1) Spin is an

**empirically** observed property of the way phenomena (specific particles) are observed to behave. So what it

**is** is a question about fundamental reality which I classify as metaphysics — being trained in physics, I will restrict myself to how it

**behaves**. One way it behaves is Thomas precession which in 1925 explained why hydrogen atoms with electron and proton with aligned spins had precisely the energy separation they do from the case with anti-aligned spins.

https://en.wikipedia.org/wiki/Spin–orbit_interaction
2) Newton didn't describe

**angular momentum** or energy, those conserved quantities were discovered by others, but the conservation laws appear to be fundamental and can be proved as theorems of classical or relativistic physics. According to Noether, that goes hand-in-hand with the physics of the universe having rotational symmetry and time-translation symmetry, respectively.

3)

**Quantum mechanics** gives a view on the behavior of things where complex numbers finally become not just clever mathematical tricks but pretty vital to physical models. Probability requires the sum of probabilities of all possible outcomes to be 1. Since quantum mechanics describes probability as the square of the modulus of a complex number, quantum mechanics requires a property called

**unitarity** to ensure the sum of probabilities of all possible outcomes does not change from 1.

4) When you combine the ways of describing inertial frames in

**special relativity**, the freedom to choose the origin of the coordinate system (

**4 time and space translations**), the freedom to choose the orientation of a right-handed spatial Cartesian coordinate system (

**3 spatial rotations**), and the freedom to choose a standard of rest or equivalently to pick out a time-like direction of the time axis (

**3 Lorentz boosts**) and relate all 10 degrees of freedom together you get the full inhomogeneous Lorentz group, which is commonly called the

**Poincaré group**. This is the symmetry group of flat space-time according to special relativity. Weird things happen when you combine boosts and rotations in 3 spatial dimensions and that's a Thomas-Wigner rotation.

5) In 1939, Wigner combined special relativity and quantum mechanics and wrote out all the

**unitarity representations of the Poincaré group**. That is he established what things could exist in a physics which respected both unitarity and the Poincaré group. So for particles with m > 0 we have those with integral and half-integral intrinsic angular momentum. In other words,

**spin is as fundamental as special relativity or quantum mechanics**. It is incorrect to assign spin to any internal motion because we have neither the empirical evidence of such motion or the physics to relate such internal motion to observable behavior.

**Spin is intrinsic angular momentum of quantum particles**.

6) Finally, the

**spin-statistics theorem** says particles (in 3-dimensional space) says particles with half-integral spin act like fermions, while particle with integral spin act like bosons which relates to the stability of matter and thermodynamics, tying fundamental particle physics to the lives and deaths of stars.

Since we can't take spin apart and examine it in any physics we have, we use it (along with mass and couplings to other particles, like electric charge) to classify particles. Because of Wigner's classification, unlike mass in the Standard model, intrinsic angular momentum is likely to remain as fundamental in our descriptions of the behavior of things unless some new theory completely overturns our understanding encapsulated in special relativity and/or quantum mechanics. In fact, spin-networks and spin foams have been raised as candidates to try and explain space-time itself, which would make spin more fundamental than the idea of distance. Heh heh.