Intuitive

One of the biggest discoveries in the last century was that elementary particles have spin, which is some kind of internal angular momentum. This was discovered by the famous Stern-Gerlach experiment.

In abstract terms you can think about spin as a label that tells us how particles behave in experiments, exactly as the mass or the electric charge. For example, a particle with electric charge behaves different than one without in experiments and the same is true for spin.

There are particles with spin $0$, particles with spin $\frac{1}{2}$ and particles with spin $1$. For each of these different particle types we have a different equationthat describes their behavior.

• Spin: The Quantum Property That Should Have Been Impossible by Paul Halpern
• https://www.scientificamerican.com/article/what-exactly-is-the-spin/
• https://www.forbes.com/sites/startswithabang/2017/11/21/spin-the-quantum-property-that-nature-shouldnt-possess/#20a3df076349

Concrete

Spin is a quantum number like mass or like the electric charge. Spin has exactly the same origin as the other quantum numbers and is therefore not as strange as most people believe it to be.

The origin of Spin

Noether's famous theorem states that there is a conserved quantity for every symmetry of the Lagrangian. An interesting subtlety of this theorem is that the corresponding conserved quantity in field theories has two parts. Only the sum of them is conserved.

One part is a result of invariance under transformation of the spacetime coordinates, and the second part is a result of the invariance under mixing of the field components.

If we consider invariance of a field under rotations, we therefore get a conserved quantity that consists of two parts. One part is a result of the rotation of the coordinates. This quantity is what we call orbital angular momentum. The second part is a result of the mixing of the field components under rotations and is what we call spin.

For some further details, see basic_notions/spin.txt · Last modified: 2019/11/29 13:13 by 129.13.36.189