Exploring Quantum Entanglement: An Online Journey

[QuantumPhys]

What is Quantum Entanglement, and what does it do?

I attempted at learning via online articles.

 

[jedishrfu]

Read about it here:

http://en.wikipedia.org/wiki/Quantum_entanglement

then ask some questions.

 

[micromass]

What about this:

 

[Drakkith]

PF isn't a good place to learn about the general overview of a subject since it's a forum. The best thing would be to look at wikipedia, other online articles, or get some books on the subject. Then if you have specific questions about something you can ask.

 

[BiGyElLoWhAt]

Hmmm... this seems like a good place to ask this question:

I was working with QE for a short period of time, but I never understood it. I also got what seems like different "definitions" of it.

Some things I read made it seem like QE behaved like such: 2 entangled particles -> you measure 1 -> that actually alters the state of the other.

Other places make it sound like this: 2 entangled particles -> you measure 1 -> the only noticible effect on the second is a collapsed wave function.

Are either of these good ways to look at QE?

 

[Nugatory]

I also got what seems like different "definitions" of it.

Some things I read made it seem like QE behaved like such: 2 entangled particles -> you measure 1 -> that actually alters the state of the other.

Other places make it sound like this: 2 entangled particles -> you measure 1 -> the only noticible effect on the second is a collapsed wave function.

Neither "behaves like" nor "sounds like" means "is", so those are descriptions not definitions.

Both also contain an hidden assumption, namely that it makes sense to talk about the setup as if it contains two particles. That's a good way of interpreting the results that come out when you crank up the computational machinery of QM, but it's not a good way of understanding what that machinery is doing.

The wikipedia definition, that "the quantum state of each particle cannot be described independently – instead, a quantum state may be given for the system as a whole" is actually not half-bad, although I would substitute "must" for "may".

 

[BiGyElLoWhAt]

Hmmm... that sounds suspiciously close to my second 'interpretation'.

I was using the term definition a little loosely, I've read entanglement, along with various articles (scholarly and non) on the subject, but I never seem to get anything solid.

I have to ask this now: If the second description above is legit, where is this 'spooky action at a distance'? Of course, assuming that the 2 engangled whatever's preserve their entanglement.

 

[bhobba]

Entanglement is simply a consequence of the vector space structure of pure states.

Suppose you have two systems both of which can be in state |a> and state |b>.

If system 1 is in state |a> and system 2 in state |b> we write it as |a>|b>. Conversely, if system 1 is in state |b> and system 2 in state |a> we write this as |b>|a>. But since pure states form a vector space it can be in a superposition of those two combined states such as 1/root 2 (|a>|b> + |b>|a>). This means the state of one system depends on the state of the other in a peculiar non classical way.

The great physicist, Bell, used an amusing analogy of Bertlmann's socks to help explain it:
http://cds.cern.ch/record/142461/files/198009299.pdf

In fact its a very deep phenomena lying right at the foundations of QM.
http://arxiv.org/abs/0911.0695

Thanks
Bill

 

[bhobba]

where is this 'spooky action at a distance'?

If such exists depends entirely on your conception of locality.

Locality in QM really is expressed by the so called cluster decomposition property:
https://www.physicsforums.com/showthread.php?t=547574

That, however, only applies to uncorrelated systems. Entangled systems are correlated so the principle doesn't apply.

Using Bell's Bertlmann's socks analogy, if you know one sock and the other sock is at the other side of the galaxy the fact it tells you about it is a very interesting thing, but may or may not be the result of some instantaneous communication between the socks depending on how you look at it.

One way for example is to look at it is via the Consistent Histories approach:
http://quantum.phys.cmu.edu/CQT/index.html

See Chapter 24 for its relevance to entanglement and locality.

Just as an aside, it's really great Griffiths has made that book freely available online because its a very good source of exactly what the issues at the foundations of QM really are, not the half garbled mumbo jumbo you get in the populist press. I really like the Consistent Histories view, but personally I find it a bit more complicated than is really required and hold to the ignorance ensemble interpretation - but that is just by the by.

Then you have guys like Stapp that criticize Griffith's:
http://arxiv.org/ftp/arxiv/papers/1111/1111.5364.pdf

I am not with Stapp in other parts of his view of QM that involves the conscious observer, which I believe is a crock of the proverbial, but on this issue I agree - correlated QM systems break locality.

However that's just me - become acquainted with the issues and make up your own mind.

Thanks
Bill

 

[BiGyElLoWhAt]

So I haven't made it very far into that paper yet, but does the "spooky action at a distance" come from the denial of the assertion that nothing 'exists' in the quantum world in advance of measurement? Am I reading this right?

In order for me to say that there IS spooky action at a distance (in the context of EPR), must I first say that nothing is definite in the quantum world before measurement, but, once measured, the object in question is forced into a state; then must I extend this assertion to not only does my measurement force the measured object into a particular state, but it also forces all entangled objects into some (probably, but not necessarily, different) state? But not in the sense that we don't know what state it's in until it's measured, but that it actually doesn't exist in a particular state until measured?

 

[BiGyElLoWhAt]

If such exists depends entirely on your conception of locality.

One way for example is to look at it is via the Consistent Histories approach:
http://quantum.phys.cmu.edu/CQT/index.html

Thanks
Bill

This is the paper I was talking about, by the way.

[EDIT*]
-.-
My bad, see below...

 

[BiGyElLoWhAt]

The great physicist, Bell, used an amusing analogy of Bertlmann's socks to help explain it:
http://cds.cern.ch/record/142461/files/198009299.pdf

Thanks
Bill

OK I lied about the paper. This is the one I'm currently reading and talking about. I was reading the link in my previous post the other day and got them mixed up. Sorry about that.

 

[BiGyElLoWhAt]

Also, ever so slightly digressive, would you happen to have a link to the '25 EPR paper handy, Bill? I remember looking a while ago, but was never able to come up with one.

Even more digressively: I find it difficult to find papers available to the public (without buying a $100 membership, or the paper individually) on experiments that I'm interested in. I believe I mentioned the book Entanglement previously. The last "chapter" was on a 10km entanglement experiment using fiber optics that took place sometime in the 90's. I tried looking it up, and I found it on some science article website place, but it was on the order of $100 for the one article! Is there a good place to find scientific papers (written by the experimenters) either free or at least reasonably? I can't justify spending $100 on 1 article that I'm going to read for sh*t's and giggles and maybe work with again in 15 years (by then, presumably, I would have forgotten most of the article anyways!). It's just a little frustrating that I'm paying for a college degree in physics, and for some reason I still can't seem to get access to these files.

 

[BiGyElLoWhAt]

hahaha, ok so scratch that link request for the EPR. I seriously couldn't find it last time I looked, but I just found it on strangepaths.com

Just in case anyone's interested
http://strangepaths.com/wp-content/uploads/2008/01/epr.pdf

EDIT
Here's the main link that I found, and this looks a lot like porn for the physicist.
#I'mAboutToHaveNoLifeForALongTime
http://strangepaths.com/resources/fundamental-papers/en/

 

[atyy]

So I haven't made it very far into that paper yet, but does the "spooky action at a distance" come from the denial of the assertion that nothing 'exists' in the quantum world in advance of measurement? Am I reading this right?

In order for me to say that there IS spooky action at a distance (in the context of EPR), must I first say that nothing is definite in the quantum world before measurement, but, once measured, the object in question is forced into a state; then must I extend this assertion to not only does my measurement force the measured object into a particular state, but it also forces all entangled objects into some (probably, but not necessarily, different) state? But not in the sense that we don't know what state it's in until it's measured, but that it actually doesn't exist in a particular state until measured?

Yes, and no. Here I will take the answer that "spooky action at a distance" has nothing necessarily to do with the idea that we only get definite results when a measurement is made, and that we are agnostic about whether the wave function is real in any sense.

So I will define "spooky action at a distance" to mean that the Bell inequalities are violated. The Bell inequalities do not assume quantum mechanics. The Bell inequalities hold if special relativity holds, if two experiments are far away enough, and if a complete knowledge of variables in the causal past of each experiment is enough to determine the outcome of the joint results of the experiments. We summarize this by saying that the Bell inequalities hold if local variables describe what we observe. Notice that we did not use quantum mechanics at all in saying what the Bell inequalities mean. So we can do an experiment without knowing quantum mechanics, and if the Bell inequalities are observed to be violated, then we know that a theory that successfully describes our observations cannot contain only local variables.

Quantum mechanics is one example of a successful theory that predicts the violation of the Bell inequalities, ie. spooky action at a distance. There are two technical elements in quantum mechanics that allow it to predict the violation of the Bell inequalities (1) non-commuting variables, which basically means that there are no particles that have classical trajectories (2) entanglement, which roughly means that the superposition principle can be applied to the wave function of a system of interacting particles.

The "non-reality" problem is that in quantum mechanics, we think that the measuring apparatus should also be in principle described by quantum mechanics. And so the measuring apparatus should have a wave function. But we can also have a measuring apparatus to measure the measuring apparatus, which should have its wave function. As far as we can tell, quantum mechanics succeeds and we can give every measuring apparatus a wave function. However, we run into serious problems if we try have a wave function of the universe, which has no measuring apparatus to measure it. It is because of this serious problem, that we say that we are agnostic about the reality of the wave function. Maybe it is just a tool to calculate the results of measurements.

There are other theories that also predict the violation of the Bell inequalities, such as Bohmian mechanics. Although Bohnian mechanics has spooky action at a distance, it does not have any variables in it that don't make sense if we try to extend the theory to the whole universe. Bohmian mechanics does not require that there is a measuring apparatus sitting outside the universe. So everything in Bohmian mechanics can be taken as real. Accordingly, Bohmian mechanics is an example of a theory with spooky action at a distance, but with no "non-reality" problem. Bohmian mechanics reproduces quantum mechanics closely enough that some form of Bohmian mechanics might be useful if quantum mechanics is experimentally falsified. But till then, we user quantum mechanics, because it is generally easier to use than Bohmian mechanics.

There are other approaches to solving the "non-reality" problem. These include the Many-Worlds approach and the Consistent Histories approach. However, I think it is fair to say that there is no consensus at the moment as to whether these really work. Bohmian mechanics itself has a limitation, in that it is not known whether it can describe relativistic observations in a way that the underlying theory is also fully relativistic.

 

[BiGyElLoWhAt]

Thanks for the reply atyy, I've heard the term Bohmian mechanics before, at least I think, I might just be thinking of that queen song. I'm unfortunately unfamiliar with the concepts that it entails. I'll have to spend some time looking into it, as it sounds pretty interesting. As always, any links to resources would be greatly appreciated. I probably won't get to it anytime soon, but I'll archive it and check it out later. Links keep me from having to weed through useless information (or near useless) when trying to read about stuff.

Thanks
BYH

 

[atyy]

Thanks for the reply atyy, I've heard the term Bohmian mechanics before, at least I think, I might just be thinking of that queen song.

:rofl:

I'll have to spend some time looking into it, as it sounds pretty interesting. As always, any links to resources would be greatly appreciated. I probably won't get to it anytime soon, but I'll archive it and check it out later. Links keep me from having to weed through useless information (or near useless) when trying to read about stuff.

I like these:

General commentary:
http://arxiv.org/abs/quant-ph/0209123

Bohmian Mechanics:
http://arxiv.org/abs/quant-ph/0611032
http://arxiv.org/abs/1206.1084
http://arxiv.org/abs/quant-ph/0308039
http://arxiv.org/abs/quant-ph/0308038

Many-Worlds:
http://philsci-archive.pitt.edu/8888/1/Wallace_chapter_in_Oxford_Handbook.pdf
http://arxiv.org/abs/0906.2718

 

[BiGyElLoWhAt]

Awesome! Thanks a million everyone. =]