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- Thread starter Silviu
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$$|S=0,M=0 \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle-|1/2,+1/2 \rangle).$$

It's true that if measuring the spin component in an arbitrary direction of particle 1 then the spin component of particle 2 in the same direction is opposite. It doesn't matter which basis you use to describe the spin-singlet state. The reason is that for total spin ##S=0## the state doesn't change under rotations, i.e., you cannot distinguish any spin direction from any other.

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