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## Entanglement question

I read an article, than when on observes an entangled particle, the other entangled particle is actually observed at the same time, no matter how far apart. Is that an accurate statement? Please see https://hudsonvalleyone.com/2020/02/...u-can-imagine/

2. For certain values of "observe". If we measure some property of one particle, thereby taking it out of a superposition of states, then the entangled particle will likewise drop out of superposition to exhibit the complementary value of the property we've measured on the first particle.

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Originally Posted by Copernicus
I read an article, than when on observes an entangled particle, the other entangled particle is actually observed at the same time, no matter how far apart. Is that an accurate statement? Please see https://hudsonvalleyone.com/2020/02/...u-can-imagine/
The article says "With entanglement, two particles are born together and secretly share a wave function. If one is observed, its wave function and that of its twin simultaneously collapse. Two items then materialize at the same moment. And they do so regardless of the distance between them.". The other particle is "observed" only in the sense that we know its state from observation of the other particle.

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Originally Posted by Reality Check
The article says "With entanglement, two particles are born together and secretly share a wave function. If one is observed, its wave function and that of its twin simultaneously collapse. Two items then materialize at the same moment. And they do so regardless of the distance between them.". The other particle is "observed" only in the sense that we know its state from observation of the other particle.
I guess that wave function collapse is not a proven theory, but when we measure one of these particles, do we have to do another measurement on the other particle to verify its spin.

5. Originally Posted by Copernicus
I guess that wave function collapse is not a proven theory, but when we measure one of these particles, do we have to do another measurement on the other particle to verify its spin.
Wave function collapse isn't a theory, it's an interpretation of quantum mechanics.
You don't have to do a separate measurement on the other particle, but you can if you want. Quantum mechanics predicts what the experimental result will be, from the result of the observation performed on the first particle.

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Originally Posted by grant hutchison
Wave function collapse isn't a theory, it's an interpretation of quantum mechanics.
You don't have to do a separate measurement on the other particle, but you can if you want. Quantum mechanics predicts what the experimental result will be, from the result of the observation performed on the first particle.

Grant Hutchison
Are you saying we can know both momentum and position for the second particle then?

7. Originally Posted by Copernicus
Are you saying we can know both momentum and position for the second particle then?
No. I don't see how what I wrote could be interpreted that way.

Grant Hutchison

8. Originally Posted by Copernicus
Are you saying we can know both momentum and position for the second particle then?
I'd go as far as saying that what we know about entanglement suggests just the opposite. What you're hoping to claim here sounds a lot like Einstein's position in the EPR thought experiment, trying to suggest that quantum theory was incomplete.

Here's the argument in a nutshell. Position and momentum aren't the only conjugate observables. Although their original argument was framed with position and momentum, it's actually a bit easier to explain in terms of others, for example, the spin in any two orthogonal directions. Since these are discrete, measuring the spin of a particle in the x direction (arbitrarily chosen by the way the experimental apparatus is set up), means that its spin in the y direction (again arbitrary, but at right angles to your first choice) is completely undetermined. Einstein, Podolsky, and Rosen suggested, though, that you could imagine measuring the spin of one entangled particle in the x direction (and thus knowing the spin for both particles), and the spin of the second particle in the y direction (thus apparently knowing the spin of both particles in the y direction). If you wait for the particles to be far enough apart, the measurement of one shouldn't be able to have any effect on the other, and so you've apparently found a clever way to determine the spin of a particle in two separate directions. Since you could in principle do your measurements at any angles, each particle must "know" its spin at every angle, and so the fact that we can't measure it directly is just a matter of classical ignorance rather than any kind of quantum indeterminacy.

But later work on entanglement, especially from Bell, including later verifying experiments, shows that quantum theory doesn't work like this. In particular, measurements at other angles, where there should be partial correlation, shows that the correlation is too good for a model where the particles just "know ahead of time" how they will respond to various measurements. The assumption that the particles have definite properties that do not change in response to things arbitrarily far away (i.e., local reality) cannot hold.

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Originally Posted by Grey
I'd go as far as saying that what we know about entanglement suggests just the opposite. What you're hoping to claim here sounds a lot like Einstein's position in the EPR thought experiment, trying to suggest that quantum theory was incomplete.

Here's the argument in a nutshell. Position and momentum aren't the only conjugate observables. Although their original argument was framed with position and momentum, it's actually a bit easier to explain in terms of others, for example, the spin in any two orthogonal directions. Since these are discrete, measuring the spin of a particle in the x direction (arbitrarily chosen by the way the experimental apparatus is set up), means that its spin in the y direction (again arbitrary, but at right angles to your first choice) is completely undetermined. Einstein, Podolsky, and Rosen suggested, though, that you could imagine measuring the spin of one entangled particle in the x direction (and thus knowing the spin for both particles), and the spin of the second particle in the y direction (thus apparently knowing the spin of both particles in the y direction). If you wait for the particles to be far enough apart, the measurement of one shouldn't be able to have any effect on the other, and so you've apparently found a clever way to determine the spin of a particle in two separate directions. Since you could in principle do your measurements at any angles, each particle must "know" its spin at every angle, and so the fact that we can't measure it directly is just a matter of classical ignorance rather than any kind of quantum indeterminacy.

But later work on entanglement, especially from Bell, including later verifying experiments, shows that quantum theory doesn't work like this. In particular, measurements at other angles, where there should be partial correlation, shows that the correlation is too good for a model where the particles just "know ahead of time" how they will respond to various measurements. The assumption that the particles have definite properties that do not change in response to things arbitrarily far away (i.e., local reality) cannot hold.
I've read Bell's theorem before. I agree with it.

10. Originally Posted by Copernicus
I've read Bell's theorem before. I agree with it.
So does the data.

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Originally Posted by Noclevername
So does the data.
That is why I agree with it. I don't like it though. I have to pinch my nose.

12. Originally Posted by Copernicus
That is why I agree with it. I don't like it though. I have to pinch my nose.
With "like" and ten cents you'd have... ten cents.

13. Originally Posted by Copernicus
That is why I agree with it. I don't like it though. I have to pinch my nose.
I'm sorry to say it, but my impression is a lot of the ATM ideas that get presented on CQ are based a lot more on how the various advocates would like the Universe to behave, rather than on how it actually behaves.
Last edited by Swift; 2020-Sep-28 at 05:45 PM. Reason: fixed the grammar

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Originally Posted by Swift
I'm sorry to say it, but my impression is a lot of the ATM ideas that get presented on CQ are based a lot more on how the various advocates would like the Universe to behave, rather than on how it actually behaves.
Why do we use 120 degrees for Bells Inequality?

15. Originally Posted by Copernicus
Why do we use 120 degrees for Bells Inequality?
We don't have to use that specific angle (and which angle you pick can depend on whether you're measuring spin or polarization), but when working through the math, there are specific angles where the correlation between measurements is better than it "should" be, if we could consider properties like spin to be locally real. So those are the angles that are used when running the experiments.

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Originally Posted by Grey
We don't have to use that specific angle (and which angle you pick can depend on whether you're measuring spin or polarization), but when working through the math, there are specific angles where the correlation between measurements is better than it "should" be, if we could consider properties like spin to be locally real. So those are the angles that are used when running the experiments.
Why would we use one specific angle when a particle could be a sum of angles of many particles? Wouldn't that throw off the whole calculation? Are we not then assuming that particles are discrete at the level we are measuring.

17. Originally Posted by Copernicus
Why would we use one specific angle when a particle could be a sum of angles of many particles? Wouldn't that throw off the whole calculation? Are we not then assuming that particles are discrete at the level we are measuring.
Particles aren't sums of angles any more than they are boson energy level transitions. Grey answered why: because it maximizes the difference between the two scenarios that they are trying to distinguish.

18. Originally Posted by Copernicus
Why would we use one specific angle when a particle could be a sum of angles of many particles? Wouldn't that throw off the whole calculation? Are we not then assuming that particles are discrete at the level we are measuring.
Any time you make a measurement of spin or polarization, you have to choose what angle you're measuring at. Doing so gives you certain information, and also limits the other information that is available about that particle (and a particle entangled with it as well). Much of the point of Bell's Theorem is that such limits on information are fundamental, not just limits on how much we can know.

So, as cjameshuff says, for both theoretical calculations involving entangled particles, and for the actual experiments we run, when we pick the angles for our measurements, we generally pick angles that will give interesting results. We'll generally also work out the results (and run our experiments) for other angles as well, just to verify that those also come out like we expect (and they do), but those often aren't reported much in popular treatments of the subject. It's a complicated enough subject to grasp without slogging through the parts of the data that are not that interesting.

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Originally Posted by Grey
Any time you make a measurement of spin or polarization, you have to choose what angle you're measuring at. Doing so gives you certain information, and also limits the other information that is available about that particle (and a particle entangled with it as well). Much of the point of Bell's Theorem is that such limits on information are fundamental, not just limits on how much we can know.

So, as cjameshuff says, for both theoretical calculations involving entangled particles, and for the actual experiments we run, when we pick the angles for our measurements, we generally pick angles that will give interesting results. We'll generally also work out the results (and run our experiments) for other angles as well, just to verify that those also come out like we expect (and they do), but those often aren't reported much in popular treatments of the subject. It's a complicated enough subject to grasp without slogging through the parts of the data that are not that interesting.
What would happen if one measured the spin on lets say 4, 5, or 6 axes?

20. Originally Posted by Copernicus
What would happen if one measured the spin on lets say 4, 5, or 6 axes?
If you measure the spin of a particle along one specific axis, any information about the spin of that particle along an orthogonal axis is lost. If you instead pick a second direction that's not orthogonal, there will be partial correlation with the initial result, and we can predict accurately what the chance of each outcome of that next spin measurement is. Each time you do one of these measurements, though, you destroy any information about the spin in any other direction. If you've measured that a given particle has spin x+, for example, that's all the information that exists, no matter how many times you had measured the spin in whatever direction prior to that. If you make 20 successive spin measurements on a particle, the first 19 are no longer relevant in making any predictions about the particle's behavior (this assumes that your particle type and your method of measuring spin are non-destructive).

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Originally Posted by Grey
If you measure the spin of a particle along one specific axis, any information about the spin of that particle along an orthogonal axis is lost. If you instead pick a second direction that's not orthogonal, there will be partial correlation with the initial result, and we can predict accurately what the chance of each outcome of that next spin measurement is. Each time you do one of these measurements, though, you destroy any information about the spin in any other direction. If you've measured that a given particle has spin x+, for example, that's all the information that exists, no matter how many times you had measured the spin in whatever direction prior to that. If you make 20 successive spin measurements on a particle, the first 19 are no longer relevant in making any predictions about the particle's behavior (this assumes that your particle type and your method of measuring spin are non-destructive).
Is there an easy way to figure out what the partial correlation would be on 6 axes.

22. Originally Posted by Copernicus
Is there an easy way to figure out what the partial correlation would be on 6 axes.
If you measure the spin on a given axis, and then measure the spin again on a different axis, the correlation will be the cosine squared of half the angle between the two axes. So if your second measurement is at 180°, cos2(90°) is zero, and you'll expect them to never match, which makes sense. A particle with spin x+ can't possibly be x-. If you pick a direction at right angles to your first, cos2(45°) is 0.5, so that's telling you that if you measure the spin in the y direction after measuring in the x direction, it will be 50-50 chance either way. If you pick 120° as your angle, cos2(60°) is 0.25, so there's a 25% chance that it will have its spin aligned with the detector.

I think I'm confused by what you mean by 6 axes, though. From any given measurement, you can only measure the spin along a single axis. And if you later measure the spin along some different axis, any information about the spin along the first axis is lost. So I'm totally unclear about why you're thinking about 6 axes specifically. You can't ever know the spin of a particle around 6 separate axes (even ignoring the fact that if you hypothetically could, it would be redundant, since you can only have 3 orthogonal axes).

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Originally Posted by Grey
If you measure the spin on a given axis, and then measure the spin again on a different axis, the correlation will be the cosine squared of half the angle between the two axes. So if your second measurement is at 180°, cos2(90°) is zero, and you'll expect them to never match, which makes sense. A particle with spin x+ can't possibly be x-. If you pick a direction at right angles to your first, cos2(45°) is 0.5, so that's telling you that if you measure the spin in the y direction after measuring in the x direction, it will be 50-50 chance either way. If you pick 120° as your angle, cos2(60°) is 0.25, so there's a 25% chance that it will have its spin aligned with the detector.

I think I'm confused by what you mean by 6 axes, though. From any given measurement, you can only measure the spin along a single axis. And if you later measure the spin along some different axis, any information about the spin along the first axis is lost. So I'm totally unclear about why you're thinking about 6 axes specifically. You can't ever know the spin of a particle around 6 separate axes (even ignoring the fact that if you hypothetically could, it would be redundant, since you can only have 3 orthogonal axes).
Just spinning my wheels, digging myself deeper.

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Originally Posted by Grey
If you measure the spin on a given axis, and then measure the spin again on a different axis, the correlation will be the cosine squared of half the angle between the two axes. So if your second measurement is at 180°, cos2(90°) is zero, and you'll expect them to never match, which makes sense. A particle with spin x+ can't possibly be x-. If you pick a direction at right angles to your first, cos2(45°) is 0.5, so that's telling you that if you measure the spin in the y direction after measuring in the x direction, it will be 50-50 chance either way. If you pick 120° as your angle, cos2(60°) is 0.25, so there's a 25% chance that it will have its spin aligned with the detector.

I think I'm confused by what you mean by 6 axes, though. From any given measurement, you can only measure the spin along a single axis. And if you later measure the spin along some different axis, any information about the spin along the first axis is lost. So I'm totally unclear about why you're thinking about 6 axes specifically. You can't ever know the spin of a particle around 6 separate axes (even ignoring the fact that if you hypothetically could, it would be redundant, since you can only have 3 orthogonal axes).
Not that I would be able to understand it, but where would the derivation for the quantum mechanics (cosine of the angle/2)^2
be found?

25. Originally Posted by Copernicus
Not that I would be able to understand it, but where would the derivation for the quantum mechanics (cosine of the angle/2)^2
be found?
I think it just ends up being the projection of a vector onto another one for the cosine part, as the amplitude of the associated wave function, and then it gets squared because the probability of a measurement goes like the square of the wave function. I'll see if I can dig up a derivation somewhere.

26. Hey, look, I found this as the solution to a homework problem. Take a look here. Looks like a decent upper undergraduate or graduate course on quantum mechanics, using Griffiths as the text, if you wanted to pursue it further. Griffiths is one of the standard texts for this kind of stuff; I'd definitely recommend picking it up and becoming comfortable with it if you're looking for a deeper understanding of the theory behind this.

27. Here's my copy.

IMG_20201001_151551.jpg

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Originally Posted by Grey
Here's my copy.

IMG_20201001_151551.jpg

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