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Why can't the magnitude of spin change for an elementary particle? All the places i have looked at so far just state that spin magnitude cannot be changed. Why is this the case?

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  • $\begingroup$ See this for more details. $\endgroup$ – Andrei Geanta Oct 31 '17 at 19:42
  • $\begingroup$ And see this for more more details. $\endgroup$ – HolgerFiedler Oct 31 '17 at 20:19
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Because it is an intrinsic property of the particle. Just like mass, charge etc. All elementary Standard Model fermions have 1/2 spin. It is not like a rotation so that you can rotate the particle faster. It is a property that particles just have.

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Spin is an intrinsic property of a particle. We can rotate the spin so that we change the probability of measuring it as spin-up or spin-down along a given axis, but the spin itself is a naturally-occurring intrinsic property of the particle, much like mass or charge.

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I can think of two answers depending on what you mean by magnitude.

First, as others have already answered, spin, mass, charge, lepton number are the mathematical labels that uniquely name electrons. If the spin was a different number, the particle would no longer be an electron. In particular, spin $\frac{1}{2}$ tells you that an electron transforms under space rotations like a 2-vector that you use a 2 x 2 matrix to rotate. In fact, spin S is just short hand for telling you the particle transforms like a (2S+1) component vector that you need a (2S+1) x (2S+1) matrix to rotate.

Second, you may already understand that particles transform like (2S+1) dimension vectors, but you are asking if the magnitude of the vector is always $\hbar S$ of angular momentum? Experimentally, I think this has been verified for photons by absorbing N circularly polarized photons on a disk and seeing that $I\omega=N\hbar$ where $I$ and $\omega$ are the observed macroscopic moment of inertia and angular velocity of the disk. The magnitude of $\hbar$ per unit of spin has also been verified experimentally for electrons using the Einstein-de Hass effect. The magnitude of angular momentum per unit of spin has not been measured for any other particle, but it is hard to conceive how it could be different for other particles.

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