# Re: Coherent states of a superposition

```
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 <javascript:>> 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.

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