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

```> On 29 Oct 2018, at 13:55, agrayson2...@gmail.com wrote:
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> On Monday, October 29, 2018 at 10:22:02 AM UTC, Bruno Marchal wrote:
>
>> On 28 Oct 2018, at 13:21, agrays...@gmail.com <javascript:> wrote:
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>> On Sunday, October 28, 2018 at 9:27:56 AM UTC, Bruno Marchal wrote:
>>
>>> On 25 Oct 2018, at 17:12, agrays...@gmail.com <> wrote:
>>>
>>>
>>>
>>> On Tuesday, October 23, 2018 at 10:39:11 PM UTC, agrays...@gmail.com
>>> <http://gmail.com/> wrote:
>>> 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? TIA, AG
>>>
>>> If you think about it, whatever value you get on a single trial for a mixed
>>> state, repeated on the same system, will result in the same value measured
>>> repeatedly. If this is true, how does measurement distinguish superposition
>>> of states, with mixed states? AG
>>
>> That is not correct. You can distinguish a mixture of particles in the up or
>> down states with a set of 1/sqrt(2)(up+down) by measuring them with the
>> {1/sqrt(2)(up+down), 1/sqrt(2)(up-down}) discriminating apparatus. With the
>> mixture, half the particles will be defected in one direction, with the pure
>> state, they will all pass in the same direction. Superposition would not
>> have been discovered if that was not the case.
>>
>> And someone will supply the apparatus measuring (up + down), and (up -
>> down)? No such apparatuses are possible since those states are inherently
>> contradictory. We can only measure up / down. AG
>
> You can do the experience by yourself using a simple crystal of calcium
> (CaCO3, Island Spath), or with polarising glass. Or with Stern-Gerlach
> devices and electron spin. Just rotating (90° or 180°) an app/down apparatus,
> gives you an (up + down)/(up - down) apparatus.
>
> I don't understand. With SG one can change the up/down axis by rotation, but
> that doesn't result in an (up + down), or (up - down) measurement. If that
> were the case, what is the operator for which those states are eigenstates?
> Which book by Albert? AG```
```
David Z Albert, Quantum Mechanics and Experience, Harvard University Press,
1992.
https://www.amazon.com/Quantum-Mechanics-Experience-David-Albert/dp/0674741137

Another very good books is

D’Espagnat B. Conceptual foundations of Quantum mechanics,  I see there is a
new edition here:

It explains very well the difference between mixtures and pure states.

Bruno

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> Bruno
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>> Bruno
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>>>
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