Russell Standish wrote:
On Thu, Feb 26, 2015 at 09:31:53AM +1100, Bruce Kellett wrote:
An eigenfunction in one basis is a superposition (potentially an
infinite superposition) in any other basis. Why do we not see
superpositions of positions?
Bruce
But we do! Whenever the two slit experiment is performed, for example,
or perform a momentum measurement of a photon.
You seem to have missed the point I was making. The measurement in the
two slit experiment is the spot on the screen where the particle lands.
The slits themselves are not measurement devices. So the eigenfunctions
of the position measurement are (ignoring HUP limitations for the
moment) delta functions along the position direction. But this is only
one possible basis of the Hilbert space for the position operator. We
could take any arbitrary rotation in this Hilbert space to form another,
equally good, basis. In that new basis our observed delta function would
be a superposition. If that new basis were preferred, our observed
outcome would be a superposition. But we observe position outcomes only
as eigenvalues and eigenfunctions in one particular basis. Why is that?
What selects that basis in the position Hilbert space?
Bruce
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