumes that any correlated measurement of spatially separated systems implies instantaneous influence of measurements.

Is there any logical obstruction to the possibility that there are conditions independent from A_n = F_A(a_n, \lambda_n) and B_n = F_B(b_n, \lambda_n)
that are compatible with locality? The fact that no one has come up with them shouldn't be a definitive impediment. In general in science statistical correlation does not necessarily imply direct influence, why should it be so in physics?

Now, what someone has shown is that QM only predicts a violation of Bell's inequality in the case where the two measurements corresponding to Alice's settings a and a' are described by noncommuting operators, and the two measurements corresponding to Bob's settings b and b' are described by noncommuting operators. But that's a fact about quantum mechanics. Bell's derivation doesn't (as far as I can see) assume anything at all about whether things commute or not. The noncommutativity is about the two choices that Alice (or Bob) might make, not about Alice's measurements versus Bob's. Alice's measurements do commute with Bob's measurements.

The experiments usually have the measurements being simultaneous so Alice's measurements versus Bob's commutativity is not what matters here. The commutativity (or lack of) is indeed about the choice(the angles) that Alice and Bob make, i.e, the measurements each one of them performs, in the inequalities the choices must commute . Why should all theories obeying locality (absence of influence at a distance) have this feature about the choice a and a'? Are all possible theories describing the measurements settings with operators automatically incompatible with absence of instantaneous influences?

 

[stevendaryl]

In other words to say that a theory is local only if and only if it assumes the inequalities is a very strong assertion and assumes that any correlated measurement of spatially separated systems implies instantaneous influence of measurements.

No, it absolutely does not assume that. That was the whole point of the inequality, was to distinguish nonlocality from mere correlation.

For example, suppose that you have a process that takes a pair of shoes and randomly selects one shoe out of a pair to send to Alice and the other one to send to Bob. When Alice sees that she has a left shoe, she immediately knows that Bob received a right shoe, and vice-verse. So the observations made by Alice and Bob are perfectly correlated. But that correlation does not imply that FTL signals go from Alice to Bob or vice-verse.

The whole point of Bell's inequality was to be able to distinguish between correlations that (classically) require distant influences from those that do not.

 

[stevendaryl]

No, it absolutely does not assume that. That was the whole point of the inequality, was to distinguish nonlocality from mere correlation.

For example, suppose that you have a process that takes a pair of shoes and randomly selects one shoe out of a pair to send to Alice and the other one to send to Bob. When Alice sees that she has a left shoe, she immediately knows that Bob received a right shoe, and vice-verse. So the observations made by Alice and Bob are perfectly correlated. But that correlation does not imply that FTL signals go from Alice to Bob or vice-verse.

The whole point of Bell's inequality was to be able to distinguish between correlations that (classically) require distant influences from those that do not.

Bell absolutely does not assume that correlation implies a causal influence. What he does assume is that correlation between two measurements implies something about their common past. Actually, it's not so much that he assumes that, but that it's part of what he means by a "hidden variable theory". The whole point of a hidden variable theory is to explain correlations by invoking a shared variable whose value was determined in their shared past (the overlap of their past light-cones, according to SR causality).

Let me try another way to describe it, in terms of flow of information. Roughly speaking, information is knowing the answer (or probabilities for possible answers) to some question about the history of the universe. Bell's concept of "local realism" basically amounts to the assumption that information about the history of the universe propagates at the speed of light (or slower). If information is available in some localized region of space, then that information must either have been created there, or it must have propagated there from some source in the backwards lightcone. If Alice at time t+\delta knows something (say, about Bob's measurement results), then that information in principle follows from

1. Information that was already available to Alice at time t
   
2. Information that came into existence in the region near Alice (a distance of less than or equal to c \delta from her)
3. Information that flowed into that region from elsewhere.

When I say information that was already available at time t, I mean information that could be deduced, in principle, from detailed knowledge of the little region near Alice. Classically, that would mean that the information is deducible from the positions and momenta of the particles near Alice, as well as the values of fields in that region. Similarly, "information that flowed into that region from elsewhere" classically would mean either particles that flowed into the region, or energy/momentum that flowed into the region, or waves that propagated into that region. When I say "information that came into existence", that is allowing for intrinsic nondeterminism. If I flip a coin and the coin is intrinsically nondeterministic, then the result is new information that didn't exist prior to flipping the coin.

Quantum mechanics seems to violate this concept of information as being created locally and flowing at the speed of light or slower.

 

[TrickyDicky]

No, it absolutely does not assume that. That was the whole point of the inequality, was to distinguish nonlocality from mere correlation.

For example, suppose that you have a process that takes a pair of shoes and randomly selects one shoe out of a pair to send to Alice and the other one to send to Bob. When Alice sees that she has a left shoe, she immediately knows that Bob received a right shoe, and vice-verse. So the observations made by Alice and Bob are perfectly correlated. But that correlation does not imply that FTL signals go from Alice to Bob or vice-verse.

The whole point of Bell's inequality was to be able to distinguish between correlations that (classically) require distant influences from those that do not.

But your example doesn't violate the inequalities, and for that case I said they are fine, they discern correlation from action at a distance, the problem is in assuming that there is not locality from violation of the inequalities.

 

[TrickyDicky]

Bell absolutely does not assume that correlation implies a causal influence. What he does assume is that correlation between two measurements implies something about their common past. Actually, it's not so much that he assumes that, but that it's part of what he means by a "hidden variable theory". The whole point of a hidden variable theory is to explain correlations by invoking a shared variable whose value was determined in their shared past (the overlap of their past light-cones, according to SR causality).

Let me try another way to describe it, in terms of flow of information. Roughly speaking, information is knowing the answer (or probabilities for possible answers) to some question about the history of the universe. Bell's concept of "local realism" basically amounts to the assumption that information about the history of the universe propagates at the speed of light (or slower). If information is available in some localized region of space, then that information must either have been created there, or it must have propagated there from some source in the backwards lightcone. If Alice at time t+\delta knows
something (say, about Bob's measurement
results), then that information in principlefollows from Information that was already available to Alice at time t

1. Information that came into existence in the region near Alice (a distance of less than or equal to c \delta from her)
2. Information that flowed into that region from elsewhere.

When I say information that was already available at time t, I mean information that could be deduced, in principle, from detailed knowledge of the little region near Alice. Classically, that would mean that the information is deducible from the positions and momenta of the particles near Alice, as well as the values of fields in that region. Similarly, "information that flowed into that region from elsewhere" classically would mean either particles that flowed into the region, or energy/momentum that flowed into the region, or waves that propagated into that region. When I say "information that came into existence", that is allowing for intrinsic nondeterminism. If I flip a coin and the coin is intrinsically nondeterministic, then the result is new information that didn't exist prior to flipping the coin.

Quantum mechanics seems to violate this concept of information as being created locally and flowing at the speed of light or slower.

You are apparently talking about determinism rather than about locality.
Does a non-deterministic theory(I don't mean non-determinism only in the stochastic or probabilistic sense that you use in your post, I mean for instance in the nonlinear sense) by definition violate the inequalities?

 

[stevendaryl]

You are apparently talking about determinism rather than about locality.

No, I'm not. Determinism, in the context of information, would mean that information never increases. So the answers to any question is already present in the initial conditions of the universe. But if there is nondeterminism, information can be created. For example, if flipping a coin is nondeterministic, then the information about what the result of a coin flip will be doesn't exist until the moment the coin is flipped.

Does a non-deterministic theory(I don't mean non-determinism in the stochastic or probabilistic sense that you use in your post, I mean for instance in the nonlinear sense) by definition violate the inequalities?

I don't know what you mean by "in the nonlinear sense". I use nondeterminism to mean that the state of the universe at a future time is not uniquely determined by the state at earlier times.

 

[TrickyDicky]

No, I'm not. Determinism, in the context of information, would mean that information never increases. So the answers to any question is already present in the initial conditions of the universe. But if there is nondeterminism, information can be created. For example, if flipping a coin is nondeterministic, then the information about what the result of a coin flip will be doesn't exist until the moment the coin is flipped.
I don't know what you mean by "in the nonlinear sense". I use nondeterminism to mean that the state of the universe at a future time is not uniquely determined by the state at earlier times.

But you surely muat have heard about nonlinear equations not being deterministic? There is more to non-determinism than the coin flip probabilistic concept.

 

[stevendaryl]

But you surely muat have heard about nonlinear equations not being deterministic? There is more to non-determinism than the coin flip probabilistic concept.

No, I don't know what you mean by that. Why would a nonlinear equation be nondeterministic? Are you talking about chaos?

 

[Derek Potter]

But you surely muat have heard about nonlinear equations not being deterministic? There is more to non-determinism than the coin flip probabilistic concept.

I'm sure stevendaryl will have heard of it, but others here, like me for instance, may not. In fact I wouldn't be at all surprised if some people are wondering whether you're confusing non-computability with indeterminacy.

 

[TrickyDicky]

No, I don't know what you mean by that. Why would a nonlinear equation be nondeterministic? Are you talking about chaos?

Well, for example, I know they are considered deterministic traditionally but they aren't precisely in the increase of information sense you mentioned above.

 

[stevendaryl]

Well, for example, I know they are considered deterministic traditionally but they aren't precisely in the increase of information sense you mentioned above.

If you are talking about chaotic systems, then they are still deterministic. The information about future conditions is present in the initial conditions, it's just computationally infeasible to extract it.