# Re: Coherent states of a superposition

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On Tuesday, December 4, 2018 at 10:13:38 AM UTC, Bruno Marchal wrote:
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> On 3 Dec 2018, at 20:57, agrays...@gmail.com <javascript:> wrote:
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> On Sunday, November 18, 2018 at 1:05:26 PM UTC, agrays...@gmail.com wrote:
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>> On Saturday, November 17, 2018 at 7:39:14 PM UTC, agrays...@gmail.com
>> wrote:
>>>
>>> If you write a superposition as a sum of eigenstates, why is it
>>> important, or relevant, or even true that the component states are coherent
>>> since eigenstates with distinct eigenvalues are orthogonal. This means
>>> there is no interference between the components of the superposition. AG
>>>
>>
>> Put another way; from what I've read, coherence among components of a
>> superposition is necessary to guarantee interference, but since an
>> eigenstate expansion of the superposition consists of orthogonal, non
>> interfering eigenstates, the requirement of coherence seems unnecessary. AG
>>
>
> *For decoherence to occur, one needs, presumably, a coherent
> superposition. But when the wf is expressed as a sum of eigenstates with
> unique eigenvalues, those eigenstates are mutually orthogonal; hence, IIUC,
> there is no coherence. So, how can decoherence occur when the state
> function, expressed as a sum of eigenstates with unique eigenvalues, is not
> coherent? I must be missing something, but what it is I have no clue. AG *
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> Decoherence never occurs, except in the mind or memory of the observer.
> Take the state up + down (assuming a factor 1/sqrt(2)). And O is an
> observer (its quantum state).
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> O has the choice to measure in the base {up, down}, in which case the Born
> rule says that he will see up, or down with a probability 1/2. He will
> *believe* that decoherence has occurred, but if we long at the evolution of
> the whole system O + the particle, all we get is
>
> O-up up + O-down down,
>
> And some other observer could in principle test this. (O-up means O with
> the memory of having seen the particle in the up position).
>
> But O could measure that particle in the base {up+down, up-down). He has
> just to rotate a little bit its polariser or Stern-Gerlach device. In that
> case he obtains up+down with the probability one, which souls not be the
> case with a mixture of up and down. In that case, coherence of up and down
> do not disappear, even from the pot of the observer.
>
> Decoherence is just the contagion of the superposition to anything
> interacting with it, including the observer, and if we wait long enough the
> whole causal cone of the observer.
>
> Bruno
>

*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*

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