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

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On Thursday, November 15, 2018 at 2:14:48 PM UTC, scerir wrote:
>
>
> Il 15 novembre 2018 alle 14.29 agrays...@gmail.com <javascript:> ha
> scritto:
>
>
>
> 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*
>
> "Hence we must conclude that the system described by the |+>x state is not
> the
> same as a mixture of atoms in the |+> and !-> states. This means that each
> atom in the
> beam is in a state that itself is a combination of the |+> and |-> states.
> A superposition
> state is often called a coherent superposition since the relative phase of
> the two terms is
> important."
>
> .see pages 18-19 here *https://tinyurl.com/ybm56whu
> <https://tinyurl.com/ybm56whu>*
>```
```

*Try answering in your own words. When the SG device is oriented along the
x axis, now effectively the z-axix IIUC, and we're dealing with
superpositions, the outcomes will be 50-50 plus and minus. Therefore,
unless I am making some error, what you stated above is incorrect. 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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