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

```> Il 16 novembre 2018 alle 18.20 agrayson2...@gmail.com ha scritto:
>
>
>
>     On Friday, November 16, 2018 at 4:39:42 PM UTC, scerir wrote:
>
>         > >
> >
> >             > > > Il 16 novembre 2018 alle 15.38 agrays...@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".
> >
> >     >
>     I'm still not sure I understand your comment. I will think about it some
> more.  But back to my original question; Is there any circumstance where the
> result could be an eigenvalue of Up + Dn  or Up - Dn? Alternately, can Up +
> Dn or Up - Dn ever be an eigenstate of the spin vector? TIA, AG
> ```
```
Try this
https://www.st-andrews.ac.uk/~www_pa/quvis/simulations_html5/sims/superposition/superposition-mixed-states.html

at "step-by-step explanation" page.

At the bottom of that page you can choose 5 options (1-2-3-4-5) and read the
explanation (and look at the "orientation of SGA")

>
>         > >
> >
> >
> >             > > >
> > >                 > > > >
> > > >                     > > > > >
> > > > >                         > > > > > >
> > > > > >
> > > > > >
> > > > > >                             > > > > > > >
> > > > > >
> > > > > > >
> > > > > > >                                 > > > > > > > >
> > > > > > > >                                 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
> > > > > > > https://groups.google.com/d/optout
> > > > > > > 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 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