Can Stern-Gerlach spin alignment be seen as a result of EM radiation of precessing magnetic dipole?

Stern-Gerlach experiment is often seen as idealization of measurement. Using strong magnetic field, it makes magnetic dipoles (of e.g. atoms) align in parallel or anti-parallel way. Additionally, gradient of magnetic field bends trajectories depending on this choice.

Magnetic dipoles in magnetic field undergo e.g. Larmor precession due to τ=μ×B torque, unless μ×B=0 what means parallel or anti-parallel alignment.

Precession means magnetic dipole becomes kind of antenna, should radiate this additional kinetic energy. Thanks to duality between electric and magnetic field, we can use formula for precessing electric dipole, e.g. from this article:

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Using which I get power like 10^−3 W, suggesting radiation of atomic scale energies (∼10^−18 J) in e.g. femtoseconds (to μ×B=0 parallel or anti-parallel).

So can we see spin alignment in Stern-Gerlach as a result of EM radiation of precessing magnetic dipole?

Beside photons, can we interpret other spin measurement experiments this way?

 

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Already for electrons they make Larmor precession ... spin echo acrobatics in EM fields: https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#Pulsed_electron_paramagnetic_resonance

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Here we have thousands times heavier oscillating magnetic dipoles - antennas radiating abundant energy, here kinetic down to μ×B=0 ... what is observed experimentally.

 

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I'll repeat here the reply I made to you on the other forum, since James may be able to comment further:

According to my (admittedly rusty) understanding, the only way an atom can radiate in this situation would be by transitioning between the different allowed space-quantised energy levels, i.e. for an atom with angular momentum J, between the 2J+1 values of M, the quantum number of the projection of the angular momentum vector along the field direction. Absorption of energy to bump up electrons from lower energy to higher levels is the basis of EPR (known as ESR in my day). The splitting of the energy levels is modest and therefore these energy transitions absorb (and emit) photons in the microwave region of the spectrum.

I'm not sure I follow what you mean by spin alignment being the result of radiation. The alignment simply occurs as an external field is applied. But, to pursue your line of thought, in the absence of a field there will be equal numbers of atoms in each of the M states, because they are degenerate. When the field is applied, this is no longer so and the atoms will adopt a Maxwell-Boltzmann distribution among the energy levels of M, with more in the lower (more aligned) energy levels and fewer in the upper (more anti-aligned) ones. This, I suppose, must involve either emission of microwave radiation or non-radiative relaxation processes. I have never seen this described and don't know which is dominant. Maybe someone else here, ideally with experience of EPR, will know.

According to my old Herzberg, the energy, W, of the states in an applied magnetic field is W(0) + hoM, where W(0) is the energy in the field-free case and o is the Larmor precession frequency. That implies that for transitions between adjacent energy states, (i.e. for which ΔM=1,), ΔW = ho = hν, i.e. the microwave frequency of the emitted or absorbed photon is the Larmor precession frequency.

I'm not sure if this deals with your query, but maybe it's a start.

James R , you will see I think there could in fact be some microwave radiation emitted when the field is applied, as the population of atoms relaxes into a Maxwell-Boltzmann distribution. However I think I recall that the Einstein transition probability for spontaneous emission goes up with the cube of frequency, so it may be that for emission in the microwave region this is something that can be neglected, i.e. the relaxation will be predominantly non-radiative.

 

For atom the dominating magnetic dipole moment can come e.g. from angular orbital momentum - in which case shouldn't Larmor precession be of angular momentum direction?

For any (also macroscopic) magnet in external magnetic field there is τ=μ×B torque leading to precession, what means oscillating dipole - type of antenna, radiating energy with power as the above formula ... until reaching the lowest energy state: μ×B=0 having minimal kinetic terms.

 

See my reply on the other forum. To avoid duplication I won't repeat it here, but will wait to see what James has to say first. (He's the only person active here who will understand this stuff.)

 

According to my old Herzberg, the selection rule is ΔM= 0, +/-1. In EPR, such transitions are stimulated by microwave radiation. But as I say, I am doubtful they occur spontaneously at any significant rate, due to the low frequency of microwaves and the ν³ dependence of transition probability for spontaneous emission.

 

Indeed this is not perfect alignment, but often quite good - e.g. in Stern-Gerlach, measurnment, ferromagnets.

I was pointed recent very nice article "Phenomenological theory of the Stern-Gerlach experimen" by Sergey A. Rashkovskiy with very detailed calculation of the alignment time getting ~10^-10s for Stern-Gerlach with atoms: https://www.preprints.org/manuscript/202210.0478/v1

Instead of radiation, he directly uses formula for magnetic dipole in external magnetic field:

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My very approximated evaluation from radiation of abundant energy suggested a few orders of magnitude fasted alignment - bringing very interesting question if they are equivalent, how does energy balance looks above (?)

Anyway, this is another confirmation that classical magnetic dipoles in external magnetic field have tendency to align in parallel or anti-parallel way.
This "classical measurement" is deterministic and time-reversible: if recreating reversed EM, in theory one could reverse the process ...

What is nonintuive here is that such EM radiation carrying energy difference here seems different than in "optical photon", might be delocalized (?).

The big question is the minimal size to be able to apply this "classical measurement" - minimal size of such magnet: a million atoms? Thousand atoms? Single atoms? Electron?
Experimentally in Stern-Gerlach they observe the same conclusion, such alignment is also well known for electrons (e.g. https://en.wikipedia.org/wiki/Sokolov–Ternov_effect ), for which they observe both Larmor precession, but also much more complex acrobatics in EM field: spin echo ( https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#Pulsed_electron_paramagnetic_resonance )
So where is the classical-quantum boundary here?

 

Right.

You have a (spin-)symmetric beam of atoms passing through a fixed magnetic field, which splits the beam and breaks the symmetry.
But what is measuring what? Can you say the magnetic field is measuring the spins of individual atoms?

Since there is clearly a change of momentum for the two beam halves, where does this come from?

 

Regarding what is measuring what, I would say external magnetic field is measuring magnetic dipole moment - enforcing it align zeroing torque.
Regarding statistics, this article has interesting calculations: https://www.preprints.org/manuscript/202210.0478/v1
E.g. spin statistics after various normalized times:

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Regarding change of momentum, the process of magnetic dipole alignment definitely changes energy - initially there is excessive kinetic energy of precession, after alignment it is reduced.
Spin has usually associated angular momentum - also changed during alignment.
Conservation laws like Noether say these differences should be compensated e.g. with EM wave:

excited atom <-> deexicted atom + EM wave carrying energy, momentum and angular momentum as optical photon
unaligned spin <-> aligned spin + EM wave carrying energy, momentum and angular momentum

In the latter case we have kind of cylindrically symmetric antenna - which might produce cylindrically symmetric EM wave, not localized like optical photon (?)

 

Well, there is an exchange between the field and the atoms.

My understanding of it is that each atom exchanges the equivalent of a photon's worth of energy, but this isn't seen because it's a part of the overall spin measurement.