# Spin of a particle and spin quantum number [duplicate]

what actually does the spin quantum number of a particle describe about? What it means when we say photon has spin 1, Higgs boson has spin 0, etc..?? What actually does that numerical value explain? I do hope the + or - sign definitely talks about direction of spin! (kindly elaborate!)

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## marked as duplicate by dmckee♦Mar 1 '13 at 18:40

All particles have an internal degree of freedom which is intimately related to their behaviour under rotations. The state of this internal degree of freedom is an element of some Hilbert space $\mathcal{H}$. The spin $s$ of a particle determines the dimension of this vector space, and thus the number of simultaneously distinguishable (i.e. orthogonal) states available, given by $2s+1$.

Thus spin 0 has dimension 1 (a single state, so no dynamics), spin $\frac12$ has dimension 2 (an "up" and a "down" state once you fix a direction), spin 1 has dimension 3, and so on.

Particles also have a "magnetic" spin quantum number, usually denoted $m$, which identifies which way the particle is spinning. Once you fix a direction, the sign and magnitude of $m$ tell you the direction and size of the particle's angular momentum component on that axis.

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To elaborate on Emilio's nice answer, let me add that spin is, as he says "an internal degree of freedom." What does this mean? One way to think about it is that its an intrinsic property of the particle in an analogous way to how mass is an intrinsic property of massive particles or charge is an intrinsic property of charged particles.

You might then ask "well mass tells us how difficult it is to change the state of motion of particles, and charge tells us how strongly a charged particle interacts with electromagnetic fields, so what does spin tell us?" As Emilio writes, the spin is related to how much of a particular kind of angular momentum a particle can have, not necessarily due to the fact that it is actually spinning.

In light of this, I personally feel that it's dangerous to identify spin with "which way the particle is spinning" since it's unclear, in the case of certain elementary particles like electrons, whether the particle is "spinning" in some sense, or what that would even mean if the particle is modeled as being truly pointlike.

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