Spin 1/2 Correlation: Chance of Measuring Spin Down

[gespex]

Hello all,

Imagine two spin 1/2 particles that are entangled, going towards two stern-gerlach apparatuses, with some relative angle. Now imagine one stern-gerlach device measures the spin of one of the particles as up. What is the chance that the other stern-gerlach device measures the spin to be down?

For 90 degrees it would be 50/50, right? So my guess is cos^2 ({1 \over 2} \alpha). Is that correct?


Thanks in advance

 

[sergiokapone]

Hello all,

Imagine two spin 1/2 particles that are entangled, going towards two stern-gerlach apparatuses, with some relative angle. Now imagine one stern-gerlach device measures the spin of one of the particles as up. What is the chance that the other stern-gerlach device measures the spin to be down?

For 90 degrees it would be 50/50, right? So my guess is cos^2 ({1 \over 2} \alpha). Is that correct?


Thanks in advance

You can look here , it is the same quastion.

 

[DrChinese]

Yes, that's correct. I may have steered you wrong at an earlier time.

 

[gespex]

You can look here , it is the same quastion.

Thanks for your answer. It doesn't seem to be the same question though - the question of that guy is a lot more advanced than mine. He is asking a question about the implication of the correlations, while I am simply looking for the actual formula for the correlation.

From what I understand from that source, he takes into account two possibilities for the case \alpha = 90°: a 50% correlation and a 100% correlation. I thought it was 50%, which would I believe indicate that I was right thinking the correlation is cos^2({1 \over 2} \alpha. However, I'm not sure what he meant with the 100% correlation.


Thanks

 

[gespex]

Yes, that's correct. I may have steered you wrong at an earlier time.

I did ask the question earlier, and you were the one to answer it. But reading up later I assumed you were talking about the correlation as (a - b)/(a + b)? So I did wonder if it was simply a miscommunication, hence me asking the question again.

But thank you again, for your answer now and for your answer last time.

 

[sergiokapone]

the question of that guy is a lot more advanced than mine.

I am thet guy.
As I understood of the answers to my question, the correct answer to your quastion it is

Particle 2 is detected with a 50% probability of having spin −ℏ/2 in the +x direction, and 50% of having spin +ℏ/2 in the -x direction.

 

[sergiokapone]

Hello all,
For 90 degrees it would be 50/50, right? So my guess is cos^2 ({1 \over 2} \alpha). Is that correct?

Thus, yes, it is correct.