What is the concept of nonlocality in quantum mechanics?

[uzername]

I don't think it was too much of a hijack. Or if it was, it was a useful one, as it's allowed us to have been able to discard Superdeterminism as untestable, which seems to make sense. onward!

 

[DrChinese]

Okay, that post just blew my mind. I sometimes think you guys do that on purpose - provide just enough of a provocative answer to open up 10 more cans of worms. :D

"Everything might in some sense be entangled" -- that in itself is a very cool idea, and kind of where I am aiming, or where my original thoughts were directed, wondering about the extent to which that might be the case, but thinking only in terms of the electrons. Not sure what you mean by it being a "slight" effect - if it's in that state, it's in that state, right?

It takes a little time to decipher a lot of this stuff. That is why I try to aim people in a reasonable direction.

Again, you will see that the words can get in the way. If I have 2 particles in a known superposition, the entanglement effect can be substantial. But if I have 3, it is noticeably less. If I have 10^30 particles... well, I think you can see the effect is very very slight. The same thing is true of gravity. So my point is that with the words "in some sense", you could make almost anything be anything else. We don't actually know, when we look at an individual particle, if it is entangled as part of a system of 2 or more particles somewhere. We could determine such entanglement if we knew *which* other particles to look at. But except in these special setups, we have no idea where to look.

I don't know what others would say, but I would say that the quarks in a proton are in fact entangled. Anyone care to comment on that?

 

[DrChinese]

... what in "nature" entangles these particles in the first place?

That is a GREAT question.

The (sorta) answer is somewhat strange: a certain kind of ignorance leads to entanglement. If you have 2 electrons in the same ground shell of an atom, I would call these entangled. They are indistinguishable, and yet their spin must net to zero. There are 2 ways for this to occur, leading to a superposition of possible states.

Anyone care to comment? I would guess there are others who could add to this explanation.

 

[uzername]

It takes a little time to decipher a lot of this stuff. That is why I try to aim people in a reasonable direction.

Again, you will see that the words can get in the way. If I have 2 particles in a known superposition, the entanglement effect can be substantial. But if I have 3, it is noticeably less. If I have 10^30 particles... well, I think you can see the effect is very very slight. The same thing is true of gravity. So my point is that with the words "in some sense", you could make almost anything be anything else. We don't actually know, when we look at an individual particle, if it is entangled as part of a system of 2 or more particles somewhere. We could determine such entanglement if we knew *which* other particles to look at. But except in these special setups, we have no idea where to look.

I don't know what others would say, but I would say that the quarks in a proton are in fact entangled. Anyone care to comment on that?

Okay, that's very interesting. I never really thought about it in terms of multiple particles greater than two, to be honest. Only 2 particles.

So I suppose to summarize what you seem to be saying (pls. correct me if I'm wrong) is that, in practical terms, when we entangle our own particles with the laser and the crystal, etc. we know which ones we're looking at, whereas when it's just "out there," in the wide world and universe at large, 1) multiple particles could be entangled together in such great numbers that it would be totally impossible to measure the extent of the entanglement effect, because the effect would be so weak between particles, and 2) even starting with any given particle, we wouldn't know which other particle/s to look at anyway, even if we could look at particles in that "world at large" condition, which I guess is ridiculous to begin with.

So I'm also just now reading your link on Bell and EPR. I think it's making a little more sense, but every time I think I understand something, a monkey wrench seems to get thrown in at the end confusing the issue.

Briefly - again, correct me if mistaken - the general idea is that all the typical things we think of in terms of quantum physics - wave/particle duality, uncertainty principle, collapse of the wave function/schroedinger's cat, etc. -- all that is Copenhagen, and Einstein's ideas of QM are in opposition to Copenhagen?

So EPR was developed to try to refute the idea that we can't know both the speed and location at the same time, but only one or the other, and the way they proposed to do it is through a 'thought experiment' involving entanglement? We entangle some particles and then separate them, and then since they're entangled, when we look at particle 1 we automatically DO know the state of particle 2, and vice versa, so there's really no uncertainty or collapse of the wave function at all? Do I have that much right?

But I don't really understand why we need to know A, B, and C simultaneously. Isn't it enough to just know one? Or are those like the 3 axis that are the minimum required to give us all the info needed to refute the uncertainty principle?

Then finally, Bell is the refutation of EPR, so actually Copenhagen is still considered true, while EPR is therefore discredited? Or... ?

Point #2 in your explanation is what confuses me:

"Specifically, a measurement setting for one member of an entangled particle pair should not affect the results of a measurement on the other member of the pair located at a distance. Otherwise, you would have so-called "spooky action at a distance".


But I thought that *was* the case. I thought that in essence is nonlocality. I've heard this phrase, "spooky action at a distance" before, I thought it was Einstein's statement. ?

 

[DrChinese]

Then finally, Bell is the refutation of EPR, so actually Copenhagen is still considered true, while EPR is therefore discredited? Or... ?

Point #2 in your explanation is what confuses me:

"Specifically, a measurement setting for one member of an entangled particle pair should not affect the results of a measurement on the other member of the pair located at a distance. Otherwise, you would have so-called "spooky action at a distance".


But I thought that *was* the case. I thought that in essence is nonlocality. I've heard this phrase, "spooky action at a distance" before, I thought it was Einstein's statement. ?

I will comment on the rest of your post tomorrow, but wanted to pass this on now.

Yes, I consider EPR's final conclusion (or speculation or whatever you want to call it) incorrect. Bell was the one that showed why it was not correct.

Yes, "spooky action at a distance" is a reference to Einstein's aversion to quantum non-locality. It is also a way of referring to non-locality, whereas locality is an assumption of the local realistic camp (which Einstein was a member of).

 

[QuantumClue]

It takes a little time to decipher a lot of this stuff. That is why I try to aim people in a reasonable direction.

Again, you will see that the words can get in the way. If I have 2 particles in a known superposition, the entanglement effect can be substantial. But if I have 3, it is noticeably less. If I have 10^30 particles... well, I think you can see the effect is very very slight. The same thing is true of gravity. So my point is that with the words "in some sense", you could make almost anything be anything else. We don't actually know, when we look at an individual particle, if it is entangled as part of a system of 2 or more particles somewhere. We could determine such entanglement if we knew *which* other particles to look at. But except in these special setups, we have no idea where to look.

I don't know what others would say, but I would say that the quarks in a proton are in fact entangled. Anyone care to comment on that?

Hasn't the LHC just experimentally shown the entanglement of the nucleus of atoms? I don't have the news off-hand. I do remember it being presented.

 

[QuantumClue]

I don't think it was too much of a hijack. Or if it was, it was a useful one, as it's allowed us to have been able to discard Superdeterminism as untestable, which seems to make sense. onward!

But doctorn Chinese seems to haven a corrupt sense of logic. It is even to the point as resembling the camps that preserve the idea in the Copenhagen Interpretation that if you cannot see it, why worry about it? The core of the interpretation states that a thing does not exist until it is measured.

Superdeterminism is simply a world we cannot directly act on. It is a world beyond our usual four dimensional sphere. Just like dr Chinese, he refutes anything at first glance. Superdeterminism is not in any way, psuedoscientific. Or a religion, as I once recall him saying. It is itself, an interpretation of quantum mechanics, a root not only to a belief system, but also the understanding of a logic driving reality.

I speak to you so freely like this, is because I don't believe that you care much about the finer points of any mathematical theory. I feel that I might be guilty of telling you what you want to hear. I guess it does not matter, so long as I tell you it right.

 

[A. Neumaier]

Thanks, that is interesting and clarifying information.

From a lay perspective, what is confusing to me is the idea that it's "real," and yet doesn't seem to be the case in most instances. [...]
So if nonlocality is an effect or a phenomenon of particular electrons, I don't understand why it wouldn't apply to all electrons, as just a general principle of how they operate.

Allow me to explain it in terms of a parable: Nonlocality is due to entanglement. But entanglement between two electrons is a very private matter; so they are very shy about it and won't let you observe it easily. Like with shy animals in the woods, you need special preparation to observe them - get up very early in the morning before everyone else, sit silently and with very open eyes in the forest, and interpret correctly every slightest movement...

In the usual terms: There is a very powerful, almost omnipresent process called decoherence that almost instantly destroys entanglement (and hence the nonlocal features) of a system unless you carefully guard your system from interacting with anything else. But the latter is never the case in ordinary life (where interaction in the form of light is everywhere) and quite difficult to achieve in the laboratory.

The degree of difficulty can be estimated from the fact that the first experiment to convincingly demonstrate the existence of entanglement, done in 1982, earned Alain Aspect in 2010 (together with Anton Zeilinger, whom you might heard of) one of the most prestigious prizes in science, the Wolf prize http://en.wikipedia.org/wiki/Wolf_Prize_in_Physics

 

[A. Neumaier]

But given the answer that A. Neumaier gave that said nonlocality isn't really a real-world or actual thing that's happening on the everyday level, the idea that everything might actually be entangled seems to be in contradiction to that.

So if it's true that everything is 'slightly' entangled, then what in "nature" entangles these particles in the first place? Space, time or gravity acts as some kind of "prism" or crystal like the one you mentioned to entangle them? Do they go in and out of entanglement, even though Neumaier said that in the 'real world' they probably weren't entangled in the first place? I don't get all the seeming contradictions.

Nonlocality is a real-world effect but observable only under specially prepared circumstances.

Entanglement is created by a number of quantum processes, the simplest being that of light passing through a doubly refracting crystal like calcite http://en.wikipedia.org/wiki/Birefringence or a half-silvered mirror http://en.wikipedia.org/wiki/Half-silvered_mirror
which both entangles momentum and polarization of a single particle. Entanglement between two particles is commonly achieved using a process called parametric down-conversion http://en.wikipedia.org/wiki/Parametric_down-conversion

But it is destroyed by _all_ uncontrolled interactions, and the latter usually dominate.

 

[A. Neumaier]

I don't know what others would say, but I would say that the quarks in a proton are in fact entangled. Anyone care to comment on that?

Strictly speaking, yes. But due to confinement, this entanglement is both unobservable and stable under decoherence. So it is somewhat inappropriate to use the notion in this context since it only conjures misleading intuitions.

 

[A. Neumaier]

a certain kind of ignorance leads to entanglement. If you have 2 electrons in the same ground shell of an atom, I would call these entangled.

Ignorance is commonly said to lead to mixtures, not to superpositions.

On the other hand, the electrons you mention might be considered to be entangled.
But again, one wouldn't use the word since one cannot access the electrons singly.

To talk usefully about entanglement , the systems that are considered to be entangled must be distinguishable (usually, by their position or momentum). This is not the case for quarks bound in a proton, or for electrons bound in an atom.

 

[uzername]

Nonlocality is a real-world effect but observable only under specially prepared circumstances.

Okay, so that's a little bit different than implying that it basically only *happens* in a laboratory setting, and saying, "This has no consequences for most real life situations," isn't it? The mating behavior of a certain species of animal might not *ever* have been observed, but that doesn't mean those animals aren't mating, right?

Entanglement is created by a number of quantum processes, the simplest being that of light passing through a doubly refracting crystal like calcite http://en.wikipedia.org/wiki/Birefringence or a half-silvered mirror http://en.wikipedia.org/wiki/Half-silvered_mirror
which both entangles momentum and polarization of a single particle. Entanglement between two particles is commonly achieved using a process called parametric down-conversion http://en.wikipedia.org/wiki/Parametric_down-conversion

But it is destroyed by _all_ uncontrolled interactions, and the latter usually dominate.

I guess I'm still not clear about whether this a natural process, happening around us all the time, or just something we discovered we can do, which helped disprove a theory? I mean, I look out my window, and there is plenty of light out there. I have to imagine there are crystalline structures or mirror-like surfaces somewhere that could be producing entangled electrons.

I think, however, I am at least seeing that my original conception of it as being almost a given property of all electrons is not 100 percent accurate, like that there are particles "out there" somewhere that this very second are entangled with ones in our bodies, for example. Although Dr.Chinese did say it's theoretically possible that all particles are entangled, even if only perhaps weakly, so there's that.

And the comment that they're entangled through our ignorance is also very interesting. Because it almost seems to be the opposite case, in fact: if hypothetically all particles are entangled, Dr.C said that the effect presumably would be so weak that we wouldn't be able to detect it, and we also wouldn't know which particles to look at (presuming again that we could). So rather it seems to be that ignorance is what is preventing us from seeing entanglement, not producing entanglement. "Ignorance" seems rather to produce the uncertainty principle, and then when we become not "ignorant" anymore about speed or position, the uncertainty vanishes.

 

[A. Neumaier]

Okay, so that's a little bit different than implying that it basically only *happens* in a laboratory setting, and saying, "This has no consequences for most real life situations," isn't it? The mating behavior of a certain species of animal might not *ever* have been observed, but that doesn't mean those animals aren't mating, right?

I'd consider my first and my second formulation as essentially synonymous. But classical imagination for quantum situations is very limited anyway, so everyone's imagination is a bit different (and unreliable).

I guess I'm still not clear about whether this a natural process, happening around us all the time,

Decoherence happens all the time; it is something very common, leading to observable mixtures. Observable nonlocality - i.e., strange superpositions = entanglement - is something rare: you must create it on purpose, though it happens to a small extent naturally (e.g., light happening to fall through a calcite crystal).

I mean, I look out my window, and there is plenty of light out there. I have to imagine there are crystalline structures or mirror-like surfaces somewhere that could be producing entangled electrons.

No. Imagined mirrors only have an imaginary effect. Normal light is in a mixed state and has no observable entanglement. But if you happen to have a calcite crystal and look through it, some of the strange quantum things happen: We see ''double''. But to find out experimentally that this had lead to entanglement needs already care...

I think, however, I am at least seeing that my original conception of it as being almost a given property of all electrons is not 100 percent accurate, like that there are particles "out there" somewhere that this very second are entangled with ones in our bodies, for example.

All the electrons are in some sense entangled, but to turn this entanglement into measurable effects requires special preparation.

And the comment that they're entangled through our ignorance is also very interesting.

This is a misunderstanding. Ignorance doesn't change the entanglement, only whether it is perceptible. Just as walking inattentively through a forest doesn't change the mating behavior of the animals but you won't notice it.

"Ignorance" seems rather to produce the uncertainty principle, and then when we become not "ignorant" anymore about speed or position, the uncertainty vanishes.

This is another misunderstanding. One cannot become certain about every property of a quantum system.

 

[DrChinese]

Ignorance is commonly said to lead to mixtures, not to superpositions.

On the other hand, the electrons you mention might be considered to be entangled.
But again, one wouldn't use the word since one cannot access the electrons singly.

To talk usefully about entanglement , the systems that are considered to be entangled must be distinguishable (usually, by their position or momentum).

I thought it had to be an INdistinguishable set of states... i.e. HV> + VH> to me is a superposition of states. Whereas if it is either HV> OR VH> AND we simply don't know which... that is a mixed state.

I agree with you that *general* ignorance of the source may be (usually is) a mixed state. But a special kind of ignorance is that we know "something" about the source but not everything. That can lead to an entangled state, and why I qualified with the word "special".

And of course a proton contains bound quarks, so we are not going to be able to test much on those babies as you say.

 

[DrChinese]

... "Ignorance" seems rather to produce the uncertainty principle, and then when we become not "ignorant" anymore about speed or position, the uncertainty vanishes.

There is always uncertainty with respect to non-commuting observables. That is true even with entangled pairs. There is no "vanishing"!

 

[A. Neumaier]

To talk usefully about entanglement , the systems that are considered to be entangled must be distinguishable (usually, by their position or momentum). This is not the case for quarks bound in a proton, or for electrons bound in an atom.

I thought it had to be an INdistinguishable set of states... i.e. HV> + VH> to me is a superposition of states. Whereas if it is either HV> OR VH> AND we simply don't know which... that is a mixed state.

I was talking about systems, not about their state.

For example, two electrons are on the fundamental level indistinguishable; their joint wave function is proportional to |12>-|21>; no other superposition is allowed. Similarly, two photons are on the fundamental level indistinguishable; their joint wave function is proportional to |12>+|21>; no other superposition is allowed. On the other hand, a photon and an electron are intrinsically distinguishable (e.g. by their spin), and arbitrary superposition are possible.

But if, on a more practical level, you know already that (by preparation) you have two electrons or two photons, one moving to the left and one moving to the right, you can use this information to distinguish the electrons or photons; and then you can assign
separate state information to each of them, and also construct arbitrary superpositions.

I agree with you that *general* ignorance of the source may be (usually is) a mixed state. But a special kind of ignorance is that we know "something" about the source but not everything. That can lead to an entangled state, and why I qualified with the word "special".

Can you give an example so that I better understand what you mean?

 

[uzername]

There is always uncertainty with respect to non-commuting observables. That is true even with entangled pairs. There is no "vanishing"!

Doesn't the "wave function" collapse though, once you know? You've reduced the probability to either 1 or 0, right? so how is the uncertainty not vanished?

 

[DrChinese]

Doesn't the "wave function" collapse though, once you know? You've reduced the probability to either 1 or 0, right? so how is the uncertainty not vanished?

Sure it collapses, and the results give you complete certainty for at least one observable - let's say position. That makes momentum, which is non-commuting with respect to position, completely UNcertain.

 

[DrChinese]

Can you give an example so that I better understand what you mean?

Sure. If I have a system of 2 particles with total spin=0, and I don't know which is which (indistinguishable), those particles are ALWAYS spin entangled. And by the term "don't know" I mean: cannot know, in principle.

 

[DrChinese]

Sure. If I have a system of 2 particles with total spin=0, and I don't know which is which (indistinguishable), those particles are ALWAYS spin entangled. And by the term "don't know" I mean: cannot know, in principle.

And just to add to that: those 2 particles can be ANY 2 particles, existing anywhere, with any prior history, at any points in spacetime. I believe that is the rule. Strange as it may seem.

 

[A. Neumaier]

Sure. If I have a system of 2 particles with total spin=0, and I don't know which is which (indistinguishable), those particles are ALWAYS spin entangled.

It is precisely this situation that I had in mind when saying that entanglement is no longer meaningful when particles are indistinguishable. Entanglement requires a tensor product state space, while in this case, you only have the symmetric or antisymmetric part of the tensor product. The state space of indistinguishable particles is very different from that of distinguishable particles. Almost nothing of the usual theory about entanglement survives this change of basic setting.

And by the term "don't know" I mean: cannot know, in principle.

I consider something that cannot be known in principle to be meaningless, not a case for ignorance.

 

[DrChinese]

It is precisely this situation that I had in mind when saying that entanglement is no longer meaningful when particles are indistinguishable.

So I guess you are saying that 2 particles with total spin 0 are NOT entangled if they are indistinguishable. Or ? Perhaps my use of terms is different than yours? Because I have never heard it described otherwise.

 

[A. Neumaier]

So I guess you are saying that 2 particles with total spin 0 are NOT entangled if they are indistinguishable. Or ? Perhaps my use of terms is different than yours? Because I have never heard it described otherwise.

The common assumption in a formal definition of of entangled systems, here quoted from http://en.wikipedia.org/wiki/Entangled_state , is: ''The Hilbert space of the composite system is the tensor product''.

This is violated for indistinguishable bosons or fermions, where the Hilbert space of the composite system is the symmetrized and antisymmetrized tensor product, respectively.

Of course, many people use the term without referring to a precise definition of the context in which it makes sense. And commonly there is a lot of imprecision in working with indistinguishable particles outside of quantum field theory!

But I like to have precise concepts determined by the usefulness of what is defined.

 

[uzername]

Sure it collapses, and the results give you complete certainty for at least one observable - let's say position. That makes momentum, which is non-commuting with respect to position, completely UNcertain.

Yes - I meant only one observable. If we claimed to know them all, is that the same or related concept as hidden variables?

 

[DrChinese]

...Of course, many people use the term without referring to a precise definition of the context in which it makes sense. And commonly there is a lot of imprecision in working with indistinguishable particles outside of quantum field theory!

But I like to have precise concepts determined by the usefulness of what is defined.

Me being one of the guilty!

Thanks for clarifying.