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

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• Shen712

#### Shen712

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}##?

Last edited by a moderator:
PeroK
Shen712 said:
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##.

ohwilleke
PeroK said:
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.

Orodruin said:
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.

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.

ohwilleke
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.

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