# Re: Coherent states of a superposition

```
On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM <agrays...@gmail.com <javascript:>> wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com
>> wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
>>>>
>>>> On Wed, Dec 5, 2018 at 2:36 AM <agrays...@gmail.com> wrote:
>>>>
>>>>>
>>>>> *Thanks, but I'm looking for a solution within the context of
>>>>> interference and coherence, without introducing your theory of
>>>>> consciousness. Mainstream thinking today is that decoherence does occur,
>>>>> but this seems to imply preexisting coherence, and therefore interference
>>>>> among the component states of a superposition. If the superposition is
>>>>> expressed using eigenfunctions, which are mutually orthogonal -- implying
>>>>> no mutual interference -- how is decoherence possible, insofar as
>>>>> coherence, IIUC, doesn't exist using this basis? AG*
>>>>>
>>>>
>>>> I think you misunderstand the meaning of "coherence" when it is used
>>>> off an expansion in terms of a set of mutually orthogonal eigenvectors.
>>>> The
>>>> expansion in some eigenvector basis is written as
>>>>
>>>>    |psi> = Sum_i (a_i |v_i>)
>>>>
>>>> where |v_i> are the eigenvectors, and i ranges over the dimension of
>>>> the Hilbert space. The expansion coefficients are the complex numbers a_i.
>>>> Since these are complex coefficients, they contain inherent phases. It is
>>>> the preservation of these phases of the expansion coefficients that is
>>>> meant by "maintaining coherence". So it is the coherence of the particular
>>>> expansion that is implied, and this has noting to do with the mutual
>>>> orthogonality or otherwise of the basis vectors themselves. In
>>>> decoherence,
>>>> the phase relationships between the terms in the original expansion are
>>>> lost.
>>>>
>>>> Bruce
>>>>
>>>
>>> I appreciate your reply. I was sure you could ascertain my error --
>>> confusing orthogonality with interference and coherence. Let me have your
>>> indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its superposition
>> expansion is also expressed in eigenfunctions with variable p. Does the
>> phase of the original wf carry over into the eigenfunctions as identical
>> for each, or can each component in the superposition have different phases?
>> I ask this because the probability determined by any complex amplitude is
>> independent of its phase. TIA, AG
>>
>
> The phases of the coefficients are independent of each other.
>```
```
When I formally studied QM, no mention was made of calculating the phases
since, presumably, they don't effect probability calculations. Do you have
a link which explains how they're calculated? TIA, AG

>
> Bruce
>
>
>

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