# Re: Measuring a system in a superposition of states vs in a mixed state

```Imagine a spin-1/2 particle described by the state psi = sqrt(1/2) [(s+)_z +
(s-)_z] .```
```
If the x-component of spin is measured by passing the spin-1/2 particle through
a Stern-Gerlach with its field oriented along the x-axis, the particle will
ALWAYS emerge 'up'..

In fact (s+)_z = sqrt(1/2) [(s+)_x + (s-)_x]

and (s-)_z = sqrt(1/2) [(s+)_x - (s-)_x]

(where _z, _x, are the z-component and the x-component of spin)

so that psi = sqrt(1/2)[(s+)_z +(s-)_z] = (s+)_x.   (pure state, not mixture
state)..

AGrayson2000 asked "If a system is in a superposition of states, whatever value
measured, will be repeated if the same system is repeatedly measured.  But what
happens if the system is in a mixed state?"

Does Everett's "relative state interpretation" show how to interpret a real
superposition (like the above, in which the particle will always emerge 'up')
and how to interpret a mixture (in which the particle will emerge 50% 'up' or
50% 'down')?

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