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

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On Monday, October 29, 2018 at 10:22:02 AM UTC, Bruno Marchal wrote:
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> 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:
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>> On 25 Oct 2018, at 17:12, agrays...@gmail.com wrote:
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>> On Tuesday, October 23, 2018 at 10:39:11 PM UTC, agrays...@gmail.com
>> wrote:
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>>> 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
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>> 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
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>> 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.
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> *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*
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> 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.
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*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 *

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> Bruno
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>> Bruno
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