Why do all fermions have the same spin 1/2?

[Shen712]

TL;DR

Why do all fermions have the same spin angular momentum $\frac{\hbar}{2}$, regardless of their different masses?

We are taught that all fermions have spin $\frac{1}{2}$, short for spin angular momentum $\frac{\hbar}{2}$, which can be added to the orbital angular momentum. Considering spin is a kind of angular momentum, it must be dependent on the mass (or moment of inertia) of the particle. However, different fermions, such as proton, neutron, quarks, neutrinos, and electron, have different masses. But why do they have the same spin angular momentum $\frac{\hbar}{2}$?

 

[Orodruin]

The premise of your question is false. Here is a counter example: https://en.m.wikipedia.org/wiki/Delta_baryon

 

[Vanadium 50]

You made the same error six years ago: https://www.physicsforums.com/threads/how-do-we-know-the-spins-of-elementary-particles.926615/

 

[PeroK]

TL;DR Summary: Why do all fermions have the same spin angular momentum $\frac{\hbar}{2}$, regardless of their different masses?

We are taught that all fermions have spin $\frac{1}{2}$, short for spin angular momentum $\frac{\hbar}{2}$, which can be added to the orbital angular momentum. Considering spin is a kind of angular momentum, it must be dependent on the mass (or moment of inertia) of the particle. However, different fermions, such as proton, neutron, quarks, neutrinos, and electron, have different masses. But why do they have the same spin angular momentum $\frac{\hbar}{2}$?

The quantisation of angular momentum is a stunning achievement of mathematical physics. Angular momentum cannot take any value, but but only multiples of $\frac \hbar 2$.

 

[Orodruin]

The quantisation of angular momentum is a stunning achievement of mathematical physics. Angular momentum cannot take any value, but but only multiples of $\frac \hbar 2$.

OP’s question was why all fermions have spin 1/2 though. They don’t.

 

[PeroK]

OP’s question was why all fermions have spin 1/2 though. They don’t.

He also suggested that spin AM should be dependent on a mass-related moment of inertia. It isn't.

 

[Vanadium 50]

The Δ is an example, but the Ω- is an even more famous one. It's not clear to me how a PhD particle physicist like the OP managed not to come across it, ever.

 

[fresh_42]

The answer has been given, i.e. the false assumptions in the OP's question have been addressed so it doesn't make sense to discuss this specific subject any further.

This thread is closed.