# Re: Coherent states of a superposition

```> On 3 Dec 2018, at 20:57, agrayson2...@gmail.com wrote:
>
>
>
> 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 ```
```

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).

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

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