Exploring Entanglement in an EPR Experiment

[tymarats]

Hi,

I have this one boggling my mind for quite some time. Let's consider a very simple EPR experiment -- pair of entangled particles are sent to Alice and Bob (separated by large distance), who (at the same time) measure its spin along different axis: Alice does the measurement on axis z (and, suppose she reads it points up), while Bob does the measurement along axis x. What will Bob read?

a) Either left or right, but in this case, we know the particle's spin on both axes in the same time, which violates Heisenberg's principle, right?

b) He will not be able to conduct the measurement. What does this mean exactly, what will he see? And if he can know that his measurement failed, wouldn't that make faster than light communication method possible? Example: Alice codes a message as, e.g. 01010011 and for every second, she decides to do the measurement along the z axis (if the next bit is 1) or not to do it (if the next bit is 0). On the other side of the galaxy, Bob does the measurement along x-axis _every_ second and if he gets the result, Alice sent him a 0. If he cannot get it (because of the Heisenberg's principle), Alice sent him a 1.

I would really appreciate the explanation of this.

 

[Nugatory]

a) Either left or right...

Yes.

...but in this case, we know the particle's spin on both axes in the same time

No. We know what the first particle's spin along the x-axis would have been if we had measured that, but we didn't - instead we measured its spin on the z-axis so its x-axis spin is completely random. Likewise, we know what the second particle's spin on the z-axis would have been if we had measured that, but we didn't - instead we measured its spin on the x-axis so its z-axis spin is completely random. When the dust settles, we know just one thing about each particle, the thing we actually measured.

You might want to google for "Bell's theorem Dr Chinese"... or wait for Dr. Chinese, a regular here, to weigh in with his explanation of Bell's theorem and the experimental evidence showing that the world really does act in this weird way.

 

[tymarats]

Thank you for your prompt response. I knew that the a) answer was true, but I mentioned b) because of what I heard here: http://www.youtube.com/watch?feature=player_detailpage&v=0x9AgZASQ4k#t=609. The reasoning is obviously wrong (or we would have messages from the future), but I couldn't really explain why a) does not violate Heisenberg principle.

So, if I understand you correctly, measuring the first particle's z-spin does not tell us what the second particle's z-spin is, just what it would have been if we had measured it? Honestly, this is very subtle difference (if there is any at all) to me. But I believe there might be a point there.

However, what's with the wave function of the entangled pair? Does it not collapse as soon as we measure first one? And if it collapsed for the entire pair, how is it that we cannot say that B's particle has definitive z-axis spin, regardless of whether we're going to perform a measurement on it, or not? Does that mean that Copenhagen interpretation does not really hold, as per Dr Garrett ()?

 

[Nugatory]

So, if I understand you correctly, measuring the first particle's z-spin does not tell us what the second particle's z-spin is, just what it would have been if we had measured it? Honestly, this is very subtle difference (if there is any at all) to me.

it is indeed a subtle difference, but it's a difference. You might want to take a look at this thread for some more, including experiments that actually test for this difference.

However, what's with the wave function of the entangled pair? Does it not collapse as soon as we measure first one? And if it collapsed for the entire pair, how is it that we cannot say that B's particle has definitive z-axis spin, regardless of whether we're going to perform a measurement on it, or not? Does that mean that Copenhagen interpretation does not really hold, as per Dr Garrett?

It means that the Copenhagen interpretation is not especially helpful if you're trying to understand the behavior of remote entangled pairs. For that problem, you're better off with some other interpretation, one that doesn't include the notion of collapse.

 

[Ilja]

I think the explanation given in the video is not optimal, but I would not say it is wrong.

He will not be able to conduct the measurement. What does this mean exactly, what will he see?

He will obtain a result.

But now think about measurements made on a single particle. You measure spin in x direction, and obtain a result. Now you can repeat the measurement in x direction as often as you like for the same particle, you will always obtain the same result.

But after this you measure the spin in y direction. You obtain some result. After this, you measure spin in x direction again. In itself, the result looks unproblematic. But if you compare it with the earlier result, measured before the y-measurement, you find that the result will be, with probability 50%, different. In other words, you have measured a random number, +1 or -1, but not the original, undistorted spin in x-direction.

So it is the same measurement apparatus, and gives the same type of possible results, +1 or -1. Without knowing the context, the fact that there has been an y-measurement between the two x-measurement, you cannot tell if the second x-measurement gives the same result as the first one (thus, measures the original spin in x-direction) or measures some random number created by the distortion by the y-measurement. So you cannot say if you have measured the original spin in x-direction or measured, instead, an irrelevant random number, because the spin in x-direction has been distorted, so that you are no longer able to measure the original spin in x-direction.

 

[tymarats]

Hm... Ilja, I think I understand what you're saying. However, the concept is still not clear to me. May I propose a following experimenet, where Alice and Bob are doing their measurements in a perfectly synchronized succession:

Timeframe 0
------------

Alice measures z (scrambles x) and gets +1/2
Bob measures x (scrambles z) and gets -1/2
Alice measures z (scrambles x) and gets -1/2
Bob measures x (scrambles z) and gets +1/2
...

Bob got 1 from Alice (he got 50% of +1/2 and 50% of -1/2, which means Alice decided to do the measurements in this timeframe).

Timeframe 1

Alice decides not to measure z
Bob measures x (scrambles z) and gets +1/2
Alice decides not to measure z
Bob measures x (scrambles z) and gets +1/2
Alice decides not to measure z
Bob measures x (scrambles z) and gets +1/2
...

Bob got 0 from Alice.

This is obviously wrong. Might there be a problem in "immediately after" formulation here?

 

[tymarats]

To answer my own question: no.

I believe that Nugatory's explanation (of the subtle difference between being in a state and would have been in a state if the measurement had been conducted) is the only real explanation so, yes, the reasoning in the video (where it's said that Bob cannot do the measurement) really is wrong.

They can both do the measurements as many times as they want, and they will both get consistent results, but the Heisenberg principle is not violated because Bob's particle was never measured along z, and therefore, never assumed any state, and never was in any state (even though we are sure what that state would be, had Bob measured it). Copenhagen interpretation just doesn't fit well for this problem.