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

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On Saturday, November 17, 2018 at 4:39:08 PM UTC, agrays...@gmail.com wrote:
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> On Saturday, November 17, 2018 at 4:22:35 PM UTC, agrays...@gmail.com
> wrote:
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>> On Friday, November 16, 2018 at 4:39:42 PM UTC, scerir wrote:
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>>> Il 16 novembre 2018 alle 15.38 agrays...@gmail.com ha scritto:
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>>> On Friday, November 16, 2018 at 10:14:32 AM UTC, scerir wrote:
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>>> Il 16 novembre 2018 alle 10.19 agrays...@gmail.com ha scritto:
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>>> On Thursday, November 15, 2018 at 2:14:48 PM UTC, scerir wrote:
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>>> Il 15 novembre 2018 alle 14.29 agrays...@gmail.com ha scritto:
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>>> On Thursday, November 15, 2018 at 8:04:53 AM UTC, scerir wrote:
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>>> 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
>>> <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".
>>>
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>> *If the SG field is oriented perpendicular to z axis, the usual situation
>> for a measurement along z, you get Up or Dn along z axis. If field is along
>> x axis, which is perpendicular to z axis, the device blocks the stream of
>> electrons, so no measurement is possible.*
>>
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> *Correction; the SG device doesn't block stream of elections when its
> field is oriented along x axis. But what has this to do with whether one
> can measure Up + Dn, or Up - Dn along z axis, or any axis? Does it show Up
> + Dn can be measured along x axis? AG*
>```
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*I still have to check your math. I think you've shown that Up + Dn can be
measured along x axis, and presumably Up - Dn can also also be measured
when a negative sign is used between elements of the above superposition. I
suppose this is what Bruno was trying to say, whereas I was focused on
measurements along z axis with the SG device in the standard orientation.
Nonetheless, I don't see that this result has anything to do with Bruno's
introduction of an infinity of universes, a concept I find totally
extraneous (and for my aesthetics, abhorrent) to this issue. AG *

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>> *Also, note that your simulation uses only Up or Dn, as I did above, to
>> show it's impossible to measure Up + Dn, or Up - Dn. Can you respond to my
>>
>>>
>>>
>>>
>>>
>>> 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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