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

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On Thursday, November 15, 2018 at 8:04:53 AM UTC, scerir wrote:
>
> 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'.
>```
```
*Why?  Won't the measured value be along the x axis in both directions, in
effect Up or Dn? AG*

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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