On Sunday, November 11, 2018 at 7:52:00 AM UTC, Bruno Marchal wrote:
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> On 10 Nov 2018, at 01:27, agrays...@gmail.com <javascript:> wrote:
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>
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> On Friday, November 9, 2018 at 12:26:52 PM UTC, Bruno Marchal wrote:
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>>
>> On 8 Nov 2018, at 18:25, agrays...@gmail.com wrote:
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>>
>>
>> On Thursday, November 8, 2018 at 11:04:20 AM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 6 Nov 2018, at 12:22, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, November 6, 2018 at 9:27:31 AM UTC, Bruno Marchal wrote:
>>>>
>>>>
>>>> On 4 Nov 2018, at 22:02, agrays...@gmail.com wrote:
>>>>
>>>>
>>>>
>>>> On Sunday, November 4, 2018 at 8:33:10 PM UTC, jessem wrote:
>>>>>
>>>>>
>>>>>
>>>>> On Wed, Oct 31, 2018 at 7:30 AM Bruno Marchal <mar...@ulb.ac.be> 
>>>>> wrote:
>>>>>
>>>>>>
>>>>>> On 30 Oct 2018, at 14:21, agrays...@gmail.com wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Tuesday, October 30, 2018 at 8:58:30 AM UTC, Bruno Marchal wrote:
>>>>>>>
>>>>>>>
>>>>>>> On 29 Oct 2018, at 13:55, agrays...@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 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 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
>>>>>>>
>>>>>>
>>>>>> *Thanks for the references. I think I have a reasonable decent 
>>>>>> understanding of mixed states. Say a system is in a mixed state of phi1 
>>>>>> and 
>>>>>> phi2 with some probability for each. IIUC, a measurement will always 
>>>>>> result 
>>>>>> in an eigenstate of either phi1 or phi2 (with relative probabilities 
>>>>>> applying). *
>>>>>>
>>>>>>
>>>>>> If the measurement is done with a phi1/phi2 discriminating apparatus. 
>>>>>> Keep in mind that any state can be seen as a superposition of other 
>>>>>> oblique 
>>>>>> or orthogonal states.
>>>>>>
>>>>>
>>>>> I don't know if you're restricting the definition of phi1 and phi2 to 
>>>>> some particular type of eigenstate or not, but in general aren't there 
>>>>> pure 
>>>>> states that are not eigenstates of any physically possible measurement 
>>>>> apparatus, so there is no way to directly measure that a system is in 
>>>>> such 
>>>>> a state?
>>>>>
>>>>
>>>> *Yes, such states exist IIUC. That's why I don't understand Bruno's 
>>>> claim that Up + Dn and Up - Dn can be measured with any apparatus, *
>>>>
>>>>
>>>> Not *any*¨apparatus, but a precise one, which in this case is the same 
>>>> apparatus than for up and down, except that it has been rotated.
>>>>
>>>>
>>>>
>>>>
>>>> *since they're not eigenstates of the spin operator, or any operator. *
>>>>
>>>>
>>>> This is were you are wrong. That are eigenstates of the spin operator 
>>>> when measured in some direction.
>>>>
>>>
>>> *If what you claim is true, then write down the operator for which up + 
>>> dn (or up - dn) is an eigenstate? AG *
>>>
>>>
>>>
>>> It is the operator corresponding to the same device, just rotated from 
>>> pi/2, or pi (it is different for spin and photon). When I have more time, I 
>>> might do the calculation, but this is rather elementary quantum mechanics. 
>>> (I am ultra-busy up to the 15 November, sorry). It will have the same shape 
>>> as the one for up and down, in the base up’ and down’, so if you know a bit 
>>> of linear algebra, you should be able to do it by yourself.
>>>
>>> Bruno
>>>
>>
>> *You don't have to do any calculation. Just write down the operator 
>> which, you allege, has up + dn or up - dn as an eigenstate. I don't think 
>> you can do it, because IMO it doesn't exist. AG *
>>
>>
>>
>> If up and down are represented by the column (1 0) and (0 1) the 
>> corresponding observable is given by the diagonal matrix 
>>
>> 1  0
>> 0 -1
>>
>> Then the up’ = 1/sqrt(2) (1 1), and down’ = 1/sqrt(2) (1 -1),
>>
>> So the operator, written in the base up down, will be 
>>
>> 0 1
>> 1 0
>>
>>  Here the eigenvalue +1 and -1 correspond to up (up’) or down (down’).
>>
>> I have no clue why you think that such operator would not exist.
>>
>
> *Because the measured spin state is Up or Dn along some axis, never 
> anything in between. Up + Dn or Up - Dn is not physically realizable in 
> unprimed basis. AG*
>
>
>
> If the measured spin state is Up or Dn along some axis, the measured spin 
> state will be Up + Dn or Up - Down along the axis obtained by rotating the 
> measuring apparatus adequately. 
>


*But NOT along the original spin axis! You can't measure Up + Dn or Up - Dn 
along any particular spin axis that you choose. That was my point. If you 
rotate the axis, the same situation exists. AG *

That is physically realisable with spin (by just rotating the Stern-Gerlach 
> apparatus) of with light polarisation (rotating the polariser or the CaCO3 
> crystal).
>
> Bruno
>
>
>
>
>
> All pure state can be seen as a superposition, in the rotated base, and 
>> you can always build an operator having them as eigenvalues.
>>
>> Bruno
>>
>>
>>
>>
>>
>>
>>
>>  
>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>> Julian Swinger (and Townsend) showed that the formalism of (discrete, 
>>>> spin, qubit) quantum mechanics is derivable from 4 Stern-Gerlach 
>>>> experiments, using only real numbers, but for a last fifth one, you need 
>>>> the complex amplitudes, and you get the whole core of the formalism.
>>>>
>>>> Bruno
>>>>
>>>>
>>>>
>>>>
>>>> *Do you understand Bruno's argument in a previous post on this topic? 
>>>> AG *
>>>>
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