Spin
The quantum spin-statistics theorem categorizes particle types by their spin: the direction of internal angular momentum relative to the direction of linear momentum. The theorem characterizes the wave function of particles according to their symmetry.
The 12 flavors of fermions have a half-integer spin, whereas bosons twirl with an integer spin. Spin is the property that distinguishes fermions from bosons.
The boson integer spin versus fermion half-integer spin means that exchanging the positions of 2 bosons does not change their wave functions: they are symmetrical.
Contrastingly, fermions have asymmetric wave functions. Swapping fermions causes a reversal in their spin (wave function) sign, flipping between positive and negative.
The implication is that the amplitude of 2 identical fermions occupying the same space must be zero. Because of this, 2 fermions cannot simultaneously occupy the same quantum state, whereas symmetrical bosons can.
This fermion phenomenon is termed the Pauli exclusion principle, formulated in 1925 by Wolfgang Pauli. Pauli was trying to envision all the possible properties that electrons might have. He realized that the data all pointed to each electron occupying only 1 of a fixed number of energy states; what is now called spin. Pauli’s exclusion principle started with electrons and was then applied across the board to all fermions. As all matter is made of fermions, the Pauli exclusion principle requires that atoms take up space; whence existence as a fulsome experience.
Electrons cannot congregate in a cloud at the lowest energy state. Instead, they must space out, into orbital shells, with higher-energy electrons at a distance from a shell of lower energy electrons. The Pauli exclusion principle underpins the fundamental properties of chemistry, including atomic stability and the segregation of atoms according to the periodic table of the elements.
Quantum spin is conceptually different than classical physics’ spin, yet the term stuck.
In classical physics, the spin of a charged particle is associated with a magnetic dipole moment: the potential exertion force of magnetism upon the particle. Because of this, when the property was discovered classically, particles were thought to literally rotate to create the magnetic moment; an unproven assumption. Whether subatomic particles actually spin is unknown.
To be clear, quantum spin is not spin as in a spinning ball. If it were, the surface of electrons would spin at several times the speed of light. That supposedly is not so.
The direction of particle spin can change, but an elementary particle supposedly spins at a speed which cannot be changed, either faster or slower.
The nuclei of atoms also exhibit spin. Nuclear spin affects the strength of atomic interactions. If 2 atoms have identical nuclear spin, they interact weakly. In contrast, atoms with different nuclear spin states interact much more strongly.
