Spin 1/2 Correlation: Chance of Measuring Spin Down

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Discussion Overview

The discussion revolves around the probability of measuring the spin of entangled spin 1/2 particles in a Stern-Gerlach experiment, particularly focusing on the correlation between measurements when one particle is measured as spin up. The scope includes theoretical considerations of quantum mechanics and entanglement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that for a 90-degree angle between the Stern-Gerlach apparatuses, the chance of measuring the other particle's spin as down is 50/50.
  • One participant suggests that the correlation can be expressed as cos²(1/2 α), questioning if this is correct.
  • Another participant acknowledges a previous misunderstanding regarding the correlation and clarifies that they were considering a different aspect of the correlation formula.
  • A participant mentions that the correlation could be interpreted as having both 50% and 100% correlation possibilities for the case of α = 90°, expressing uncertainty about the implications of these correlations.
  • One participant confirms that the probability of detecting the second particle with spin −ℏ/2 in the +x direction is indeed 50%, while also noting the possibility of spin +ℏ/2 in the -x direction.

Areas of Agreement / Disagreement

Participants generally agree on the 50/50 probability for the case of 90 degrees, but there are multiple interpretations regarding the correlation formula and its implications, indicating that the discussion remains unresolved.

Contextual Notes

There are unresolved aspects regarding the interpretation of correlation percentages and the specific conditions under which these probabilities apply, as well as the potential for miscommunication about the correlation formula.

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

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