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:
>>
>>
>>
>> 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 
>>> <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". 
>>>
>>
>> *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.*
>>
>
>
> *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*
>

*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 *

>
>  
>
>>
>> *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 
>> comments above? AG *
>>
>>>  
>>>
>>>   
>>>
>>> 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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