4 ms·

Apart from in a mathematical sense, how do you actually rotate a spin 1/2 particle say 360 degrees? Does this only apply in derived theorems like the spin-stati

Apart from in a mathematical sense, how do you actually rotate a spin 1/2 particle say 360 degrees? Does this only apply in derived theorems like the spin-statistics swap of identical particles or is there an actual physical process where say an electron can itself be rotated 360 degrees and then acquire the -1 sign on the quantum amplitude (and then this could be measured by interfering the rotated version of it with itself, sort of like in a double-slit experiment)?

evanb 6y ago
Yes. If you take an electron beam, put it through an [electron] beam splitter, put half through a magnetic field that would spin the electron around once, and recombine the beams you will see interference effects.
- l33tman 6y ago
  Thanks, yeah think I've read about that version before. But "the magnetic field spins the electron around once", doesn't this feel a bit weak? You could conceivably just define "spin around once" as the B-field manipulation that returns the amplitude to +1, not -1. How do you define the B-field interaction in a way that is comparable to "spinning something around once"? I'm not trying to be annoying :) I feel this really is at the core of the spin-1/2 "rotate twice to rotate completely" confusion.. Because it's the "rotation" in comparison to the surroundings that cause the change in amplitude, a global rotation of the electron particle and the rest of the universe doesn't cause the electron to change amplitude, as then it's just a global coordinate transformation.
  - evanb 6y ago
    Well, if you took a little bar magnet and shot it through it'd go around one time.
wnoise 6y ago
Depends on the spin-1/2 particle. You need something to "grab it with". Electrons "want to" stay aligned with magnetic fields[1]. Imagine two bar magnets, north to south: NNNSSS e- NNNSSS, with an electron in the middle. Spin the magnets around once. Tada! You've spun the electron too. The problem is that slight imperfections in the magnetic fields, as well as everything needed to move them greatly complicate what the actual effect will be on the electron. To really observe interference patterns, you'll need multiple paths, and many many measurements to tease out statistics. In addition to the fragility, moving stuff around for each measurement is infeasible for this reason. Continuous beams of electrons split and merged by magnet fields, with a continuous parameter on of the paths that can alter how much it is effected is needed. And at this point what's happening to the electrons look a lot more like math than like straightforward rotations. [1] Actually, they'll precess around the magnetic field axis, but if that axis starts close to the electron's axis, and is moved slowly, it will stay close.

evanb 6y ago

Yes. If you take an electron beam, put it through an [electron] beam splitter, put half through a magnetic field that would spin the electron around once, and recombine the beams you will see interference effects.

l33tman 6y ago
Thanks, yeah think I've read about that version before. But "the magnetic field spins the electron around once", doesn't this feel a bit weak? You could conceivably just define "spin around once" as the B-field manipulation that returns the amplitude to +1, not -1. How do you define the B-field interaction in a way that is comparable to "spinning something around once"? I'm not trying to be annoying :) I feel this really is at the core of the spin-1/2 "rotate twice to rotate completely" confusion.. Because it's the "rotation" in comparison to the surroundings that cause the change in amplitude, a global rotation of the electron particle and the rest of the universe doesn't cause the electron to change amplitude, as then it's just a global coordinate transformation.
- evanb 6y ago
  Well, if you took a little bar magnet and shot it through it'd go around one time.

wnoise 6y ago

Depends on the spin-1/2 particle. You need something to "grab it with". Electrons "want to" stay aligned with magnetic fields[1]. Imagine two bar magnets, north to south: NNNSSS e- NNNSSS, with an electron in the middle. Spin the magnets around once. Tada! You've spun the electron too. The problem is that slight imperfections in the magnetic fields, as well as everything needed to move them greatly complicate what the actual effect will be on the electron. To really observe interference patterns, you'll need multiple paths, and many many measurements to tease out statistics. In addition to the fragility, moving stuff around for each measurement is infeasible for this reason. Continuous beams of electrons split and merged by magnet fields, with a continuous parameter on of the paths that can alter how much it is effected is needed. And at this point what's happening to the electrons look a lot more like math than like straightforward rotations. [1] Actually, they'll precess around the magnetic field axis, but if that axis starts close to the electron's axis, and is moved slowly, it will stay close.