> On 29 Oct 2018, at 13:55, agrayson2...@gmail.com wrote:
> 
> 
> 
> 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:
>> 
>> 
>> 
>> 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:
https://www.amazon.com/Conceptual-Foundations-Quantum-Mechanics-Advanced/dp/0738201049/ref=sr_1_1?s=books&ie=UTF8&qid=1540889778&sr=1-1&keywords=d%27espagnat+conceptual+foundation+of+quantum+mechanics&dpID=41NcluHD6fL&preST=_SY291_BO1,204,203,200_QL40_&dpSrc=srch

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

Bruno








> 
> Buy the book by David Albert. It will help you a lot, I think.
> 
> Bruno
> 
> 
> 
> 
> 
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> 
>>> 
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