Spin

An angular momentum without rotation

One more property, purely quantum

A quantum particle is not described only by its position and its energy. It also possesses an internal property, spin, which has no equivalent in classical physics. It is one of the strangest — and most important — quantities in the entire field.

A useful analogy... but a misleading one

The word "spin" (from the English to spin, to turn) suggests a little spinning top: the electron would be turning on itself like a planet. This image helps to get started, but it is wrong:

the electron is point-like (with no measurable size): it cannot "turn on itself" in the usual sense;
if the image were taken seriously, its surface would have to turn faster than light;
spin takes quantized values, impossible for a real rotation.

Spin is therefore an intrinsic angular momentum: the particle behaves as if it were turning (it has an angular momentum, it reacts to a magnetic field like a small magnet), but with nothing actually turning. It is a fundamental property, on the same footing as its charge or its mass.

Spin is quantized

Like any quantum quantity, spin takes only discrete values. For the electron (and the proton, the neutron...), measuring the spin along a direction can give only two results:

   spin "up"     ->  written  +1/2   or   |↑⟩
   spin "down"   ->  written  -1/2   or   |↓⟩

There is no intermediate value. A measured electron is either "up" or "down" — never "slightly tilted". It is this two-valued quantization that makes the electron the natural support of the qubit (the states |0⟩ and |1⟩).

Fermions and bosons

Spin separates all the particles of the universe into two families, with radically opposite behaviors:

   HALF-INTEGER spin (1/2, 3/2, ...)   ->  FERMIONS
        electron, proton, neutron          "individualists" (Pauli, ch.2)
        -> make up MATTER

   INTEGER spin (0, 1, 2, ...)          ->  BOSONS
        photon, gluon                      "gregarious"
        -> carry the FORCES

This distinction, which one might think abstract, governs the entire structure of matter — it is the subject of the next chapter. Fermions, because of their half-integer spin, obey an exclusion rule that prevents matter from collapsing.

In summary