In quantum mechanics and particle physics, rotation is one of the intrinsic properties exhibited by elementary particles.

They also have gyrus hadrons (protons and neutrons, which are composite particles) and atomic nuclei.

Spin is also known as intrinsic angular momentum with spin angular momentum or spin quantum number.

Spin, along with other intrinsic properties such as mass or electrical charge, identify the different types of particles:

Fermions: Fermions (electrons, positrons, quarks, etc) and hadrons (compounds of quarks such as protons and neutrons) have a half-integer spin value (+1/2, -1/2, 3/2, 5/2 ). bosons: Bosons, like photons, gluons, and W and Z particles, have an all spin value (0, 1, 2).The behavior of each type of particle is very different. Fermions are the mass-carrying particles, while bosons are the force-carrying particles (electroweak, strong interaction, gravity), which can give you an idea of the importance of spin.

the unit of rotation in the International System is N ms (equivalent to kg mtwoss−1), but in practice the spin is usually given as a dimensionless, unitless number resulting from dividing the spin by the reduced Planck constant (ħ).

This reduced rotation, however, is not the full actual calculation of the intrinsic angular momentum value.

## But what really is rotation?

In classical mechanics, a rotating object has a form of inertia known as angular momentum which is related to the size, shape, mass and rate of rotation of the object.

This classical angular momentum is usually represented as a vector (L) whose direction coincides with the axis of rotation:

Angular momentum in a macroscopic objectClassic angular momentum interacts with the force of gravity and is responsible for the forces of inertia.

Elementary particles and subatomic particles, to explain spin, are usually explained as rotating particles, but it would be a quantum rotation, the logic of rotation of macroscopic objects would not apply.

While classical rotation is related to all three dimensions (1 revolution is equal to a 360º turn), in quantum mechanics spin is related to the reduced Planck constant (ħ = h/2π), a very small number, dimensions where the quantum properties of the particles.

Unlike macroscopic angular momentum, spin can only be measured in concrete integer or semi-integer values (0, 1/2, 3/2, 2, 5/2, …):

Elementary particles with half-integer spin are fermions (quarks and leptons). Elementary particles with integer spin are bosons.Take the electron as an example. The electron is a type of elementary particle. type of fermone specifically, it is a lepton type. Electric charge, like spin, is an intrinsic property of elementary particles. electron spin is 1/2 and electric charge is -1.

Spin and other intrinsic properties of elementary particlesIf an electron has a spin of 1/2, it means it needs to “spin twice” to return to its initial state. In a boson, whose spin is 1, a single complete revolution would be enough to return to the initial state.

As the electron has an electrical charge, when it spins, it creates a magnetic field around it. The detection of this magnetic field is the main way to study electrons.

But we cannot think of this magnetic field as we think of the magnetic field created by macroscopic objects. Quantum mechanics is a little weirder.

If we rotate an electrically charged sphere, we will create a magnetic field with dimensions that are a multiple of the angular momentum.

But the spin doesn’t really represent a rotation through the 360º of space, but represents the flow of energy through the wave function of the particle, the function that calculates the probability of finding a particle in a certain place and at a certain time.

In addition to the fact that the generated magnetic field does not correspond to what classical mechanics predicts for a rotating sphere, the rotation represented by spin cannot occur in any direction, but is an intrinsic property of each particle that only occurs at certain values.

Let’s think about Earth. We can say that it rotates upwards inclined 23.5 degrees with respect to the orbital plane. But when detecting the magnetic field of an electron, we always get it to spin 100% up (1/2) or 100% down (-1/2), never in intermediate or “tilted” positions.

And that brings us to another weird aspect of electrons. If we give a spin 1/2 electron one complete turn, its spin becomes -1/2, we have to “spin” it again so that it returns to the initial state of 1/2.

But it doesn’t really matter the value of the wavefunction is exactly the same for both cases since the electron wavefunction uses spin squared, and the square of a positive value and the square of the same value in negative are equal (eg : the square of 2 is 4, and the square of -2 is also 4).

This is why two electrons with opposite spins can occupy the same atomic orbital. Both have the same wave function.

## Fermions, Bosons and Quantum Spin

The consequences of having an integer-valued spin or a half-integer-valued spin seem to determine the behavior of each type of elementary particle.

the fermions (semi-integer spin) they obey the Pauli Exclusion Principle and carry mass.

bosons (whole spin) do not have this restriction and are the force-carrying particles responsible for the so-called fundamental forces.

Basically, the Pauli exclusion principle holds that two fermions cannot exist in the same quantum state (with all four quantum numbers identical), and this fact seems to be very important in the construction of the different chemical elements.

the electron following this principle, will occupy the different orbitals two by two. As we saw before, two electrons of opposite spins can occupy the same orbital, but if more electrons are added, they will occupy higher and higher orbitals, each of which corresponds to a different energy state or principal quantum number.

In this way, as the elements acquire more electrons, these are incorporated into more outer orbitals and the different elements appear.

If this did not happen, all electrons would occupy the lowest energy level. The same can be deduced for the other fermions, including quarks, which are also subject to the Pauli exclusion principle and are therefore capable of forming the different atomic nuclei.