Another thought experiment about spin 1/2

In summary: It doesn't result in spin impurity. It results in loss of coherence. The spin state remains pure, you just can't tell what it was with certainty anymore.Ah, OK, I had thought that 'decoherence' was a phenomenon that affected the spin state itself.In summary, the conversation discusses the preparation of a beam of spin 1/2 particles in the state |up> in the Z direction, passing it through a Stern& Gerlach apparatus in the X direction to get two beams of spin |right> and spin |left>, and then redirecting these two beams directly in another inverted S&G to reunite them in one unique beam. The question is whether the resulting
  • #1
Christian Thom
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TL;DR Summary
Let's take a beam of spin 1/2 particles prepared in the state |up> in the Z direction, let's pass it through a Stern& Gerlach apparatus in the X direction and then directly in another inverted S&G to reunite the two beams. My question is : will we get only spin |up> particles at the exit of the system ?
Let's take a beam of spin 1/2 particles prepared in the state |up> in the Z direction, let's pass it through a Stern& Gerlach apparatus in the X direction to get two beams of spin |right> and spin |left>, and then redirect these two beams directly in another inverted S&G to reunite them in one unique beam. My question is : will we get only spin |up> particles in this beam ?
 
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  • #2
Christian Thom said:
Summary:: Let's take a beam of spin 1/2 particles prepared in the state |up> in the Z direction, let's pass it through a Stern& Gerlach apparatus in the X direction and then directly in another inverted S&G to reunite the two beams. My question is : will we get only spin |up> particles at the exit of the system ?

Let's take a beam of spin 1/2 particles prepared in the state |up> in the Z direction, let's pass it through a Stern& Gerlach apparatus in the X direction to get two beams of spin |right> and spin |left>, and then redirect these two beams directly in another inverted S&G to reunite them in one unique beam. My question is : will we get only spin |up> particles in this beam ?
Yes.
 
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  • #3
Thank you.
 
  • #4
PeroK said:
Yes.
Would you mind elaborating on this just a bit? It was always my understanding that a beam of left- (or right-) spin particles would be a 50-50 mix of up- and down- spin particles, regardless of the preparation before the left-right split. What am I missing?
 
  • #5
sandy stone said:
Would you mind elaborating on this just a bit? It was always my understanding that a beam of left- (or right-) spin particles would be a 50-50 mix of up- and down- spin particles, regardless of the preparation before the left-right split. What am I missing?
It's not a mix, it's a superposition of spin states that equate to z-spin-up. If the spatially separated superposition is perfectly recombined, then you still have a beam of z-spin-up particles.

If, however, you pass either spatially separated component of the superposition through a z-aligned SG magnet and measure the outcome, you will find a 50-50 split representing z-spin-up and z-spin-down (i.e. either x-spin up in one component and x-spin-down in the other).
 
  • #6
Thanks for the clarification. Back to QM kindergarten I go.
 
  • #8
PeroK said:
Yes.
How this result depends on the equality of the path lengths of the two separated beams ?
 
  • #9
Christian Thom said:
How this result depends on the equality of the path lengths of the two separated beams ?
It's a thought experiment because the recombination would have to be perfect. I don't believe it's a experiment that is practically achievable.
 
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That reminds me of the "Humpty Dumpty Papers" by Schwinger et al.

https://link.springer.com/article/10.1007/BF01909939
https://link.springer.com/article/10.1007/BF01384847
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.40.1775

Of course you cannot do such experiments with the original SGE, because it's impossible to make the magnets as accurate as needed, but in a sense a setup like a Penning trap is a kind of SGE too.

Another modern realization of a coherent-spin experiment is here:

https://www.nature.com/articles/ncomms3424?origin=ppub
 
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  • #11
PeroK said:
It's a thought experiment because the recombination would have to be perfect. I don't believe it's a experiment that is practically achievable.
I would think that there must be some leeway, otherwise free beams of definite spin particles would loose more or less quickly their spin definiteness due to spurious magnetic gradients that are always present in actual experiments.
 
  • #12
Christian Thom said:
I would think that there must be some leeway, otherwise free beams of definite spin particles would loose more or less quickly their spin definiteness due to spurious magnetic gradients that are always present in actual experiments.
You'll need to explain what you mean by that.

Note that the SG experiment itself is fuzzy rather than precisely clear-cut.
 
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  • #13
PeroK said:
You'll need to explain what you mean by that.

Note that the SG experiment itself is fuzzy rather than precisely clear-cut.
If you consider a beam like the one at the origin of the experiment above, in absence of S&G devices, the slightest natural magnetic gradients would play the same role as the S&G device, and if the recombination was so difficult to obtain, that would result in the loosing of the spin purity of the original beam after some propagation. This effect would have surely already been observed (maybe it has ?).
 
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  • #14
Christian Thom said:
If you consider a beam like the one at the origin of the experiment above, in absence of K&G devices, the slightest natural magnetic gradients would play the same role as the K&E device, and if the recombination was so difficult to obtain, that would result in the loosing of the spin purity of the original beam after some propagation. This effect would have surely already been observed (maybe it has ?).
What you are describing is simply state evolution. You would gradually lose the spatial coherence of the beam.

For SG, you need a powerful magnet with a specific varying magnetic field to create a superposition of spatially distinct wavefunctions. Putting those together by perfectly reversing that separation process is theoretically possible but practically very difficult.
 
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  • #15
The SG experiment requires a very specific and controlled magnetic field. Just any weak background field won't do.
 
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Thank you all.
 

Related to Another thought experiment about spin 1/2

1. What is a spin 1/2 in physics?

A spin 1/2 is a quantum mechanical property of a particle that describes its intrinsic angular momentum. It is a fundamental property of particles such as electrons, protons, and neutrons.

2. How is spin 1/2 represented in a thought experiment?

In a thought experiment about spin 1/2, the particle is often represented as a spinning object with two possible orientations, either up or down. This represents the two possible spin states of a particle, which can be measured along a particular axis.

3. What is the significance of the spin 1/2 thought experiment?

The spin 1/2 thought experiment is significant because it helps us understand the behavior of particles at the quantum level. It also demonstrates the concept of superposition, where a particle can exist in multiple states simultaneously until it is measured.

4. How does the spin 1/2 thought experiment relate to the Pauli exclusion principle?

The Pauli exclusion principle states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. In the spin 1/2 thought experiment, the two possible spin states of a particle represent the two possible quantum states that cannot be occupied by another particle at the same time.

5. Can the spin 1/2 thought experiment be applied to real-world situations?

Yes, the spin 1/2 thought experiment has real-world applications in fields such as quantum computing and nuclear magnetic resonance imaging (MRI). It also helps us understand the behavior of particles in experiments such as the Stern-Gerlach experiment.

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