Question

Why do all fermions have 1/2 spin? How is it that every single quark and electron out there has the exact same angular velocity?

Answer 1

The concept of "spin" in quantum mechanics is not directly related to a physical spinning motion like that of a macroscopic object. Spin is an intrinsic property of particles in quantum mechanics, and it is a fundamental characteristic similar to mass or charge.

In quantum mechanics, particles are described by wavefunctions, which are mathematical representations that contain information about the particle's properties. The spin of a particle is a quantized property, meaning it can only take certain discrete values. The spin of a particle is denoted by a quantum number, usually represented as $s$, and it is measured in units of "spin angular momentum."

The spin of a fermion, such as an electron or a quark, is determined by its intrinsic properties and the mathematical structure of the theory. It is a fundamental property of these particles, and all fermions are characterized by having a spin of $1/2$. This means that the spin angular momentum of a fermion can take only two possible values: $+\frac{1}{2}\hslash$ or $-\frac{1}{2}\hslash$, where $\hslash$ is the reduced Planck's constant.

It is important to note that the concept of spin does not imply that these particles are physically spinning like a classical object. It is a mathematical property that arises from the nature of quantum mechanics. The term "spin" was historically used because it shares some mathematical similarities with the angular momentum of rotating objects, but the analogy is not exact.

In summary, the spin of fermions is a fundamental property in quantum mechanics, and all fermions have a spin of $1/2$ due to the mathematical structure of the theory. Spin is not related to a physical spinning motion but is a quantized intrinsic property of particles.