Consider a spin-half particle measured, in some direction, to be up. If we put the particle again in the measurement device rotated by an angle of 180 degrees (around an axis orthogonal to the axis of the measurement), the measure should be down. Am I right?
Let $m \in \frac{1}{2}\mathbb{N}$ and consider a particle of spin $m$. Assume that it is measured to have spin up in some direction by a device. By what angle should one turn the measurement device to be sure that if we put the particle back, the spin should be measured as down?
In fact, I would like to find out, by myself, what the symmetries of a $m$-spin particle should be, in terms of matrices; this is why I would like to know, from a physical point of view, what to expect, in order to be able to carry out the mathematical computations.
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