Pascal Wery
Spin is an intrinsic quantum property, like mass, that defines a kinetic moment: an angular instant, that is to say an angle which returns constantly in sequence. In other words, a "spin" that allows the particle to return to its original state. It shows the nature of the form: boson or fermion? The properties are completely different: the boson (energy) is typically characterized by a rotation of 360°, while the fermion (matter) requires two rotations, therefore 720°. Thus, energy, which has a whole-number spin, is undifferentiated because it fits in the same space, but not the half-integer spin (matter), which suffers from Pauli's exclusion principle, that is to say it is impossible for identical matter to be at the same place in the same moment. Thus, in quantum mechanics, one is concentrated and the other dispersed. Similarly, restricted relativity imposes other conditions: the symmetries corresponding to the geometry of space-time. These are symmetries of rotations, translations or references. But they are only respected by certain objects. Indeed, the particles are either scalar (Higgs boson) that are numbers, Gauge bosons (transfers energy), that are vectors, or fermions (real and virtual matters), that are spinners. A number is always equal to itself. No matter how you look at it, from the top or the side, it’s always the same number! That’s why spin 0 does not seem to "rotate". So is the scalar Higgs boson. The Gauge boson is a vector, so it depends on a direction. A direction that depends on a reference. By changing the reference, we change the orientation of the vector. The orientation becomes the same again only after a full turn. That is why it is called the whole-number spin. The matter (fermion) is subtler; it’s a spineur (good at turning)! It has an interaction that gives it exotic properties : a 360° rotation turns it into its opposite. Thus, it must turn twice to find its initial state. In short, the spin represents a rotation, but it's not! In classical physics, a rotation is a complete turn on oneself, so 360°. However, in quantum mechanics this "rotation" is impossible. Indeed, a spin rotation of ½, therefore a complete turn of 720°, is illusory. Moreover, the special relativity is firmly opposed to it because such a rotation of the electron would exceed the speed of light. So, what’s the truth about the spin? If we consider particles, it's a mystery but if we consider quantum fields, quanta of energy and pair creation, it becomes clearer : spin is a constant interaction with quantum fields that leads to pair creation with half-integer spin.