Einstein-Podolsky-Rosen (EPR) Paradox

[Mr_Mo]

Hi. I have read a little about the EPR paradox; however I haven’t fully understood it yet, therefore I was hoping for someone to answer my questions, so I can get a better understanding.

I have read the link underneath, however I don’t get it.
http://en.wikipedia.org/wiki/EPR_paradox
Suppose we prepare the system consisting of two particles, A and B, initially interacting with each other but separated far away after that. However, by the help of measurement of one, we can know the state of the other. Here, the point is that this measurement is done when the two cannot interact because of a great separation.

Suppose you measure the momentum of A, then you know the momentum of B as well. Likewise you could measure the position of A and then you know the position of B. However the quantum mechanics implies that the two cannot be real at the same time. So you could either measure the position or the momentum.

Suppose we measure the momentum of A and the position of B, then we both know the momentum and the position for both A and B. However we have just stated that this is not possible. But what could prevent us from measuring it? This measurement is done when the two cannot interact because of a great separation. And even if they could interact with each other, what would happen, which would prevent us from measuring both things?

In wikipedia they use an example with measuring the spin. So what will prevent us from measuring the spin along the z-axis for A, and the spin along the x-axis for B. Again, this measurement is done when the two cannot interact because of a great separation. Then we would know both the spin along the z-axis and x-axis for both A and B. However this is not possible. But what could prevent us from measuring it? And even if A and B could interact which each other, what would happen, which would prevent us from measuring both things?

I hope someone can explain this for me.
Thanks in advance.

 

[vanesch]

There are three distinct aspects to the EPR "paradox":

1) the experimental reality
2) the "objective" predictions of the quantum formalism
3) the interpretational issues

I'm going to limit myself here to 2), that is, the predictions of the quantum formalism about the probabilities of outcomes of experiments. The two other points are highly debated, even though there is overwhelming indirect evidence that 1) corresponds to 2)

So, what does the quantum formalism say about the situation ?
Simply, that the conditional probability of observation at B depends on the outcome at A, even though there is no direct interaction.

As such, if you measure "position" at A, and "momentum" at B, then the result of the "position measurement" at A, will alter the conditional probability of the "momentum" measurement at B, *as if* you did the two measurements on one and the same particle.
However, the *unconditional* probability at B will NOT be affected by what was measured at A (so that locally, at B, you cannot know that the measurement at A took place). It is only when you compare the results, that you can observe the conditional effect.

In the conventional quantum formalism, the measurement at A changes the quantum state upon which the measurement at B will be acting (but in such a way that this is locally not noticable by B).
This "protects" the uncertainty principle from violation using the EPR proposal.

 

[DrChinese]

There are three distinct aspects to the EPR "paradox":

1) the experimental reality
2) the "objective" predictions of the quantum formalism
3) the interpretational issues

I'm going to limit myself here to 2), that is, the predictions of the quantum formalism about the probabilities of outcomes of experiments. The two other points are highly debated, even though there is overwhelming indirect evidence that 1) corresponds to 2)

So, what does the quantum formalism say about the situation ?
Simply, that the conditional probability of observation at B depends on the outcome at A, even though there is no direct interaction.

As such, if you measure "position" at A, and "momentum" at B, then the result of the "position measurement" at A, will alter the conditional probability of the "momentum" measurement at B, *as if* you did the two measurements on one and the same particle.

As usual, Vanesch covers this very well. To further address the OP's question: there is absolutely nothing to prevent you from performing the experiments you describe on the 2 particles. The issue is: what do you actually learn from the 2nd observation? Do you gain any information about the particle on which you performed the first observation? The answer is: NO, you cannot learn more than the Heisenberg Uncertainty Principle allows.