Binney's interpretation of Violation of Bell Inequalities

[stevendaryl]

stevendaryl, your description seems to imply the common misconception of thinking "mixed" vs "pure" is a system observable.

I didn't mean to imply that. I'm just saying that they are treated differently by the formalism of quantum mechanics, and that they mean different things. It's a separate question as to how (and if) the difference shows up in experiments.

What we mean by Entanglement of a composite pair is two things which are mutually compatible. One: all pairs of measurements on the two factor systems are correlated (in the general sense of correlated or anti-correlated outcomes) and Two: There is a specific composite measurement of the whole system which we have observed and which does not decompose into a product of two factor measurements.

I'll have to think about that purely observational definition of entanglement.

 

[Derek Potter]

Derek, I assert that in this setting the many worlds interp (and any ontological interp) is analogous with a "aether" explanation of special relativity (thence taking away the relativity part but keeping the predictions).

I did not say "interpretation". I said "model". That was quite deliberate. The claim that I was replying to was Dr Chinese's "How can you explain perfect correlation at any angle setting in this situation without invoking quantum non-locality?". An MW model does this.

The rest of your reply - about incorporating fundamentally unobservable elements - does not apply to MW as it has no such elements. The "other worlds" are not incorporated into the model but are emergent on unitary evolution. But even if you represented MW correctly it would be off-topic since ontological interpretation of MW has nothing to do with whether perfect correlation can be explained locally in the model.

 

[Derek Potter]

Binney's error is to think the issue is about directions vs hemispheres.

His error is to think that because hemispheres can create some correlation locally that he has thereby explained quantum correlation locally! "Binney correlation" is not quantum. It is, in fact, the best possible correlation under local realism but it still doesn't violate the Bell Inequality. See my reply to pat71, post #25 this thread.

 

[zonde]

But at least he has no error in this:

Nonlocality is not even entertained as a possibility!

 

[Pat71]

Yes, that's a nice experiment.
However, I don't think Binney would have the slightest difficulty with it. In Binney's world, a cos^2 rule can be derived from the overlap of two hemispheres. So presumably Binney would consider the Bell states to be like red/green and yellow/blue pairs, perfectly correlated - Alice just inspects the colours she has and deduces the other two. [/QUOTE]

Well, if he faced up to what seems to be the inevitable "un-locally real" reality that's demonstrated by the violation of Bell inequalities he would have difficulties. It's eccentric enough to think that the overlap of two hemispheres might provide a loophole, but to actually derive a cos^2 rule from it...?
Anyway, how do you think Binney's world deals with the experiment I linked to before, in which the quantum state of a photon is teleported to a crystal over a long distance?

Here's an article on it: phys.org/news/2014-09-quantum-teleportation.html

"Passing from light into matter, using teleportation of a photon to a crystal, shows that, in quantum physics, it is not the composition of a particle which is important, but rather its state, since this can exist and persist outside such extreme differences as those which distinguish light from matter."

"...As Felix Bussieres, the lead author of this publication explains, one observes 'that the quantum state of the two elements of light, these two entangled photons which are like two Siamese twins, is a channel that empowers the teleportation from light into matter.' From there, it is a small step to conclude that, in quantum physics, the state takes precedence over the 'vehicle' - in other words an item's quantum properties transcend classical physical properties. A step that maybe one can now take."

 

[Derek Potter]

in other words"

Three little words that mean so little.

in other words an item's quantum properties transcend classical physical properties. A step that maybe one can now take."

I don't think it would ever have occurred to me that QM didn't transcend classical, but I guess some people will always be trying to square the circle.

It's eccentric enough to think that the overlap of two hemispheres might provide a loophole, but to actually derive a cos^2 rule from it...?

Speculation about unobservable properties such as Binney's state of mind is metaphysics, not science, and against forum rules.

Anyway, how do you think Binney's world deals with the experiment I linked to before, in which the quantum state of a photon is teleported to a crystal over a long distance?

Oh that's simple enough. "This is left as an exercise for the reader. It follows from the same kind of argument as the overlapping hemispheres."

Think we've had enough of Binney yet?

 

[zonde]

Anyway, how do you think Binney's world deals with the experiment I linked to before, in which the quantum state of a photon is teleported to a crystal over a long distance?

Here's an article on it: phys.org/news/2014-09-quantum-teleportation.html

"Passing from light into matter, using teleportation of a photon to a crystal, shows that, in quantum physics, it is not the composition of a particle which is important, but rather its state, since this can exist and persist outside such extreme differences as those which distinguish light from matter."

"...As Felix Bussieres, the lead author of this publication explains, one observes 'that the quantum state of the two elements of light, these two entangled photons which are like two Siamese twins, is a channel that empowers the teleportation from light into matter.' From there, it is a small step to conclude that, in quantum physics, the state takes precedence over the 'vehicle' - in other words an item's quantum properties transcend classical physical properties. A step that maybe one can now take."

This experiment does not demonstrate any non-locality. Pay attention that teleportation is heralded by joint measurement of photon who's state is to be teleported and one photon from entangled pair. So even in theoretically perfect experiment you throw out half of the attempts in "teleportation". So basically you just decide in which attempts information is aligned as you want and in which it is not (and dump these attempts).

And without teleportation part that comment you put in bold looses any meaning.

 

[atyy]

I don't think it would ever have occurred to me that QM didn't transcend classical, but I guess some people will always be trying to square the circle.

Quite an exact use of the idiom!

As one can see in Fig 1 of http://arxiv.org/abs/1107.5849, the quantum state space is a circle, while the classical one is something with sharp edges, like a triangle or a square.

 

[TrickyDicky]

So is it agreed that what violates Bell's inequalities is the change in measurement angle, and if so aren't the violations at any angle explained simply by the non-commuting of operators in QM, so that the correlations are attributed to change of angle of measurement subject to an observable with only two discrete possible outcomes correlated by the quantum non-commutation?
Compare with the absence of correlation for entangled particles in Popper's experiment http://en.wikipedia.org/wiki/Popper's_experiment when the observable is continuous

 

[Pat71]

This experiment does not demonstrate any non-locality.

I wasn't suggesting it did. I was thinking about Binney's claim that " 'entangled' is just quantum jargon for 'correlated.'"

 

[TrickyDicky]

The way I see it the issue is just one of using different algebras, Bell inequalities assume classical commutative algebra while quantum algebra is non-commutative and therefore it should not be surprising to find the inequalities violated when performing quantum experiments that are set up precisely to easily show the working of non-commutative algebra between non-commuting operators like spin and angle(position along the unit circle) for different angles or non-commutativity of angular momentum operators , namely those experiments involving two only possible discrete outcomes for the measured observable, like spin or polarization. Why people turns an algebraic issue into spooky action at a distance when trying to explain why the algebraic correlation between entangled particles is not determined from the start when that fact is explained by the algebra is really beyond me. More so when it is admitted by everyone that the case not involving non-commuting relation between operators- i.e. measuring only in an axis- is compatible with the correlation being fixed at the outset.
It is simply the algebra of quantum indeterminacy (HUP) and it is totally unrelated with action at a distance(again, see Popper's experiment where a continuos observable prevents us from exhibiting clearly the quantum algebra and no "at a distance" correlation is observed).

 

[zonde]

I wasn't suggesting it did. I was thinking about Binney's claim that " 'entangled' is just quantum jargon for 'correlated.'"

In that case I would suggest to stick with Bell theorem. It is specifically aimed at showing incompatibility between quantum entanglement and Binney's type classical correlation.

 

[stevendaryl]

The way I see it the issue is just one of using different algebras, Bell inequalities assume classical commutative algebra while quantum algebra is non-commutative and therefore it should not be surprising to find the inequalities violated when performing quantum experiments that are set up precisely to easily show the working of non-commutative algebra between non-commuting operators like spin and angle(position along the unit circle) for different angles or non-commutativity of angular momentum operators , namely those experiments involving two only possible discrete outcomes for the measured observable, like spin or polarization. Why people turns an algebraic issue into spooky action at a distance when trying to explain why the algebraic correlation between entangled particles is not determined from the start when that fact is explained by the algebra is really beyond me. More so when it is admitted by everyone that the case not involving non-commuting relation between operators- i.e. measuring only in an axis- is compatible with the correlation being fixed at the outset.
It is simply the algebra of quantum indeterminacy (HUP) and it is totally unrelated with action at a distance(again, see Popper's experiment where a continuos observable prevents us from exhibiting clearly the quantum algebra and no "at a distance" correlation is observed).

Well, there certainly is no consensus that violations of Bell's inequalities imply action at a distance, but I don't think that saying "quantum algebra is noncommutative" resolves the matter. Yes, there is a sense in which the violations follow from the noncommutativity of quantum observables, but the issue is what kind of reality can produce that kind of behavior.

Bell's starting point is the assumption that there is such a thing as "the state of the universe at a particular time", whether or not we have complete knowledge of that state. That seems like an innocuous enough assumption, independent of the details of our physical theories. But that assumption, together with the predictions of quantum mechanics for EPR type experiments lead to the conclusion that there are nonlocal interactions connecting distant parts of the universe.

Of course, it's not necessary to assume that there is such a thing as the state of the universe at a moment in time. For the purpose of performing experiments, it's enough to have a calculus of observations: If I observe $X$ at time $t_1$, what's the probability of observing $Y$ at time $t_2$? That way of characterizing questions of physics, purely in terms of observations, avoids the question of what the universe is doing when nobody's looking at it.

 

[stevendaryl]

In that case I would suggest to stick with Bell theorem. It is specifically aimed at showing incompatibility between quantum entanglement and Binney's type classical correlation.

Right. It seems to me that Binney's model is exactly the one considered by Bell in his "toy model" for explaining EPR correlations (described in Bell's book "Speakable and Unspeakable in Quantum Mechanics"). In Bell's toy model, he assumes that spin-1/2 particles have an intrinsic spin axis $\vec{S}$, and that measurements of spin along an axis $\vec{a}$ results in "spin-up" if $\vec{S} \cdot \vec{a} > 0$ and "spin-down" otherwise. Specifying a spin axis is exactly the same as specifying a hemisphere, and the result can be described as "spin-up" if $\vec{a}$ is in this hemisphere, and spin-down otherwise. This can be mathematically described as a spin function $A(\vec{a}, \vec{S}) = sign(\vec{a} \cdot \vec{S})$ relating a measuring device setting $\vec{a}$ and a "hidden variable" $\vec{S}$. Bell's inequality shows that no such spin function can reproduce the predictions of quantum mechanics. So it seems to me that Bell explicitly refutes Binney's model.

 

[DrChinese]

However, I don't think Binney would have the slightest difficulty with it. In Binney's world, a cos^2 rule can be derived from the overlap of two hemispheres. So presumably Binney would consider the Bell states to be like red/green and yellow/blue pairs, perfectly correlated - Alice just inspects the colours she has and deduces the other two.

Of course, we all agree that none of this is actually Binney's words or thinking.

But it is no easy matter (I would say impossible) to explain how 2 photons - never in contact - could be described by any local causal model AND could exhibit perfect correlation at ANY angle selected by me. Only 2 entangled photons will exhibit this behavior. And how would you entangle 2 photons via a local mechanism which are never in causal contact?

So no, hand-waving by Binney (or anyone) will not work here.

 

[TrickyDicky]

Bell's starting point is the assumption that there is such a thing as "the state of the universe at a particular time", whether or not we have complete knowledge of that state. That seems like an innocuous enough assumption, independent of the details of our physical theories.

That assumption is anything but innocuous or innocent, that assumption about what is not observable is developed mathematically as QM first postulate and all the Hilbertian formalism derived from it, and yet nobody looks in that direction, it is much safer to play with ftl and spooky actions I guess.

 

[stevendaryl]

That assumption is anything but innocuous or innocent, that assumption about what is not observable is developed mathematically as QM first postulate and all the Hilbertian formalism derived from it, and yet nobody looks in that direction, it is much safer to play with ftl and spooky actions I guess.

I don't understand what you're talking about. What do you mean, nobody looks in what direction? What direction are you talking about, and what purpose are you talking about looking in it?

 

[TrickyDicky]

I don't understand what you're talking about. What do you mean, nobody looks in what direction? What direction are you talking about, and what purpose are you talking about looking in it?

I was quite clear, the direction of alternatives to the "innocuous" assumption. And when I say nobody I mean very few people, at least within what is considered mainstream in physics foundations research.

 

[stevendaryl]

I was quite clear, the direction of alternatives to the "innocuous" assumption.

By some definition of "clear", it wasn't clear, because I have no idea what you are saying. Alternatives in what sense?

Bell describes a class of theories that are sometimes called "local realistic theories". He proves that no such theory can reproduce the predictions of quantum mechanics. So that's where "locality" comes in, via the notion of a local realistic theory. A nonlocal theory, such as Bohm's, can reproduce the predictions of quantum mechanics.

So what are you looking for an alternative to?

 

[ddd123]

I was quite clear, the direction of alternatives to the "innocuous" assumption. And when I say nobody I mean very few people, at least within what is considered mainstream in physics foundations research.

It's not clear to me either, and I'm interested in all possible alternatives to explaining EPR. If anything, you're quite laconic, can you point to a paper which shares your views? Or if you really have a personal new idea, but maybe don't have enough skills to fully expand on it, at least lay down a formal pointer to your interpretation in which noncommutative algebra in some way eliminates the ftl action problem?

 

[TrickyDicky]

By some definition of "clear", it wasn't clear, because I have no idea what you are saying. Alternatives in what sense?
Bell describes a class of theories that are sometimes called "local realistic theories". He proves that no such theory can reproduce the predictions of quantum mechanics. So that's where "locality" comes in, via the notion of a local realistic theory. A nonlocal theory, such as Bohm's, can reproduce the predictions of quantum mechanics.
So what are you looking for an alternative to?

I'm not looking for any alternative, just reacting to what you said.
You wrote: "Bell's starting point is the assumption that there is such a thing as "the state of the universe at a particular time", whether or not we have complete knowledge of that state. That seems like an innocuous enough assumption, independent of the details of our physical theories." And that:"that assumption, together with the predictions of quantum mechanics for EPR type experiments lead to the conclusion that there are nonlocal interactions connecting distant parts of the universe"
What I'm saying is that the way that assumption is formalized is the formalism of QM so the assumption is not independent of the details of our physical theories, and you are describing Bell's theorem above with that assumption.
I showed in #46 that abstracting from that assumption one can explain operationally the results of those experiments just using the non-commutative algebra of QM. Not having anything to do with locality or causality or realism so completely compatible with Bell's theorem math. You can say it is not a complete picture because it doesn't say what the universe is doing when we are not looking and I think it is a fair criticism

 

[zonde]

But it is no easy matter (I would say impossible) to explain how 2 photons - never in contact - could be described by any local causal model AND could exhibit perfect correlation at ANY angle selected by me. Only 2 entangled photons will exhibit this behavior. And how would you entangle 2 photons via a local mechanism which are never in causal contact?

So no, hand-waving by Binney (or anyone) will not work here.

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.

 

[Derek Potter]

Sure, Alice's operator and Bob's operator don't commute. That's the point. If the photons and their measurements were local, they would be independent subsystems and the operators would commute. As they don't, the measurement operators are non-local - Alice's measurerment of "her" photon indavertently projects the state of both photons

Of course, we all agree that none of this is actually Binney's words or thinking.

But it is no easy matter (I would say impossible) to explain how 2 photons - never in contact - could be described by any local causal model AND could exhibit perfect correlation at ANY angle selected by me. Only 2 entangled photons will exhibit this behavior. And how would you entangle 2 photons via a local mechanism which are never in causal contact?

So no, hand-waving by Binney (or anyone) will not work here.

Sorry to be pedantic here, but you do need to say exactly what you mean by "perfect" correlation. Very strong correlation that depends on the angle (a-b) can be generated by local hidden variables. The "best classical" law is a capital lambda shape and does not violate the Bell Inequality.

It is easily generated by a single hidden variable, the "real" orientation of the particle's spin (r). (Each detector reponds to the sign of the projection of r onto a. When the results are combined, X = sign(a-r) x sign(b-r). In this case, r serves as a shared but random variable and a lambda shaped distribution results.

Of course I know that what you really mean is quantum correlation, the perfection being perfect agreement with quantum mechanics. The quantum law is a cosine(a-b) shape and does violate the Bell inequality. So what I'm getting at is that this quantum non-locality isn't properly characterized as dependency on "any angle": the actual law must be right if it is to indicate violation.

 

[zonde]

You wrote: "Bell's starting point is the assumption that there is such a thing as "the state of the universe at a particular time", whether or not we have complete knowledge of that state. That seems like an innocuous enough assumption, independent of the details of our physical theories." And that:"that assumption, together with the predictions of quantum mechanics for EPR type experiments lead to the conclusion that there are nonlocal interactions connecting distant parts of the universe"
What I'm saying is that the way that assumption is formalized is the formalism of QM so the assumption is not independent of the details of our physical theories, and you are describing Bell's theorem above with that assumption.

This indeed is innocuous assumption. The argument is philosophical but there is not much that can be done about it as you are questioning philosophical assumption.
Practicing scientific inquiry requires that there is such a thing as "the state of knowledge at a particular time" and because our knowledge is recorded in physical matter it follows that practicing scientific inquiry requires that there is such a thing as "the state of the universe at a particular time". Do you agree?

 

[atyy]

Practicing scientific inquiry requires that there is such a thing as "the state of knowledge at a particular time" and because our knowledge is recorded in physical matter it follows that practicing scientific inquiry requires that there is such a thing as "the state of the universe at a particular time". Do you agree?

I don't agree, as that would require knowing that time is fundamental in all future scientific theories. However, locally causal theories are a significant class of theories. Indeed, it is often said that relativity is a theory of causality. Relativistic quantum theories show that that is not neccessarily the case.

 

[TrickyDicky]

This indeed is innocuous assumption. The argument is philosophical but there is not much that can be done about it as you are questioning philosophical assumption.
Practicing scientific inquiry requires that there is such a thing as "the state of knowledge at a particular time" and because our knowledge is recorded in physical matter it follows that practicing scientific inquiry requires that there is such a thing as "the state of the universe at a particular time". Do you agree?

One must define mathematically both state and particular time, this is the not innocuous part.

 

[zonde]

I don't agree, as that would require knowing that time is fundamental in all future scientific theories. However, locally causal theories are a significant class of theories. Indeed, it is often said that relativity is a theory of causality. Relativistic quantum theories show that that is not neccessarily the case.

Not sure I follow. How you can talk about future scientific theories if you don't have some idea about time that is independent from these scientific theories.

 

[TrickyDicky]

I don't agree, as that would require knowing that time is fundamental in all future scientific theories. However, locally causal theories are a significant class of theories. Indeed, it is often said that relativity is a theory of causality. Relativistic quantum theories show that that is not neccessarily the case.

Isn't QFT locally causal?

 

[stevendaryl]

I'm not looking for any alternative, just reacting to what you said.
You wrote: "Bell's starting point is the assumption that there is such a thing as "the state of the universe at a particular time", whether or not we have complete knowledge of that state. That seems like an innocuous enough assumption, independent of the details of our physical theories." And that:"that assumption, together with the predictions of quantum mechanics for EPR type experiments lead to the conclusion that there are nonlocal interactions connecting distant parts of the universe"
What I'm saying is that the way that assumption is formalized is the formalism of QM

I don't agree with that. QM is not a way of describing the state of the universe. Or at least, the claim that it describes the state of the universe is controversial. In the Many-Worlds Interpretation, the QM state is interpreted as the state of the universe. But in other interpretations, it is not considered to necessarily be an object fact about the universe.

I showed in #46 that abstracting from that assumption one can explain operationally the results of those experiments just using the non-commutative algebra of QM.

I would say that QM describes the results, but I wouldn't say that it explains them. It tells how to calculate them.

 

[TrickyDicky]

I don't agree with that. QM is not a way of describing the state of the universe. Or at least, the claim that it describes the state of the universe is controversial. In the Many-Worlds Interpretation, the QM state is interpreted as the state of the universe. But in other interpretations, it is not considered to necessarily be an object fact about the universe.

No, I was referring to defining a state of a quantum system as an element of a Hilbert space, not necessarily to the state of the universe as discussed in MW, etc.

 

[stevendaryl]

No, I was referring to defining a state of a quantum system as an element of a Hilbert space, not necessarily to the state of the universe as discussed in MW, etc.

Well, that sounds like the opposite of what you were saying. I thought you were saying that Hilbert space was the QM way of formalizing the state of the universe at a given moment.

 

[atyy]

Isn't QFT locally causal?

It depends on what one means by locally causal. In terms of the classical idea of relativity as a theory of causality, QFT is not locally causal.

 

[TrickyDicky]

Well, that sounds like the opposite of what you were saying. I thought you were saying that Hilbert space was the QM way of formalizing the state of the universe at a given moment.

Of formalizing the assumption that a system(the universe, whatever) is in a certain state at a certain time, this is QM's first postulate, and I'd say it covers the assumption you mentioned above as the starting point of Bell's theorem.

 

[TrickyDicky]

It depends on what one means by locally causal. In terms of the classical idea of relativity as a theory of causality, QFT is not locally causal.

The classical idea of SR as a theory of causality was global, not local(relativity of simultaneity), that idea must have surely been preserved in QFT?

 

[atyy]

The classical idea of SR as a theory of causality was global, not local(relativity of simultaneity), that idea must have surely been preserved in QFT?

The classical idea of causality in SR is that the causes of an event are entirely in its past light cone - that idea is not preserved in QFT. What is preserved in QFT is a weaker sense of causality - that classical information cannot be sent faster than light.