# Quantization of magnetic coupling instead of quantization of angular momentum?

In quantum mechanics - e.g. the Bohr model - would it be possible to replace the quantization of angular momentum with quantization of the magnetic properties of the orbiting electrons?

E.g. also the spin property of an electron is essentially a magnetic property and it's quantization may be understood as a quantization of that magnetic property.

EDIT: According to Emilio Pisanty (see his answer) this is a misconception.
However. The Einstein-de Haas demonstrates that spin angular momentum is of the same nature as classical angular momentum (which I btw did not disagree on), but also that the magnetism of the material is related to a certain angular momentum. And that is one reason why I am asking this question (the other reason being orbital angular momentum).
Maybe saying spin is essentially a magnetic property is misleading. It was not my intention to contradict that spin represents angular momentum, but I tried to stress that its angular momentum is always connected to magnetism.
Or perhaps better: spin and magnetism are both connected to angular momentum in such a way that you will never have spin without magnetism.

I never heard of a neutral particle orbiting anything. Were that the case, then indeed quantization of angular momentum would be leading.

Otherwise it seems to me that it must be equivalent to speak of quantization of magnetism instead of quantization of angular momentum?

A possible advantage would be that by not stressing the angular momentum, it becomes more easy to let go of the naive popular picture of a model similar to the structure of the solar system.

Do you know of any arguments against this opinion?

• Perhaps interesting physics.stackexchange.com/q/320710 – HolgerFiedler Jul 14 '17 at 4:06
• – HolgerFiedler Jul 14 '17 at 4:08
• @HolgerFiedler apart from the angular momentum part, it looks like the same question ... maybe when I find some extra time I will take a look at your papers – Gerard Jul 14 '17 at 14:42

This is pretty much completely wrong:

the spin property of an electron is essentially a magnetic property.

The spin of any particle is the generator of the rotation group on the particle's state space and its quantization is directly due to the properties of the Lie algebra of the rotation group. As such, the spin of the particle is the conserved quantity that's associated with the rotational invariance of its dynamics, i.e. the quantity that's otherwise known as angular momentum. Moreover, as the Einstein-de Haas effect shows, it is very much interchangeable with plain old mechanical angular momentum.

Now, spin also plays a role in that the coupling to an external electromagnetic field includes a term of the form $$H_\mathrm{mag} = g\mu \mathbf S\cdot\mathbf B,$$ but that's actually much less surprising than it looks: because of its symmetry properties (i.e. time-odd pseudovector), the spin is constrained with the types of quantities that it can couple to (i.e. other time-odd pseudovectors), which in the case of an external electromagnetic field turns out to be the magnetic part of the force field. However, that's got much more to do with the fact that the magnetic field is a rather 'rotation-y' property of the external field (so it can then couple to the rotation properties of the particle) than with the spin being a magnetic property.

• Ok. I completely overlooked these facts. Do you think that the idea is valid (in principle) for angular momentum sec, without considering spin? – Gerard Jul 14 '17 at 14:35
• Question in between: are there also other time-odd pseudovectors force fields that do not belong to magnetism? – Gerard Jul 14 '17 at 14:41
• @Gerard Your first comment is barely grammatical (sec?), but if you're asking whether the answer changes if you change 'spin' for a general angular momentum: obviously not, and for the same reasons as already stated. – Emilio Pisanty Jul 14 '17 at 14:48
• On your second comment: yes, many. Angular momentum, for instance. And on the implied question (does posting an answer mean that I'm interested in a protracted back-and-forth discussion?), the answer is no. – Emilio Pisanty Jul 14 '17 at 14:49
• Another question. People have always found it puzzling that a neutron has a magnetic moment. So the idea of rotation+electrical charge has always been around regarding the spin property. I understand that the underlying quark-model has solved this puzzle. Doesn't this show that spin is conceptually coupled to rotation+charge? Just asking. – Gerard Jul 14 '17 at 14:53