> On 16 Apr 2021, at 11:04, Alan Grayson <agrayson2...@gmail.com> wrote:
>
>
>
> On Thursday, April 15, 2021 at 5:58:59 AM UTC-6 Bruno Marchal wrote:
>> On 14 Apr 2021, at 16:33, Alan Grayson <agrays...@gmail.com
>> <applewebdata://7C8D0BE9-228A-4C0B-A6E2-02664A05D3AD>> wrote:
>>
>>
>>
>> On Wednesday, April 14, 2021 at 4:40:08 AM UTC-6 Bruno Marchal wrote:
>>> On 10 Apr 2021, at 13:55, Alan Grayson <agrays...@gmail.com <>> wrote:
>>>
>>>
>>>
>>> On Saturday, April 10, 2021 at 5:21:46 AM UTC-6 Bruno Marchal wrote:
>>>> On 9 Apr 2021, at 06:42, Alan Grayson <agrays...@gmail.com <>> wrote:
>>>>
>>>> When the box is closed, and before the measurement, why can't it be
>>>> claimed that the Cat is in a Mixed State, not a Superposition of States?
>>>> Only the latter leads to the paradox of a cat which is Alive and Dead
>>>> simultaneously. AG
>>>
>>>
>>> Because the Wave equation in this setting leads to a pure state dead+alive,
>>> and twe know that such pure state leads to different prediction than any
>>> possible corresponding mixed states. (Assuming the SWE).
>>>
>>> Without any mathematical representation of the individual states of Dead
>>> and Alive, how can it be claimed that Dead and Alive each satisfy the SWE?
>>
>> By NOT adding the collapse postulate. Then even a state as “macroscopic” as
>> being a dead or alive cat will inherit the superposition ilmplied by
>> Schroedinger’s setting. That follows from the double linearly of both the
>> wave evolution and of the tensor products. The fact that a correct
>> description would use a huge number of dimension and a lot of tensor
>> products cannot be used to make the superposition going away.
>>> And how will the superposition of states Dead + Alive give different
>>> predictions than a mixed state of Dead and Alive? AG
>>
>> Because all pure superposition state gives different predictions than their
>> corresponding mixed state.
>>
>> Is this your idea of a proof, or even a plausibility argument? AG
>
> It is elementary quantum mechanics. If you measure “1/sqrt(2)(spin-up +
> spin-down)” is the base {spin-up, spin-down}, you get different results than
> measuring a half-half mixture of spin-up and spin-dow. This is usually
> illustrate with polarisers in the textbook.
>
> Bruno
>
> Can you give an example why the result will be different for superposition,
> say with 70%/30% probability amplitudes,
Define the following pure state:
phi = sqrt(7/10) up + sqrt(3/10) down
Prepare 100% of your particles in that pure state. Each individual particle is
in that state, and so as a probability 1 to be found in that state, and 0 for
the orthogonal state.
> versus a mixed state with same amplitudes.
Prepare 70% of your particle in the state up, and 30% in the state down, and
mix them.
> It may be simple to show, but I admit to not being able to see any difference
> between the cases. AG
Consider the measuring apparatus MA’ corresponding to the base:
up’ = sqrt(7/10) up + sqrt(3/10) down,
down’ = sqrt(7/10) up - sqrt(3/10) down
On the pure state defined above, measuring MA’, the probability to get a
particle in the state up' is 1, and thus the probability to get down’ = 0, as
said above.
Measuring MA’ on the particles on the mixed state has to be different.
The probability to get up’ will be the square of the scalar product (up, up’)
for 70% of the particle, and will be given by the square of the scalar product
(down, up’) for the remaining 30% of your particles. The result for the
probability of getting down’ cannot be null in this case.
(I have to go, I leave you the details; you need to make the relevant change of
basis, but you don’t need to compute this to understand that for each of the
mixed particles, you will have a non null probability for down’, yet that is
null for the pure state).
Bruno
>
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