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

```> Il 16 novembre 2018 alle 15.38 agrayson2...@gmail.com ha scritto:
>
>
>
>     On Friday, November 16, 2018 at 10:14:32 AM UTC, scerir wrote:
>
>         > >
> >
> >             > > > Il 16 novembre 2018 alle 10.19 agrays...@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'
> >
> >     >
>     I'll probably get back to on the foregoing. In the meantime, consider
> this; I claim one can never MEASURE Up + Dn or Up - Dn with a SG apparatus
> regardless of how many other instruments one uses to create a composite
> measuring apparatus (Bruno's claim IIUC). The reason is simple. We know that
> the spin operator has exactly two eigenstates, each with probability of .5.
> We can write them down. We also know that every quantum measurement gives up
> an eigenvalue of some eigenstate. Therefore, if there existed an Up + Dn or
> Up - Dn eigenstate, it would have to have probability ZERO since the Up and
> Dn eigenstates have probabilities which sum to unity. Do you agree or not,
> and if not, why? TIA, AG
> ```
```
I think the question should rather be how to prepare a superposition state like
sqrt(1/2) [(s+)_z +(s-)_z] . But when you have this specific state, and when
you orient the SG along "x", you always get "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')?
> > > > > >
> > > > > >                     > > > > >
> > > > >
> > > > >
> > > > >                     --
> > > > >                     You received this message because you are
> > > > > subscribed to the Google Groups "Everything List" group.
> > > > >                     To unsubscribe from this group and stop receiving
> > > > > emails from it, send an email to everything-li...@googlegroups.com.
> > > > >                     To post to this group, send email to
> > > > > everyth...@googlegroups.com.
> > > > >                     Visit this group at
> > > > > https://groups.google.com/group/everything-list
> > > > > https://groups.google.com/group/everything-list .
> > > > >                     For more options, visit
> > > > > .
> > > > >
> > > > >                 > > > >
> > > >             > > >
> > >
> > >
> > >             --
> > >             You received this message because you are subscribed to the
> > > Google Groups "Everything List" group.
> > >             To unsubscribe from this group and stop receiving emails from
> > > it, send an email to everything-li...@googlegroups.com.
> > >             To post to this group, send email to
> > >             Visit this group at
> > >             For more options, visit https://groups.google.com/d/optout
> > >
> > >         > >
> >     >
>
>
>     --
>     You received this message because you are subscribed to the Google Groups
> "Everything List" group.
>     To unsubscribe from this group and stop receiving emails from it, send an
>     To post to this group, send email to everything-list@googlegroups.com
>     Visit this group at https://groups.google.com/group/everything-list.
>     For more options, visit https://groups.google.com/d/optout.
>

--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email