[1] https://www.feynmanlectures.caltech.edu/II_36.html
[2] This intuition debunks many types of incorrect "infinite energy of magnets" ideas that lead to perpetual motion. Although it can't debunk the "perpetual motion solely from an uneven static (electromagnetic or gravitational) field" idea, which is even older.
Spin is a type of intrinsic angular momentum that is not associated with any spatial motion.
The Feynman lecture you linked to is an explanation why currents fail to explain ferromagnetism. You need to read the next chapter, but being a lecture for undergrads, it doesn't go deep into the subject anyway. If you're really interested, any modern book on magnetism would be much helpful.
> Ferromagnetism has nothing to do with currents
This is why I said ferromagnetism is circulating current in the sense of "to a first approximation" and "heuristically". Wiktionary defines "heuristic" to be:
> a practical method [...] not following or derived from any theory, or based on an advisedly oversimplified one.
I think that if you ask Feynman, he would probably agree or sympathize with the naive idea of "atomic currents" as a heuristic argument in the introduction of this topic... which is nothing new anyway, and has been a heuristic argument used in electromagnetism for a long time, at least before QM.
In Feynman's own words,
> These days, however, we know that the magnetization of materials comes from circulating currents within the atoms—either from the spinning electrons or from the motion of the electrons in the atom. It is therefore nicer from a physical point of view to describe things realistically in terms of the atomic currents [...] sometimes called “Ampèrian” currents, because Ampère first suggested that the magnetism of matter came from circulating atomic currents.
You said,
> Spin is a type of intrinsic angular momentum that is not associated with any spatial motion.
Yet the concept of spin in quantum mechanics was originally developed using macroscopic rotations as an analogy, although today we know that spin is an intrinsic property of subatomic particles (thus the joke, "Imagine a ball that is spinning, except it is not a ball and it is not spinning.") In the same sense that Ampère's concept of "atomic currents" was developed using circulating electric current as an analogy.
> The Feynman lecture you linked to is an explanation why currents fails to explain ferromagnetism. You need to read the next chapter.
Of course, "The actual microscopic current density in magnetized matter is, of course, very complicated." This is surely explained in the next chapter. I could've mentioned "atomic currents" without citing any link, but I included it to allow anyone who's interested to read the whole thing in context.
You read some Wikipedia pages and Feynman lectures of physics. I'm a physicist who has done well over a decade of research in magnetic materials.
In understanding of ferromagnetism, many incorrect theories have been proposed. By connecting ferromagnetism to circulating currents (i.e, paramagnetism and diamagnetism), you just repeated the same mistake.
You're trying to bend the words to avoid being wrong. Physics is not philosophy or debate club. There is no approximation in physics in which electron is a ball with some radius, or its spin is due to a circulating current in physics. Any such explanation attempt fails spectacularly if you actually try to do the math (which gives an electron surface that is moving faster than speed of light, as Uhlenbeck/Goudsmit who proposed this incorrect idea quickly found out), so it doesn't even work as an approximation of any kind.
> Yet the concept of spin in quantum mechanics was originally developed using macroscopic rotations as an analogy,
Who developed this theory in quantum mechanics, where and when? Pauli, who first introduced it into quantum mechanics and the namesake of spin 1/2 matrices, insisted that it is purely quantum mechanical with no classical analogue. And regardless of who said what over 100 years ago, today, it is well understood that spin has nothing to with electric charges that move or rotate in space.
More importantly, the reason ferromagnetism develops in the first place is due to exchange interaction (as I wrote above) between magnetic moments, which is due to Pauli exclusion principle and also has nothing to do with movement of charges.
Furthermore, such magnetic moments (called magnetic impurities in that context) ruin the superconducting order by breaking the time-reversal symmetry, so trying to make a connection to ferromagnetism in the context of superconductivity is even worse.
In the same way that a geodesist navigates using a reference ellipsoid defined by WGS-84, while a city commuter uses Cartesian coordinates on a flat map. The commuter's navigational tool will never work in geophysics research, and it doesn't need to be.
> To the parent and its sibling comments: There is no atomic or subatomic current that can explain ferromagnetism in any approximation. [...] Any such explanation attempt fails spectacularly if you actually try to do the math (which gives an electron surface that is moving faster than speed of light, as Uhlenbeck/Goudsmit who proposed this incorrect idea quickly found out), so it doesn't even work as an approximation of any kind.
I consider "circulating currents create ferromagnetism" to be as true as "an atom's structure is similar to a solar system." Both concepts break down when it's examined in details, so its use by research physicists is obviously unacceptable, but I consider it's nevertheless as an useful mental image in introductory discussions among non-physicists.
Would you consider Rutherford's original atom model to be a first approximation? Can it be considered a very oversimplified but useful heuristic, at least when people who know anything about atoms are first introduced to this concept? Alternatively, would you consider Rutherford's atom to be "an explanation attempt that fails spectacularly if you actually try to do the math (which gives an electron that collapses into the nucleus in picoseconds, as Rutherford's colleagues quickly found out)?
If you believe the latter case, everyone can stop this conversation right now. Because it means the entire disagreement is entirely down to what kinds of "metal images" are acceptable, rather than any factual, like "whether a full quantum treatment of ferromagnetism is necessary to completely explain ferromagnetism (of course it is)." The rest of us who don't solve research problems believe a toy model is still interesting, but don't deny (nor mention) better models. You, as a professional physicist, believe many "what if?" metal models from history are just not legitimate physics, and should not be mentioned at any circumstances to avoid poisoning the minds of youths - an approach known as Whig history, in which scientific progress marches from one victory to another, and all losers be damned - a perfectly valid approach for teaching physics to students who only care about pure physics science, instead of "who said what."
As a side note, I know some engineers who really hate the idea that electric circuits works due to an electron flow. The most extreme one I've seen of wanted to ban this concept in introductory textbooks, calling it a big lie (an explanation attempt that fails spectacularly if you actually try to do the math, which gives the speed of an electron 30 billion times slower than the speed of light in free space). As we all know, the steady-state electron flow was only a result of the transient propagation and reflection of electromagnetic waves in free space or dielectric materials. Thus, they believe the wave model should be the only interpretation in a science textbook, since "they're high-school teachers, I'm a design engineer who work with high-speed digital systems with 20 years of experience, and I know for sure that high-speed circuits and computers can't even be made functional if you ignore fields and transmission line effects." Meanwhile, I believe the electron flow model still works as an introductory mental image (although the field view perhaps needs to be mentioned earlier).
> Who developed this theory in quantum mechanics, where and when? Pauli, who first introduced it into quantum mechanics and the namesake of spin 1/2 matrices, insisted that it is purely quantum mechanical with no classical analogue.
The earlier "electron as a rotating ball" idea was considered by Ralph Kronig and Uhlenbeck-Goudsmit in 1925. Pauli personally never accepted it due to its unphysical flaws. Only in 1927 did Pauli publish a rigorous QM treatment. Thus, "electron spin using classical rotation as analogue" was still an intermediate step before establishing this concept in QM. It was a footnote in history since Pauli was a great physicist and already considered the problem himself earlier and found the solution before everyone else. Otherwise this intermediate step may last longer than 2 years.
> Furthermore, such magnetic moments (called magnetic impurities in that context) ruin the superconducting order by breaking the time-reversal symmetry, so trying to make a connection to ferromagnetism in the context of superconductivity is even worse.
This, in comparison, is a more interesting criticism.
In its original sense, an electric current is any kind of movement of electric charge. In this wide sense, it also applies to the source of ferromagnetism.
Its meaning can be restricted to refer to the translational movement of electrically charged particles. With this narrower sense, there is still no need to use quantum mechanics to explain ferromagnetism. Even in classical electromagnetism, with the narrower-defined current, the sources of magnetic fields are decomposed into distributions of electric current densities and of magnetic moment densities, where the latter are the source of ferromagnetism. If necessary, it is possible to also use distributions of higher-order moment densities and the series of moments when the "electric current" is used in the narrow sense (of a first order moment) corresponds to the "electric current" used in its original, wide sense.
The isolated sentence "Spin is a type of intrinsic angular momentum that is not associated with any spatial motion" is logically contradictory (because, by definition, angular momentum is a characteristic of moving bodies). It can be correct only when you first specify that by "spatial motion" you mean only a certain kind of spatial motion.
The joke mentioned by another poster "Imagine a ball that is spinning, except it is not a ball and it is not spinning" is just a joke, because there is no doubt that the elementary particles are spinning.
Even when you model the elementary particles in the standard way, as point-like bodies (and it is debatable whether this is a good model), you cannot say that they are not rotating, because this would be the same mistake as saying that a delta distribution has a null value in the origin.
On the contrary, while you cannot say other things about the value of a delta distribution in the origin, what you can say with certainty is that it is not null.
In the same way, while you cannot say anything about characteristics of an electron like radius, mass density, angular velocity, electric current density and so on, you can say with certainty the values of various integral quantities (which integrate the corresponding delta distributions), like mass, electric charge, angular momentum and magnetic moment, so you can say with certainty that any electron is rotating (i.e. it has a non-null angular momentum).
I’ll add that the Dirac equation (governing electron field) correctly predicts magnetic moment given the inputs of charge and mass. * I interpret this as indicating that magnetic moment is a derived phenomenon just as it would be in the classical picture of a spinning ball of charge; I.e. the quantum picture refines but does not totally discard the classical understanding.
* Well, technically, sympathetic vibrations with all the other standard model fields also make tiny contributions to the magnetic moment.
If you wouldn't mind reviewing https://news.ycombinator.com/newsguidelines.html and taking the intended spirit of the site more to heart, we'd be grateful.