Are spin-up and spin-down electrons distinguishable or indistinguishable?

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In summary, the conversation discusses the concept of distinguishability between quantum particles, specifically electrons and protons. It is mentioned that electrons with the same spin are indistinguishable, but can be distinguished if a specific measurement is done. However, in the context of statistical mechanics, they are not distinguishable. The same applies to protons in a helium nucleus, which are considered identical due to their same mass and eigenvalue of the squared Pauli-Lubanski pseudovector. It is also noted that the Pauli exclusion principle only applies to elementary particles, not composite particles like protons. Finally, the conversation touches on the idea of swapping protons and the effect on the quarks within them.
  • #1
wdlang
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i am puzzled by this problem
 
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They are indistinguishable if they have the same spin or a measurement is done such that their spin is a superposition (like an Sx measurement). In theory though they are distinguishable between each other (i.e. a spin, Sz=+1/2 is distinguishable from an Sz=-1/2) provided, as I said, something like an Sx measurement is not done.
 
  • #3
Depends on the context, doesn't it? The total spin of a system is conserved (non-relativistically), so if you have 5 up and 3 down, you'll always have 5 up and 3 down.

But for any interacting electrons they can swap spins, so you can never tell which one is or was which.
So they're 'distinguishable' from the thermodynamic sense since the total number of each spin is conserved,
and you have Fermi-Dirac statistics and all that. But they're not distinguishable in the sense that you can tell one from the other.
 
  • #4
Well I feel like you're muddling picture here. In statistical mechanics we have an indistinguishability amongst those of the same spin. Thus, it's essentially, how can you distribute 5 ups amongst 8 spins. However, if we treat this instead with pure quantum with the schrodinger (or Dirac) solution of 8 distinct electrons it's different. Our solutions must be the same under permutation of ups and downs but it's a different situation where we have initial values conditions and such. Of course I could just be talking out of my arse here.
 
  • #5
The trick with distinguishable or not is simple: two quantum systems are identical, if their intrinsical attributes are the same. For elementary particles a\ la Wigner, two elementary particles are identical/indistinguishable, iff they have the same mass and eigenvalue of the squared Pauli-Lubanski pseudovector.
 
  • #6
Do the protons in a helium nuclei have spin 0 in the ground state? Or does Pauli's exclusion principle only apply to elementary particles, thus allowing the protons to have spin 1?

Is the correct interpretation to say that the protons are made from 3 quarks, so swapping the two protons swaps 3 quarks (u of one with the u of the other, d of one with d of the other) which produces a negative sign since 3 is an odd number of swaps?
 

1. Are spin-up and spin-down electrons distinguishable?

Yes, spin-up and spin-down electrons are distinguishable based on their spin states. Spin is an intrinsic property of electrons that can have two possible values: spin-up and spin-down. This means that these two types of electrons have different orientations in space, making them distinguishable from one another.

2. Can spin-up and spin-down electrons be in the same state?

No, according to the Pauli exclusion principle, no two electrons in an atom can have the same set of quantum numbers, including spin. This means that spin-up and spin-down electrons cannot occupy the same state at the same time.

3. How do we distinguish between spin-up and spin-down electrons?

We can distinguish between spin-up and spin-down electrons using various experimental techniques. One common method is through the use of a Stern-Gerlach apparatus, which applies a magnetic field to separate particles based on their spin orientations.

4. Are spin-up and spin-down electrons interchangeable?

No, spin-up and spin-down electrons cannot be interchanged as they have different properties. For example, in a magnetic field, spin-up electrons will experience a different force compared to spin-down electrons, making them distinguishable and non-interchangeable.

5. Why is it important to distinguish between spin-up and spin-down electrons?

Distinguishing between spin-up and spin-down electrons is important in understanding the behavior and properties of particles at the quantum level. It also has practical applications in fields such as spintronics and quantum computing.

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