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

[Duda Jarek]

5 hours ago, exchemist said:

No, that is wrong for this situation, because it is a bound system and therefore quantised. I pointed out to you earlier that electrons in atoms do not radiate and fall into the nucleus.

But excited atoms radiate abundant energy - getting to the lowest energy: ground state?

So why shouldn't unaligned spin radiate abundant kinetic energy - getting to the lowest energy: aligned spin? ... especially that this is exactly what they observe in Stern-Gerlach ... and EM says that oscillating dipoles should radiate energy.

5 hours ago, exchemist said:

Forget brehmsstralung. It's irrelevant. That is for free, i.e. unbound, particles.

Indeed, and in Stern-Gerlach we have free unbounded objects - having magnetic dipole, in external magnetic field - as also e.g. electrons in synchrotron radiating energy as EM waves.

4 hours ago, swansont said:

Yes, this is what I asked you about. How did you arrive at this conclusion? I want your reasoning, not just a repetition of the statement.

Magnetic dipole in external magnetic field gets torque - Larmor precession ... rotating dipole creates varying EM fields - like antenna radiating energy as EM waves, of power given by the used formula.

4 hours ago, swansont said:

But other effects are not classical (the deviation of the beam), so why should the alignment be classical? The discrete deviation is an indication that you do not have randomly-aligned spins that come into alignment over some period of time.

Larmor precession comes from torque - works in all scales: from electron to macroscopic magnets.

For non-polarized beam, the original direction of magnetic dipole is random, the final in Stern-Gerlach is aligned in parallel or anti-parallel way - exactly as we would expect for a classical magnet in external magnetic field.

[exchemist]

4 hours ago, Duda Jarek said:

But excited atoms radiate abundant energy - getting to the lowest energy: ground state?

So why shouldn't unaligned spin radiate abundant kinetic energy - getting to the lowest energy: aligned spin? ... especially that this is exactly what they observe in Stern-Gerlach ... and EM says that oscillating dipoles should radiate energy.

Indeed, and in Stern-Gerlach we have free unbounded objects - having magnetic dipole, in external magnetic field - as also e.g. electrons in synchrotron radiating energy as EM waves.

Magnetic dipole in external magnetic field gets torque - Larmor precession ... rotating dipole creates varying EM fields - like antenna radiating energy as EM waves, of power given by the used formula.

Larmor precession comes from torque - works in all scales: from electron to macroscopic magnets.

For non-polarized beam, the original direction of magnetic dipole is random, the final in Stern-Gerlach is aligned in parallel or anti-parallel way - exactly as we would expect for a classical magnet in external magnetic field.

Atoms "radiate abundant energy" is irrelevant, as well as being untrue. Atoms in the ground state do not and cannot radiate energy. This flatly contradicts the predictions of classical EM theory. That is one of the chief reasons why QM was developed. 

But you seem to adopting a wild, scattergun approach to this topic now. Unless you can stick to the point it will soon become a waste of time discussing this with you. 

[Duda Jarek]

13 minutes ago, exchemist said:

Atoms "radiate abundant energy" is irrelevant, as well as being untrue. Atoms in the ground state do not and cannot radiate energy.

Excited atoms have tendency to deexcite - releasing abundant energy as EM wave (photon), through dynamics of electrons in e.g. electric potential of the nucleus.

The ground state e.g. of hydrogen is just the lowest energy state for proton+electron. In theory they could be taken closer down to zero distance (->neutron), but it would require investing ~782keV energy. This kind of orbit quantization is also observed in hydrodynamical QM analogs, e.g. double quantization: https://www.nature.com/articles/ncomms4219 - of distance R and angular momentum Lz:

The discussion indeed starts going in circles, and I don't think I understand the problem.
So do you agree classical magnet would precess in external magnetic field?
That rotating, oscillating dipole radiates energy as EM wave like antenna?
That radiating all the energy such classical magnet would align in parallel or anti-parallel way?
That this is the same conclusion as observed in Stern-Gerlach?
Do you have an alternative explanation of such alignment in Stern-Gerlach?

Alignment known also e.g. in NMR: https://www.cis.rit.edu/htbooks/nmr/chap-3/chap-3.htm

Quote

When a group of spins is placed in a magnetic field, each spin aligns in one of the two possible orientations

 

[exchemist]

25 minutes ago, Duda Jarek said:

Excited atoms have tendency to deexcite - releasing abundant energy as EM wave (photon), through dynamics of electrons in e.g. electric potential of the nucleus.

The ground state e.g. of hydrogen is just the lowest energy state for proton+electron. In theory they could be taken closer down to zero distance (->neutron), but it would require investing ~782keV energy. This kind of orbit quantization is also observed in hydrodynamical QM analogs, e.g. double quantization: https://www.nature.com/articles/ncomms4219 - of distance R and angular momentum Lz:

The discussion indeed starts going in circles, and I don't think I understand the problem.
So do you agree classical magnet would precess in external magnetic field?
That rotating, oscillating dipole radiates energy as EM wave like antenna?
That radiating all the energy such classical magnet would align in parallel or anti-parallel way?
That this is the same conclusion as observed in Stern-Gerlach?
Do you have an alternative explanation of such alignment in Stern-Gerlach?

Alignment known also e.g. in NMR: https://www.cis.rit.edu/htbooks/nmr/chap-3/chap-3.htm

 

This may be my last post to you on this, unless you can avoid dragging other side issues into the discussion.

From what you write, I wonder if perhaps you may may suffer from one basic misunderstanding. In space quantisation of angular momentum, the angular momentum vector does not completely align with the applied field. Ever. It continues to precess (in the semi-classical picture). It is only a component of the vector that is parallel or anti-parallel to the z direction of the field. It is impossible for the angular momentum to align totally, as that would violate the uncertainty principle*. There is always a component of the vector in the x,y plane, whose orientation is indeterminate - that is the real QM meaning of the "precession". So it carries on in this state of partial alignment, without any radiation occurring.

So your analogy of a magnet oscillating, and then radiating until the oscillation ceases, does not apply. That is not what we observe in the Stern-Gerlach experiment.

 

*The operators for angular momentum along x, y and z axes do not commute. Therefore only angular momentum along one axis can be precisely defined at a time, at the expense of definition of the others.

[Duda Jarek]

I completely agree that quantum mechanically the spin alignment is never perfect, however, often is nearly perfect - e.g. in Stern-Gerlach, NMR, ferromagnets.

If you could elaborate on my questions regarding classical magnet - should it precess in external magnetic field? If so radiating energy as EM waves? Until reaching nearly perfect alignment?

[exchemist]

26 minutes ago, Duda Jarek said:

I completely agree that quantum mechanically the spin alignment is never perfect, however, often is nearly perfect - e.g. in Stern-Gerlach, NMR, ferromagnets.

If you could elaborate on my questions regarding classical magnet - should it precess in external magnetic field? If so radiating energy as EM waves? Until reaching nearly perfect alignment?

No. It is never "nearly perfect". That is bullshit. The maximum degree of alignment is determined by the uncertainty principle limitation I referred to previously and that limitation applies in any situation.

The magnitude of the angular momentum vector is √(J(J+1))h/2π, but the maximum value of its projection along the field direction is J.h/2π . This projection can have values of J.h/2π, (J-1).h/2π,.....0,..... -J.h/2π , and only those values. That is what space quantisation of angular momentum is all about.  

And no, I am not going to get into a side discussion about a piece of classical physics.   

[swansont]

9 hours ago, Duda Jarek said:

Magnetic dipole in external magnetic field gets torque - Larmor precession ... rotating dipole creates varying EM fields - like antenna radiating energy as EM waves, of power given by the used formula.

What I asked was how you came to conclusion that the power would be radiated in femtoseconds. 

 

9 hours ago, Duda Jarek said:

Larmor precession comes from torque - works in all scales: from electron to macroscopic magnets.

For non-polarized beam, the original direction of magnetic dipole is random, the final in Stern-Gerlach is aligned in parallel or anti-parallel way - exactly as we would expect for a classical magnet in external magnetic field.

But there are things that we would also expect from classical physics that don’t happen. Has anyone detected the radiation you expect? 

3 hours ago, Duda Jarek said:

Do you have an alternative explanation of such alignment in Stern-Gerlach?

The explanation is the same - two orientations are allowed. The objection is to the claim that this is a classical situation. The observed results are not what is expected of classical physics, which is why it was a groundbreaking result

[exchemist]

13 hours ago, swansont said:

Yes, this is what I asked you about. How did you arrive at this conclusion? I want your reasoning, not just a repetition of the statement.

But other effects are not classical (the deviation of the beam), so why should the alignment be classical? The discrete deviation is an indication that you do not have randomly-aligned spins that come into alignment over some period of time.

Yes. It is also worth noting that the beam splits into 2J+1 parts. So if the atom has J>1/2, you get more than two parts, something that the classical idea of little compass needles can't account for at all. 

[Duda Jarek]

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:





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%E2%80%93Ternov_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?

[exchemist]

1 hour ago, Duda Jarek said:

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:





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%E2%80%93Ternov_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?

The passage you quoted is not a classical treatment, but a QM treatment. That's what the wave function integral is about.

There is no way for a classical treatment to give you a series of beams, corresponding to discrete orientations. You would get a continuum, since all possible orientations are allowed - or just one spot if the particles had time to orient themselves with the field before exiting it.     

[Duda Jarek]

4 minutes ago, exchemist said:

The passage you quoted is not a classical treatment, but a QM treatment. That's what the wave function integral is about.

There is no way for a classical treatment to give you a series of beams, corresponding to discrete orientations. You would get a continuum, since all possible orientations are allowed - or just one spot if the particles had time to orient themselves with the field before exiting it.  

The article ( https://www.preprints.org/manuscript/202210.0478/v1 ) uses classical electromagnetism - just a magnet in external magnetic field: should not only precess, but also finally align in parallel or anti-parallel way, what can be imagined e.g. as EM radiation of abundant (kinetic) energy, or direct calculation in this article.

Please point mistake, problem in this derivation ... or if you cannot, the size boundary where it no longer works?

As classical it should work for large magnets - made from how many of atoms? A million? A thousand? ... a single atom? electron?

Experimentally it agrees also with the last two ... so where do you see the classical-quantum boundary here?

[exchemist]

5 minutes ago, Duda Jarek said:

The article ( https://www.preprints.org/manuscript/202210.0478/v1 ) uses classical electromagnetism - just a magnet in external magnetic field: should not only precess, but also finally align in parallel or anti-parallel way, what can be imagined e.g. as EM radiation of abundant (kinetic) energy, or direct calculation in this article.

Please point mistake, problem in this derivation ... or if you cannot, the size boundary where it no longer works?

As classical it should work for large magnets - made from how many of atoms? A million? A thousand? ... a single atom? electron?

Experimentally it agrees also with the last two ... so where do you see the classical-quantum boundary here?

Why do you keep saying "abundant" energy? What do you mean?

[Duda Jarek]

Ok, maybe I should use e.g. "excessive" word instead - generally a system having excessive energy (larger than minimal), has tendency to release this energy.

E.g. excited atom has tendency to release excessive energy as EM radiation (photon carrying the difference of energy, momentum, angular momentum) - deexciting to energy minimum of the ground state.

I see unaligned "classical" magnetic dipole in external magnetic field analogously - this field causes precession, which means excessive kinetic energy - which can be released through EM radiation, leading to aligned magnetic dipole without this excessive energy.

If you want more formal classical calculation, there is a deep analysis in the linked article.

 

Sure this is different description than quantum, the big question is where is the boundary?

Why cannot they be just different perspectives on the same systems? Like phonons which are both normal modes, and effects of creation operator in perturbative QFT ...

Edited January 27, 2023 by Duda Jarek

[exchemist]

25 minutes ago, Duda Jarek said:

Ok, maybe I should use e.g. "excessive" word instead - generally a system having excessive energy (larger than minimal), has tendency to release this energy.

E.g. excited atom has tendency to release excessive energy as EM radiation (photon carrying the difference of energy, momentum, angular momentum) - deexciting to energy minimum of the ground state.

I see unaligned "classical" magnetic dipole in external magnetic field analogously - this field causes precession, which means excessive kinetic energy - which can be released through EM radiation, leading to aligned magnetic dipole without this excessive energy.

If you want more formal classical calculation, there is a deep analysis in the linked article.

 

Sure this is different description than quantum, the big question is where is the boundary?

Why cannot they be just different perspectives on the same systems? Like phonons which are both normal modes, and effects of creation operator in perturbative QFT ...

What you are overlooking is that spontaneous emission has a probability that goes up with the cube of frequency. The atoms in the higher energy alignment states can't just radiate freely. The transition would involve microwave emission and the probability of this occurring spontaneously is very low, because the frequency of the emitted photons would be so low. The atoms in the higher states are trapped there, until something interacts with them to allow them to lose energy.

[Duda Jarek]

You are focusing on internal atomic physics of these atoms, but please also take a look at the classical picture e.g. in calculation of this article.

Imagine you have a nanonmagnet built of a thousand of atoms - I think you agree we can treat it as a classical magnet, so this classical calculation should be valid (?)

EM radiated energy during such classical alignment might not necessarily be localized like photons (?) - rather as EM radiation of cylindrically symmetric antenna, suggesting such EM wave might be e.g. cylindrically symmetric ... I don't know if atomic physics describes well antennas?

Now reduce the number of atoms one by one to a single atom ...

Edited January 27, 2023 by Duda Jarek

[exchemist]

28 minutes ago, Duda Jarek said:

You are focusing on internal atomic physics of these atoms, but please also take a look at the classical picture e.g. in calculation of this article.

Imagine you have a nanonmagnet built of a thousand of atoms - I think you agree we can treat it as a classical magnet, so this classical calculation should be valid (?)

EM radiated energy during such classical alignment might not necessarily be localized like photons (?) - rather as EM radiation of cylindrically symmetric antenna, suggesting such EM wave might be e.g. cylindrically symmetric ... I don't know if atomic physics describes well antennas?

Now reduce the number of atoms one by one to a single atom ...

The problem is you can't do the Stern-Gerlach experiment with a solid array of atoms. In a solid, the atoms are in a much more complex potential field. Changes to their alignment will depend on interactions with the lattice as well as any external field. You seem to think that there will be radiation from a compass needle oscillating about North position. Maybe that's right. But you are dealing with a conductor, that is with a sea of electrons in the conduction band of a metal.   

[Duda Jarek]

So please take a look in the attached article - calculations for classical magnet in external magnetic field - satisfying below equation (3), do you disagree with it?

Sure such magnet is built of atoms, but I don't think atomic physics is a proper description for antenna (?)

 

 

[joigus]

On 1/23/2023 at 5:19 PM, Duda Jarek said:

I have described classical radiation explanation leading to the same conclusion as Stern-Gerlach: of finally aligned spins.

On 1/23/2023 at 5:05 PM, swansont said:

I must have missed it. 

I made a mistake. The SG experiment is not about charged particles. It's about particles with a permanent magnetic moment. They'd better be non-charged if you want to show just the beam-splitting effect without any qE Lorentz dragging term.

Anyway, the force (classically) is a vector gradient of the effective potential energy term. You can do quantum mechanical calculations to show that --quantum mechanically--the beams split into 2S+1 levels. No purely classical calculation can give you that. The essence of this calculation is that (1) There is an inhomogeneous magnetic field in the window of the Stern-Gerlach device, and (2) the states of the particles can be described with a quantum-mechanical function that has 2S+1 distinct basis states.

Use of vector identity,

 

∇(A⋅B)=A⋅∇B+B⋅∇A+A×∇×B+B×∇A

allows you to expand,

\[ \nabla\left(-\boldsymbol{\mu}\cdot\boldsymbol{B}\right)=-\left(\boldsymbol{\mu}\cdot\nabla\right)\boldsymbol{B}-\boldsymbol{\mu}\times\nabla\times\boldsymbol{B} \]

where μ is the magnetic moment of the particles --you can think of gaseous paramagnetic Ag atoms as an example-- and B(z) is the z-dependent magnetic field inside the window.

Because the window is very small, you can do a Taylor expansion,

\[ \boldsymbol{B}\left(z\right)\simeq\left[\boldsymbol{B}\left(0\right)+z\boldsymbol{B}'\left(0\right)\right] \]

 

Because quantum mechanics of spin introduces a discrete set of states --e.g., S=1/2 has 2 states--, you can expand the incoming states with,

\[ \boldsymbol{\mu}=g\frac{\hbar q}{2mc}\left(\begin{array}{cc} 1 & 0\\ 0 & -1 \end{array}\right) \]

Use of the quantum mechanical evolution operator with,

\[ e^{-iHt/\hbar}\simeq e^{\left(\boldsymbol{\mu}\cdot\nabla\right)\boldsymbol{B}\tau/\hbar} \]

(valid only for the small time τ the particles spend inside the window), you can show that the salient states are waves deflected in momenta by amounts --S=1/2--,

\[ \triangle p_{z}\simeq\pm g\frac{\hbar q}{2mc}\boldsymbol{B}'\left(0\right) \]

So part of the beam goes up, and the other goes down.

You can see a more detailed discussion of this in David Bohm's Quantum Theory. No part of your calculation shows this. Instead, as @exchemist said, a classical situation would have the beams deflect in every other intermediate direction, as I said too.

 

Edited January 27, 2023 by joigus
Latex editing

[swansont]

7 hours ago, Duda Jarek said:

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

So…not femtoseconds.

 

[Duda Jarek]

4 minutes ago, swansont said:

So…not femtoseconds.

Indeed, while both calculations suggest alignment already for classical magnets, they seem to lead to essentially different times for such process - bringing interesting question of which is more appropriate, has better agreement with experiment.

[swansont]

5 hours ago, Duda Jarek said:

Indeed, while both calculations suggest alignment already for classical magnets, they seem to lead to essentially different times for such process - bringing interesting question of which is more appropriate, has better agreement with experiment.

There’s an experiment that’s detected the radiation you propose?

[Duda Jarek]

Radiation of linear antenna is probably detected everyday, the question is minimal size of rotating dipole to still radiate EM waves?

So what is the minimal number of atoms building a dipole, such that the radiation power formula from the first post still works?

[exchemist]

14 hours ago, Duda Jarek said:

Radiation of linear antenna is probably detected everyday, the question is minimal size of rotating dipole to still radiate EM waves?

So what is the minimal number of atoms building a dipole, such that the radiation power formula from the first post still works?

If your magnetic dipole is made of gas (though hard to see how this could be managed) you won't get any radiation. If it is made of a metallic conductor, in which the conduction band electrons are free to move within the conductor, then I suppose in theory you might, since the electron flow in a metallic conductor is more or less classical. 

Do not muddle up the two. 

 

[swansont]

A single quantum object can have its spin aligned without radiation because it was in a superposition. What you’re doing us collapsing the wave function.

The macroscopic object is not a quantum particle if its magnetic moment is not due to its intrinsic angular momentum.