Physical difference between singlet and triplet states

[Wminus]

Hey!

How are the two m=0 spin states (<up,down> + <down,up>) and (<up,down> - <down,up>) physically different? I realize that according to the math, the first one has a total spin of $2 \hbar$ while the second has a total spin of $0$. But wouldn't you, intuitively, expect both states to have zero total spin? I mean the particles have opposite spin in both of them.

What do you think?

 

[ShayanJ]

I intuitively expect that different states have different properties.
But it seems you think those states aren't different. It seems to me its a problem you have with the meaning of wave-function. The two states $|\uparrow\downarrow\rangle \pm |\downarrow\uparrow\rangle$ don't mean that one particle's spin points upward and another points downward. Quantum states can't be interpreted this way. They don't tell you what each particle is doing exactly.
Quantum states give you the probability distribution for the values of each of the quantities you may measure. And the two states above will give you different probability distributions and so they are different states.

 

[Vanadium 50]

Your misunderstanding isn't quantum mechanical, it's classical.

I have a state where the angular momentum about the z-axis is zero. Classically I don't know if this system is not rotating, or if it is rotating about some orthogonal axis.