Spin 1/2 Correlation: Chance of Measuring Spin Down

In summary, the chance of the other stern-gerlach device measuring the spin to be down is determined by the formula cos^2 ({1 \over 2} \alpha), with a 50% probability for a 90 degree angle. This was confirmed by the source provided by the person asking the question. The question was previously answered but there may have been a miscommunication about the correlation formula. The correct answer is that there is a 50% chance of Particle 2 having spin -ℏ/2 in the +x direction and 50% chance of having spin +ℏ/2 in the -x direction.
  • #1
gespex
56
0
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 [itex]cos^2 ({1 \over 2} \alpha)[/itex]. Is that correct?


Thanks in advance
 
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  • #2
gespex said:
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 [itex]cos^2 ({1 \over 2} \alpha)[/itex]. Is that correct?


Thanks in advance

You can look here , it is the same quastion.
 
  • #3
Yes, that's correct. I may have steered you wrong at an earlier time.
 
  • #4
sergiokapone said:
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 [itex]\alpha = 90°[/itex]: 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 [itex]cos^2({1 \over 2} \alpha[/itex]. However, I'm not sure what he meant with the 100% correlation.


Thanks
 
  • #5
DrChinese said:
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.
 
  • #6
gespex said:
the question of that guy is a lot more advanced than mine.
I am thet guy. :smile:
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.
 
  • #7
gespex said:
Hello all,
For 90 degrees it would be 50/50, right? So my guess is [itex]cos^2 ({1 \over 2} \alpha)[/itex]. Is that correct?

Thus, yes, it is correct.
 

FAQ: Spin 1/2 Correlation: Chance of Measuring Spin Down

1. What is the concept of spin 1/2 correlation?

Spin 1/2 correlation refers to the relationship between two particles with spin 1/2, where their spins are entangled and cannot be described independently. This means that measuring the spin of one particle will affect the spin of the other particle, regardless of the distance between them.

2. How is spin 1/2 correlation measured?

Spin 1/2 correlation is measured through experiments that involve measuring the spin of one particle and then measuring the spin of the other particle. The results are then compared to determine the level of correlation between the two spins.

3. What is the chance of measuring spin down in spin 1/2 correlation?

The chance of measuring spin down in spin 1/2 correlation depends on the specific experiment being conducted. In some cases, the chance may be 50%, while in others it may be higher or lower. It ultimately depends on the initial state of the particles and the measurement being performed.

4. What factors affect the chance of measuring spin down in spin 1/2 correlation?

The chance of measuring spin down in spin 1/2 correlation can be affected by various factors, such as the orientation of the particles' spins, the distance between the particles, and any external forces or interactions that may be present.

5. How is spin 1/2 correlation used in scientific research?

Spin 1/2 correlation is a fundamental concept in quantum mechanics and is used in various areas of scientific research, such as quantum computing, cryptography, and quantum entanglement. It allows scientists to better understand the behavior of particles at the quantum level and has potential applications in advanced technologies.

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