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

```> Il 16 novembre 2018 alle 10.19 agrayson2...@gmail.com ha scritto:
>
>
>
>     On Thursday, November 15, 2018 at 2:14:48 PM UTC, scerir wrote:
>
>         > >
> >
> >             > > > Il 15 novembre 2018 alle 14.29 agrays...@gmail.com 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
> >
> >     >
>     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
> ```
```
sqrt(1/2) [(s+)_z +(s-)_z]  is a superposition, but since sqrt(1/2) [(s+)_z
+(s-)_z]  =  (s+)_x 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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> > >         > >
> >     >
>
>
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