On 6/23/2018 10:05 PM, Bruce Kellett wrote:
From: *Brent Meeker* <meeke...@verizon.net <mailto:meeke...@verizon.net>>

Of course in theory any pure state can be taken to be a basis vector and there is an operator for which that state is an eigenvector, i.e. a basis in which it is not a superposition.  But in practice we don't know what that basis is and in general we cannot physically realize the corresponding operator.  That's why a photon passing thru Young's slits is said to be in a superposition of passing thru slit 1 and passing thru slit 2.  We know how to create an operator that measures "passing thru slit 1" and we know how to create an operator that measures "passing thru slit 2", but we don't know how to construct an operator that measures "passes thru both slit 1 and slit 2".  We can write down the wf in the basis of "passing thru slit 1" and "passing thru slit 2" and it's a coherent sum, i.e. a superposition of those two.  Decoherence theory says that we can't construct an instrument which will measure "passes thru both slit 1 and slit 2" because such an instrument would quickly decohere into one of the two stable states "passed thru 1" or "passed thru 2" and the interference pattern would not form (in repeated trials).

I am glad that you seem to have finally got the point of the basis problem, Brent.

Yeah, I understood we were talking past one another.  You were considering changing to a different basis of measurement, not just expressing a measurement in a different basis.

Brent

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