Why don't spinning protons stop?

Question

The Bohr model in which electrons orbit a nucleus can be shot down quickly on the grounds that the electron would have to be accelerating in order to stay in an orbit, an accelerating charge radiates EM, and the loss of energy as EM would cause the orbit to decay.

Then I read about the magnetic dipole moment of the nucleus and it always seems to get explained by someone with one foot on each side of the QM/classical divide - the protons and neutrons have spin, hence in many cases the nucleus has spin, and a spinning charge generates an MDM. Fine, except that implies that the spinning charge is moving in a circle, rather than being associated with a quantum number that happens to be called spin. That would mean it's accelerating, which means it should be radiating EM and collapsing.

My understanding of QM stops somewhere around solving Schroedinger's equation, but this particular problem is bugging me. Is it explainable without diving into QFT?

Answer 1

The following

the spinning charge is moving in a circle (hah), which means it's accelerating,

would be true in the Newtonian sense, because mechanical moving and acceleration are Newtonian concepts. In QM, they are not applicable*. Instead, objects are only eligible to be in possible eigenstates of the system, and dynamics happens by transition of states.

At the beginning, when the presence of magnetic moment in point particles, quantum spin, was 'out of the world' discovery, theories at hand were utilized to explain and model the phenomenon. Just like the charge of a particle is expressed by means of $\mathrm{e}$, Bohr magneton $\mu_B$ was suggested to serve similar role to standardize magnetic moment of particles. Bohr magneton is obtained via Amperian loop model, in which the magnetic field is generated by a current loop (often identified as a simple circle), per Ampere's circuital law. And of course, the current is thought of as 'moving' charge, because that's what was in hand.

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*unless in the case of the correspondence principle, which states that collection of sufficiently large amount of quanta will eventually behave in accordance with classical mechanics.

Answer 2

For historical reasons, an acceptance of the electron and the proton (as well as their antiparticles) as a duality of magnetic dipole and electric charge seems unthinkable. We are talking about electric charges and this terminology alone displaces the possibility to consider these subatomic particles also as magnetic dipoles (without any need of explanation of their cause).

The magnetic moment is a constant quantity just like the charge (see the fundamental physical constant of the electrons magnetic moment). One can always try to find an even deeper explanation behind a phenomenon. But an explanation of the magnetic moments of the subatomic particles brings in my experience no additional knowledge gain. The historically assumed circular currents are not comprehensible by any observation.