Quantum entanglement?

davefoc

Philosopher
davefoc
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orange country, california
I've just read the Wikipedia article and a Discover article on quantum entanglement and have read several other articles on it in my life.

I still don't quite get it.

OK, I've a two entangled things, thing 1 and thing 2. I test thing 1 and find out it's in the A state. I now know that wherever thing 2 is it will be in the B state.

OK, but what's the mystery here? Suppose thing 1 was in the A state all along and thing 2 was in the B state all along. No faster than light connection needed at all. Thing 2 was in the B state all along whenever and wherever I test it.

I have several other questions but that is the main one.

The answer seems to be that thing 1 was actually in a state that wasn't either A or B before we tested it. The state it was in was some intermediate state between A and B and only after it is tested does it become clearly in one state or the other.

OK, assuming I have gotten that right. What is the theoretical or experimental evidence that thing 1 was not actually in one state or the other and we just couldn't know it until we tested it?

ETA: I'm picturing thing 1 as a roulette wheel with recesses marked as A or B that is completely covered except for a window that allows us to see the recess where the ball is after the wheel has stopped. The wheel can only be tested once. I've got lots of these wheels and I test them like mad. Some of them come up A and some of them come up B. So one theory I have is that wheels are all the same with an equal number of A and B recesses. The other theory I have is that there are wheels with A recesses and wheels with B recesses. How do I decide what the actual case is?
 
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davefoc said:
I still don't quite get it.
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Tell me about it ... :confused:

"Pass me the gun, then show me the cat" - The Man That Shot Schroedinger's Cat (apologies to Ian M Banks)

OK, assuming I have gotten that right. What is the theoretical or experimental evidence that thing 1 was not actually in one state or the other and we just couldn't know it until we tested it?
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Bring on the cat-lovers ...
 
Hi CD,
I always enjoy seeing a post from you. I quote you (poorly I'm afraid) at times in various discussions.

My daughter is off to France and the UK with her French class today. Where do you live in the UK?

On the topic: It seems like a lot of modern physics is inaccessible to those unwilling or unable to plow through the math. But this seems like a simple enough issue that it should be understandable by the less mathematically capable amongst us. It could be one of those issues which is devilishly complicated and the writers in the popular press don't really understand it so they just put together a bunch of words that make it seem like it might be simple when it isn't. Hopefully one of JREF's resident physics geniuses will stop by to sort this out.
 
davefoc said:
OK, but what's the mystery here? Suppose thing 1 was in the A state all along and thing 2 was in the B state all along.
...
The answer seems to be that thing 1 was actually in a state that wasn't either A or B before we tested it.
Click to expand...

Indeed, that's the case. Let's look a bit at how we know this is true.

The most basic example is a spin system, where if you measure the spin along one axis, you find it's either up or down. So let's call A spin up and B spin down along the z axis. Now let's suppose that particle 1 is in state A and particle 2 is in state B. We measure the spin along the z axis, and we get the expected result. No mystery.

But what happens if we don't measure spin along the z axis, but along the y axis? If particle 1 starts in state A, then we only know its spin along the z direction. Along the y direction, its spin is completely unknown, and there's a 50/50 chance of it being spin up or spin down along this direction. Same with particle 2. In fact, not only is the chance of any one measurement coming out 50/50, but we should also get absolutely no correlation between the two. And you can demonstrate this by preparing two particles in such an initial state. So if the two particles start out in states A and B respectively, then we will find that they're perfectly correlated if we measure spin along z, but totally UNcorrelated if we measure along y.

But that's not what we find with entangled particles. We can prepare them in states such that they're perfectly correlated regardless of which axis we measure along. Quantum mechanics actually tells us that the only way to get such a correlation is for the two particles to not have a definite spin along any axis until we measure one of them. And that's where the strangeness comes in: it doesn't matter which one we measure, or where we measure, or even what axis we measure, we always know that the other one will be perfectly correlated with it. For a perfectly entangled state we have no prior knowledge of which one will come out A and which will come out B, but we know that they always come out opposite, regardless of the axis.

The math behind all this is actually fairly simple, believe it or not.
 
davefoc said:
OK, assuming I have gotten that right. What is the theoretical or experimental evidence that thing 1 was not actually in one state or the other and we just couldn't know it until we tested it?
Click to expand...

There's a theorem - called Bell's theorem - which proves that IF the thing was actually in a definite state, THEN one can define an experiment which will always give a certain result. But experiment does not give that result; hence, the thing was not in a definite state.

So try googling "Bell's theorem" as a start.
 
davefoc said:
I've just read the Wikipedia article and a Discover article on quantum entanglement and have read several other articles on it in my life.

I still don't quite get it.

OK, I've a two entangled things, thing 1 and thing 2. I test thing 1 and find out it's in the A state. I now know that wherever thing 2 is it will be in the B state.

OK, but what's the mystery here? Suppose thing 1 was in the A state all along and thing 2 was in the B state all along. No faster than light connection needed at all. Thing 2 was in the B state all along whenever and wherever I test it.

I have several other questions but that is the main one.

The answer seems to be that thing 1 was actually in a state that wasn't either A or B before we tested it. The state it was in was some intermediate state between A and B and only after it is tested does it become clearly in one state or the other.

OK, assuming I have gotten that right. What is the theoretical or experimental evidence that thing 1 was not actually in one state or the other and we just couldn't know it until we tested it?

ETA: I'm picturing thing 1 as a roulette wheel with recesses marked as A or B that is completely covered except for a window that allows us to see the recess where the ball is after the wheel has stopped. The wheel can only be tested once. I've got lots of these wheels and I test them like mad. Some of them come up A and some of them come up B. So one theory I have is that wheels are all the same with an equal number of A and B recesses. The other theory I have is that there are wheels with A recesses and wheels with B recesses. How do I decide what the actual case is?
Click to expand...

I have the same question. I may be totally interpreting this wrong, but I think of it in classical physics, say you have invisible billiard balls, two of which were in a known state then acted upon by a 3rd, and that we can derive the position and momentum of the second ball by measuring and seeing the momentum of the first ball, no faster than light communication between the two necessary but the two balls are mathematically entangled until the measurement breaks this purely mathematical relationship between them...but I may be way wrong on this and will defer to the experts.
 
davefoc said:
I've just read the Wikipedia article and a Discover article on quantum entanglement and have read several other articles on it in my life.

I still don't quite get it.

OK, I've a two entangled things, thing 1 and thing 2. I test thing 1 and find out it's in the A state. I now know that wherever thing 2 is it will be in the B state.

OK, but what's the mystery here? Suppose thing 1 was in the A state all along and thing 2 was in the B state all along. No faster than light connection needed at all. Thing 2 was in the B state all along whenever and wherever I test it.

I have several other questions but that is the main one.

The answer seems to be that thing 1 was actually in a state that wasn't either A or B before we tested it. The state it was in was some intermediate state between A and B and only after it is tested does it become clearly in one state or the other.

OK, assuming I have gotten that right. What is the theoretical or experimental evidence that thing 1 was not actually in one state or the other and we just couldn't know it until we tested it?
Click to expand...

I haven't read it too carefully, but this looks like it might be what you want:
http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html
 
Ziggurat said:
Indeed, that's the case. Let's look a bit at how we know this is true.

The most basic example is a spin system, where if you measure the spin along one axis, you find it's either up or down. So let's call A spin up and B spin down along the z axis. Now let's suppose that particle 1 is in state A and particle 2 is in state B. We measure the spin along the z axis, and we get the expected result. No mystery.
Click to expand...

Did you create this particle pair so that particle 1 was spin up and particle 2 was spin down or do you mean you determined that after you did the test?

But what happens if we don't measure spin along the z axis, but along the y axis? If particle 1 starts in state A, then we only know its spin along the z direction.
Click to expand...
How did you know its spin in the z direction? This is where I'm getting confused I think.
Along the y direction, its spin is completely unknown, and there's a 50/50 chance of it being spin up or spin down along this direction. Same with particle 2. In fact, not only is the chance of any one measurement coming out 50/50, but we should also get absolutely no correlation between the two. And you can demonstrate this by preparing two particles in such an initial state. So if the two particles start out in states A and B respectively, then we will find that they're perfectly correlated if we measure spin along z, but totally UNcorrelated if we measure along y.
Click to expand...
I'm not quite following this although I might be able to if I was sure about the answer to my first questions. Is part of what you are saying here that a spin up characteristic in the z direction puts a physical limitation on the chances that spin up will be detected in the y direction?
 
69dodge said:
I haven't read it too carefully, but this looks like it might be what you want:
http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html
Click to expand...

That, plus some of the other posts do appear to be an answer to my questions . Unfortunately, I just couldn't understand it fast enough and I need to go to the airport now to drop my daughter off. After years of trying to understand this I feel like I might be close. I am looking forward to giving it another go when I get back.
 
davefoc said:
Hi CD,
I always enjoy seeing a post from you. I quote you (poorly I'm afraid) at times in various discussions.
Click to expand...

Most kind :blush:. Your name draws me to threads as well. It's pure coincidence that you're a Californian rather than a real American, of course ...

My daughter is off to France and the UK with her French class today. Where do you live in the UK?
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Cardiff, South Wales. Out of the way, but under the protection of Torchwood.

On the topic: It seems like a lot of modern physics is inaccessible to those unwilling or unable to plow through the math. But this seems like a simple enough issue that it should be understandable by the less mathematically capable amongst us. It could be one of those issues which is devilishly complicated and the writers in the popular press don't really understand it so they just put together a bunch of words that make it seem like it might be simple when it isn't. Hopefully one of JREF's resident physics geniuses will stop by to sort this out.
Click to expand...

No doubt.

I know when the maths is beyond me, so I have to conceptualise. The concept of questions which are unresolved until they need to be works for me. Two-slit interference is a classic example : there's no need to know which slit a photon passed through when the question is only where it arrived.
 
davefoc said:
Did you create this particle pair so that particle 1 was spin up and particle 2 was spin down or do you mean you determined that after you did the test?
Click to expand...

I mean you prepare two particles so that they are in this state. Preparing them can be though of as a measurement, but it doesn't have to be destructive: once they're in this state, you can play with them and do further measurements of their spin or anything else you want to. See my link at the end for how one can do this. Such particles are not entangled, BTW.

How did you know its spin in the z direction? This is where I'm getting confused I think.
Click to expand...

In my non-entangled case, I prepare them that way, and they will stay that way until I either do something to rotate that spin or try to measure the spin along some other axis.

I'm not quite following this although I might be able to if I was sure about the answer to my first questions. Is part of what you are saying here that a spin up characteristic in the z direction puts a physical limitation on the chances that spin up will be detected in the y direction?
Click to expand...

Absolutely. It's another version of the uncertainty principle: if I know the spin along one axis completely, I have no information about the spin along any perpendicular axis. This is also the basic conclusion of one of the major early quantum mechanics experiments known as Stern-Gerlach.
 
sol invictus said:
There's a theorem - called Bell's theorem - which proves that IF the thing was actually in a definite state, THEN one can define an experiment which will always give a certain result. But experiment does not give that result; hence, the thing was not in a definite state.
Click to expand...

The unstated extension being : Cope with it.
 
69dodge said:
I haven't read it too carefully, but this looks like it might be what you want:
http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html
Click to expand...

Bell's theorem is what Dave's talking about, but I think he will need to do some more reading before he he tries to tackle Bell's theorem directly.

Start out with Stern-Gerlach. This provides the basics of quantum spin, and any measurement of spin for other particles is going to be formally equivalent in terms of the math. Then read up on the EPR paradox, which introduces the problem of particles with entangled spin states. Bell's theorem is sort of the final analysis (so far, at least) of the EPR paradox - don't bother tackling it until you think you've got a handle on the first parts.
 
portlandatheist said:
I have the same question. I may be totally interpreting this wrong, but I think of it in classical physics, say you have invisible billiard balls, two of which were in a known state then acted upon by a 3rd, and that we can derive the position and momentum of the second ball by measuring and seeing the momentum of the first ball, no faster than light communication between the two necessary but the two balls are mathematically entangled until the measurement breaks this purely mathematical relationship between them...but I may be way wrong on this and will defer to the experts.
Click to expand...

You don't need (or get) any FTL signalling in such a classical case, but the thing is, entanglement doesn't make sense in a purely classical system. You can have correlations, but that's not the same thing as entanglement. Basically, entanglement is important in quantum mechanics because you can have superposition states with indeterminate values for an observable (in plain English, the system doesn't have a single value for some property until you measure that property). That doesn't exist in classical physics (your system always has a specific value for any property, even if you don't know what that value is), so there's really nothing equivalent to entanglement.
 
davefoc said:
What is the theoretical or experimental evidence that thing 1 was not actually in one state or the other and we just couldn't know it until we tested it?
Click to expand...


As the real physicists said, the evidence is in how Bell's Theorem, when tested experimentally (many decades after it was formulated), did not apply to what was observed- ie, it was not a situation where the the state was predetermined and was just unmasked when tested.

some less rigorous pages (hopefully accurate)-

http://www.drchinese.com/Bells_Theorem.htm#Overview_5

http://plato.stanford.edu/entries/qt-epr/#2

http://www-ece.rice.edu/~kono/ELEC565/Aspect_Nature.pdf
 
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Ziggurat said:
Absolutely. It's another version of the uncertainty principle: if I know the spin along one axis completely, I have no information about the spin along any perpendicular axis. This is also the basic conclusion of one of the major early quantum mechanics experiments known as Stern-Gerlach.
Click to expand...

I think the third diagram on the "Sequential experiments" bit was one of the most illuminating things for me when I was learning (and invariably forgetting) some of the basics of QM.
 
QM & Entanglement Books.

If you are into reading the occasional book ...

Speakable and Unspeakable in Quantum Mechanics by J.S. Bell (the same Bell as in Bell's Theorem), Cambridge University Press, 2004 (2nd edition). A collection of papers by Bell, a mix of some which use more advanced math than simple algebra, and some that don't. Good for physicists, but much of it is accessible to non-physics types.

Entangled Systems: New Directions in Quantum Physics by Jürgen Audretsch, Wiley-VCH, 2007. This is not a general readers book, so you will need to know something about quantum mechanics and its associated mathematics. But if you do have the physics background, this is the book you can learn about entanglement from.

The central conceptual problem is that quantum mechanics is not deterministic. In classical physics you can predict the exact outcome of an experiment, the only uncertainty being associated with the necessity of making measurements with finite precision. However, in quantum physics one can only predict the probability that an experiment will result in one of a family of possible outcomes. So we say that classical physics is deterministic, whereas quantum physics is not. It's that lack of determinism that eventually leads to entanglement, and a small host of other equally strange affairs.
 
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