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

```
On Tuesday, November 6, 2018 at 11:22:21 AM UTC, 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:
>>>>>
>>>>>
>>>>> 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 *
>```
```
*If you measure up/dn in one orientation, and then rotate the apparatus to
measure up/dn in another orientation, how does that result in an up + dn
or up - dn measurement which is now an eigenstate of some spin operator? AG*

>
>
>> 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 *
>>
>> --
>> You received this message because you are subscribed to the Google Groups
>> "Everything List" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> To post to this group, send email to everyth...@googlegroups.com.
>> Visit this group at https://groups.google.com/group/everything-list.
>> For more options, visit https://groups.google.com/d/optout.
>>
>>
>>

--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email