When I first started to study quantum mechanics, my physics text book told that particles have spin of either 1/2 or -1/2. Then I recently read an article saying that gravitons are expected to be massless and have a spin of 2. What does this mean ?
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11$\begingroup$ Shouldn't you have asked the same question - what it means - already when you were told that the electron has spin 1/2? Because if you followed what that meant, you must follow the same sentence about spin 2, too. $\endgroup$– Luboš MotlMay 1, 2015 at 9:17
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$\begingroup$ What does it mean to have 1/2 spin. If you can answer that, then you have the tools to answer this. $\endgroup$– Jimmy360May 1, 2015 at 11:39
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$\begingroup$ @LubošMotl you are kind of right, the concept of spin was not clear to me even back then, but the problem reoccurred when I read that article. $\endgroup$– Al.KaMay 1, 2015 at 11:59
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1$\begingroup$ possible duplicate of What is spin as it relates to subatomic particles? $\endgroup$– ACuriousMind ♦May 1, 2015 at 14:27
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1$\begingroup$ Dear @Al.Ka - to really understand it, you have to comprehend the basics of quantum mechanics. Observables (quantities) like the angular momentum are given by operators... In particular, the angular momentum generates rotations around an axis,and rotation by 4.pi has to be trivial - 2.pi is allowed to change the sign. That's why the spin components are always multiples of hbar/2 or 1/2 in the usual conventions. The spin - without a component - is the maximum value of a component in the multiplet. For massless particles, we must measure th angular momentum componen along the direction of motion $\endgroup$– Luboš MotlMay 1, 2015 at 15:21
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When I first started to study quantum mechanics, my physics text book told that particles have spin of either 1/2 or -1/2.
That's wrong. Particles can have any integer or half-integer spin. (There are some deeply technical reasons that fundamental particles are expected to have spin ranging from -2 to 2, but if you include composite particles, any integer or half-integer spin is allowed.)
When you are first introduced to spin in the context of nonrelativistic quantum mechanics, it's typical to talk about particles with spin $\pm\frac{1}{2}$ simply because the most common particles (electrons and protons) have that spin. You should have learned that the spin is the amount of intrinsic angular momentum the particle has. See this question and this one for more details.
