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

```> On 15 Nov 2018, at 09:04, 'scerir' via Everything List
>
> 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'..
>
> 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’)?
>
With a lot of difficulties, no doubt. But with much less difficulties than with
a “physical collapse”, I would say.```
```
What is hard with up’ = up + down (renormalised) is that the physical state up’
*is* the same as two (times infinity) particles in the state up and down, with
me being in both universe, without any means to distinguish which one before I
do the measurement. It is weird, but that is QM. Similarly a particle with a
definite position *is* that particles with an indefinite momentum, and in the
many-world, that is an infinity of universes/histories possibles, with each
momentum being definite in each universe. Measuring a position is the same as
putting myself in *all* those universe where the momentum is unknown.

Bruno

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