# Re: A superposition in QM is just due to a choice of basis?

```On 8/28/2010 12:29 PM, Stephen P. King wrote:
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Hi Bret,

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Could you elaborate on this point and/or point me to a good discussion of it? From what I have studied so far there is no solution to the measurement problem so far in terms of an explanation of the way that the choice is made in each successive event, world or whatever. Even decoherence does not help things from what I can tell,
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That's sort of true. Decoherence explains that measurements necessarily involved interactions with the environment and hence the reduced density matrix will necessarily become diagonal FAPP - but not exactly diagonal. Since it's not *exactly* diagonal it can't be interpreted as providing just probabilities on the diagonal.
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but this business that "What's a superposition in one basis is still an eigenfunction in some basis." is new to me. The one to one and reversible aspect was the state itself, but this is a different situation, no?
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Right, that's the time evolution in the absence of measurments.

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There is a subscript i in the symbolic representations of the eigenvalues, eigenvectors and eigenfunctions, no? What does this represent?
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Those are the eigenvectors of the measurement operator. If the state you're measuring is a pure state in say basis X and you measure in basis X then you will get just that one state as an eigenvector. But if you measure in a different basis Y then you will get projections of X onto the eigenvectors of Y.
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Brent

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```Onward!

Stephen P. King

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```*Sent:* Saturday, August 28, 2010 1:42 PM
*Subject:* Re: What's wrong with this?

snip.

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A superposition in QM is just due to a choice of basis. What's a superposition in one basis is still an eigenfunction in some basis. The evolution of the state is one-to-one and time reversible. The problem is the measurement or "measurement like" processes which give us classical behavior. Everett's relative states (aka multiple worlds) is one answer to this problem.
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Brent

snip

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