﻿ International Physics Masterclasses

## Spin

In addition to mass and electric charge, which you have encountered so far, particles have a fundamental property called spin. Spin is a pure product of quantum mechanics with far reaching spin-offs in modern technologies and information processing. Spintronics or spin electronics exploits spin properties instead of or in addition to electric charge, thus offering devices with a greater diversity of functionality: media storage, quantum computation, to name only those.

So what is spin? To understand this, we must first introduce the concept of angular momentum. Angular momentum is a vector quantity, which is to rotational motion what the momentum is to linear motion. In classical mechanics, the angular momentum can consist of both orbital motion (like the annual revolution of the Earth around the Sun) and "spin" (like the daily rotation of the Earth about the north-south axis). In analogy with the classical theory, spin is introduced as the intrinsic angular momentum of a fundamental particle. Since one cannot imagine that a point-like particle rotates in the same way as the Earth rotates, the classical analogy should not be pushed too far.

In a simplified wording, spin has to do with what the particle at rest looks like from different directions. In everyday life it is possible to rotate an object and study its degree of (an)isotropy. This is not the case in the microworld, especially when dealing with point-like particles. Emphasis is then put on the behaviour of particles and characterisation of their intrinsic properties, including spin.

In particle physics, we rely on the decay products of short-lived particles to determine their spin. Angular momentum is a conserved vector quantity analogous to momentum. A vector quantity needs both magnitude (vector length) and a direction. Electric charge, mass and temperature are called scalar quantities, as magnitude is sufficient to characterise them.

Quantum mechanics assigns definite spin values, in discrete chunks, to particles, which fall into 2 categories. Fermions possess half-integer spin (1/2, 3/2, 5/2, ...). Bosons have integer spin (0, 1, 2, ...). Let us discuss the ones familiar to us. Particles making up matter (leptons, quarks, protons, neutrons) are fermions with spin 1/2. The force particles and the Higgs particle are bosons. The photon, gluon, W and Z are spin-1 bosons. The Higgs is a spin-0 boson.

Fermions and bosons have opposite collective behaviours. Bosons are social particles in the sense that identical bosons, with exactly the same properties can occupy the same state. The principle of lasers is due to that a large number of photons can share the same state. Fermions are solitary particles, subject to the exclusion principle: no 2 identical fermions can be found in exactly the same state. This explains the periodic table of elements and all of chemistry.