Spin (physics)

Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.

Possible values are half integer numbers: 0, 1/2, 1, 3/2, and so on.

The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.

Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:

Originally done with (neutral) silver atoms in 1921, but even clearer theoretically was the hydrogen reproduction in 1927 by T. E. Phipps and J. B. Taylor.

The hydrogen experiment was apparently harder to do and the result is less visible, TODO why: physics.stackexchange.com/questions/33021/why-silver-atoms-were-used-in-stern-gerlach-experiment

Needs an inhomogenous magnetic field to move the atoms up or down: magnetic dipole in an inhomogenous magnetic field. TODO how it is generated?

Basic component in spintronics, used in both giant magnetoresistance

I like relativistic quantum mechanics.

Best mathematical explanation: Section "Spin comes naturally when adding relativity to quantum mechanics".

Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles" has an amazing summary of the preceding chapters the spin value has a relation to the representations of the Lorentz group, which encodes the spacetime symmetry that each particle observes. These symmetries can be characterized by small integer numbers:

Bibliography:

Leads to the Klein-Gordon equation.

Leads to the Dirac equation.

Leads to the Proca equation.

Theorized for the graviton.

More interestingly, how is that implied by the Stern-Gerlach experiment?

physics.stackexchange.com/questions/266359/when-we-say-electron-spin-is-1-2-what-exactly-does-it-mean-1-2-of-what/266371#266371 suggests that half could either mean:

Initially a phenomenological guess to explain the periodic table. Later it was apparently proven properly with the spin-statistics theorem, physics.stackexchange.com/questions/360140/theoretical-proof-of-paulis-exclusion-principle.

And it was understood more and more that basically this is what prevents solids from collapsing into a single nucleus, not electrical repulsion: electron degeneracy pressure!

Bibliography:

The name actually comes from "any". Amazing.

Can only exist in 2D surfaces, not 3D, where fermions and bosons are the only options.

All known anyons are quasiparticles.

On particle exchange:so it is a generalization of bosons and fermions which have $\theta =0$ and $\theta =\pi$ respectively.

Key physical experiment: fractional quantum Hall effect.

Exotic and hard to find experimentally.

Video "The Biggest Ideas in the Universe | 17. Matter by Sean Carroll (2020)" at youtu.be/dQWn9NzvX4s?t=3707 says that no one has ever been able to come up with an intuitive reason for the proof.