Wondering if anyone could recommend a layman's introduction to "spin". I've read the Wikipedia article, I broadly understand it, but just curious as to how it was discovered, why it is considered an "intrinsic" form of angular momentum, and why it is so fundamental a concept in our universe.
I like Physics from Symmetry by Jakob Schwichtenberg as an explanation of how spin arises from a modern understanding of physics. The book was written while the author was a Masters student, and so it is much closer to the way an undergrad physics student would explain it to another student. The author is willing to skip details in favor of more general understanding.
The way the book will describe it is from the perspective of group theory. If you assume that the laws of nature in a relativistic flat spacetime do not change under rotations, translations (in both space and time), and boosts (transformation between frames of reference of constant velocity), then these transformations define a Lie group called the Poincaré group. Representation theory then says that the representations of the Poincare group are characterized by two numbers. These two numbers are identified as a nonnegative mass and a spin. One interpretation is that these representations are indeed what "particles" are in Quantum Field Theory.
Objects with spin can be point-like but carry angular momentum. The electron is one such particle.
It is "intrinsic" because it has no known moving parts. If it had moving parts, and that motion had net angular momentum, we would refer to it in many contexts as "orbital angular momentum".
Spin should seem counterintuitive. There are no macroscopic objects that I am aware whose spin you can feel with your hands. Our research group has an object with 10^23 polarized spins (and negligible net magnetic moment) -- observing the angular momentum effects directly requires a sensitive modern torsion balance. https://arxiv.org/abs/0808.2673
It's totally counterintuitive. Classical angular momentum requires a choice of origin. All angular momentum is then relative to that origin. Any point particle lying at the origin should not be able to have any angular momentum.
Imagining the classic "figure skater experiment", the figure skater speeds up as she draws her arms inward, due to conservation of angular momentum. If she could shrink down to a point, her angular speed would tend to infinity. This is what I imagine happening to a black hole.
You need not worry about infinity in the black-hole case. Known physics ends at the black hole's event horizon, for an external observer. Black holes of a given mass can only have so much angular momentum.
As a rule of thumb, that angular momentum corresponds to that at which the equator of the black hole is moving at the speed of light.
This has important consequences for the mergers of two high-spin black holes that have aligned spins. The merger is actually delayed for a little while, just before merger, as the binary dumps angular momentum through gravitational radiation.
Excitations can carry dynamical properties. For example, jerk a rope once, and you will see a wave travel down the rope, which carries energy and momentum. If you give the rope a quick twist, the wave carries angular momentum.
I have the same problem with this analogy. The rope itself is just excitations of a quantum field. It feels like there is very little underpinning everything.
Magnetic moments, for the (essentially all) particles that have them are aligned parallel to the spin axis, as there isn't any other axis in the problem, but that doesn't mean that there is a direct link between magnetism and spin.
One example: Neutrinos have just as much spin as electrons, but they have not yet been observed to have magnetic moments.
It is true that most magnets get some, if not all, of their magnetism from polarized electrons. We often state that the magnetism comes from "spins", as it is an effective shorthand, but it is not strictly correct. Some magnets get substantial amounts of magnetization from orbital magnetic moments of electrons (SmCo_5, for example).
Furthermore, one can create a magnetic field simply by moving an electric charge. From that perspective, a magnetic field is consequence of combining special-relativity with electrostatics.
We know a lot, but there is so much more left to learn.
It was called spin because for a time the model of an electron was a solid sphere of charge that was spinning on its axis. It was known that the electron made a magnetic field, and since charge in motion makes a magnetic field that could be explained by a spinning electron. But if you actually do the math you'll be off by a factor of about two. Quantum mechanics had to be invented to explain this discrepancy and the name stuck.
I recommend reading about the Stern Gerlach experiment. I think that nails down what makes spin counterintuitive, and is a really clear example of how the predictions of quantum mechanics can't come from classical mechanics. The fundamental nature of it and the units can be reasoned out by looking at conservation of angular momentum.
Typically, angular momentum is just linear momentum plus an attachment. Imagine two weights spinning around each other in a circle, tied together with a rope. At a moment in time, each weight has some linear momentum, each in the opposite direction. The system has angular momentum because part of it has linear momentum in one direction and another part has linear momentum in another direction. In classical mechanics, it's all like that, with different pieces in different locations moving in different directions. But with a particle, there's only one piece. If it has angular momentum, it's gotta be a property of that piece, instead of the more emergent property of a system made of multiple pieces. Hence "intrinsic."
