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

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On Thursday, November 15, 2018 at 3:03:09 PM UTC, Bruno Marchal wrote:
>
>
> 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
>```
```
Let's forget it. This discussion has degenerated into gobblygook and now
with the introduction of an infinity of universes it's gotten infinitely
worse. I say FORGET IT! I AM NOT INTERESTED!!  AG

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