# Re: Coherent states of a superposition

```On Wed, Dec 5, 2018 at 10:52 PM <agrayson2...@gmail.com> 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.

Bruce

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